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Types of Variables in Research & Statistics | Examples

Published on September 19, 2022 by Rebecca Bevans . Revised on December 2, 2022.

In statistical research , a variable is defined as an attribute of an object of study. Choosing which variables to measure is central to good experimental design .

If you want to test whether some plant species are more salt-tolerant than others, some key variables you might measure include the amount of salt you add to the water, the species of plants being studied, and variables related to plant health like growth and wilting .

You need to know which types of variables you are working with in order to choose appropriate statistical tests and interpret the results of your study.

You can usually identify the type of variable by asking two questions:

Table of contents

Types of data: quantitative vs categorical variables, parts of the experiment: independent vs dependent variables, other common types of variables, frequently asked questions about variables.

Data is a specific measurement of a variable – it is the value you record in your data sheet. Data is generally divided into two categories:

A variable that contains quantitative data is a quantitative variable ; a variable that contains categorical data is a categorical variable . Each of these types of variables can be broken down into further types.

Quantitative variables

When you collect quantitative data, the numbers you record represent real amounts that can be added, subtracted, divided, etc. There are two types of quantitative variables: discrete and continuous .

Categorical variables

Categorical variables represent groupings of some kind. They are sometimes recorded as numbers, but the numbers represent categories rather than actual amounts of things.

There are three types of categorical variables: binary , nominal , and ordinal variables .

*Note that sometimes a variable can work as more than one type! An ordinal variable can also be used as a quantitative variable if the scale is numeric and doesn’t need to be kept as discrete integers. For example, star ratings on product reviews are ordinal (1 to 5 stars), but the average star rating is quantitative.

Example data sheet

To keep track of your salt-tolerance experiment, you make a data sheet where you record information about the variables in the experiment, like salt addition and plant health.

To gather information about plant responses over time, you can fill out the same data sheet every few days until the end of the experiment. This example sheet is color-coded according to the type of variable: nominal , continuous , ordinal , and binary .

Example data sheet showing types of variables in a plant salt tolerance experiment

Experiments are usually designed to find out what effect one variable has on another – in our example, the effect of salt addition on plant growth.

You manipulate the independent variable (the one you think might be the cause ) and then measure the dependent variable (the one you think might be the effect ) to find out what this effect might be.

You will probably also have variables that you hold constant ( control variables ) in order to focus on your experimental treatment.

In this experiment, we have one independent and three dependent variables.

The other variables in the sheet can’t be classified as independent or dependent, but they do contain data that you will need in order to interpret your dependent and independent variables.

Example of a data sheet showing dependent and independent variables for a plant salt tolerance experiment.

What about correlational research?

When you do correlational research , the terms “dependent” and “independent” don’t apply, because you are not trying to establish a cause and effect relationship ( causation ).

However, there might be cases where one variable clearly precedes the other (for example, rainfall leads to mud, rather than the other way around). In these cases you may call the preceding variable (i.e., the rainfall) the predictor variable and the following variable (i.e. the mud) the outcome variable .

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Once you have defined your independent and dependent variables and determined whether they are categorical or quantitative, you will be able to choose the correct statistical test .

But there are many other ways of describing variables that help with interpreting your results. Some useful types of variables are listed below.

You can think of independent and dependent variables in terms of cause and effect: an independent variable is the variable you think is the cause , while a dependent variable is the effect .

In an experiment, you manipulate the independent variable and measure the outcome in the dependent variable. For example, in an experiment about the effect of nutrients on crop growth:

Defining your variables, and deciding how you will manipulate and measure them, is an important part of experimental design .

A confounding variable , also called a confounder or confounding factor, is a third variable in a study examining a potential cause-and-effect relationship.

A confounding variable is related to both the supposed cause and the supposed effect of the study. It can be difficult to separate the true effect of the independent variable from the effect of the confounding variable.

In your research design , it’s important to identify potential confounding variables and plan how you will reduce their impact.

Quantitative variables are any variables where the data represent amounts (e.g. height, weight, or age).

Categorical variables are any variables where the data represent groups. This includes rankings (e.g. finishing places in a race), classifications (e.g. brands of cereal), and binary outcomes (e.g. coin flips).

You need to know what type of variables you are working with to choose the right statistical test for your data and interpret your results .

Discrete and continuous variables are two types of quantitative variables :

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Statistics Research Paper Writing Guide + Examples

statistics research paper

A statistics research paper discusses and analyzes the numerical data. A statistics research paper should cover all the aspects regarding the distribution of data, frequency tables and graphs..

A statistics research paper is similar to a survey research paper in many ways. Both papers focus on collecting information about some specific topic using surveys. They both use statistical methods to collect, analyze and present this information..

To explain how they are different, consider two types of statistics: means and relationships; it may be easier to understand this by first explaining how they’re related: The mean is (most often) calculated through addition while relationships are typically found through multiplication. This also explains why you calculate means at the beginning of a statistics project (before any relationship has been discovered), while responsibility for calculating relationships typically falls to the end of a statistics project. The next time you’re in class, try to count how many times your instructor mentions “mean,” as opposed to “relationship!”

A statistics paper is based on a relationship between two or more variables (often referred to as independent and dependent variables). You can think of these variables almost like social security numbers—each person has one SSN that distinguishes them from all other people; similarly, each data point (a unique combination of values for an independent variable) has its own set of values for one or more variables..

An example: if we are interested in knowing whether there is a relationship between hospital beds per 1,000 residents and the reading scores of senior citizens, defined as ages 65 and over, in a given city or country, then we must gather data on both variables. We will need to find out how many hospital beds there are per 1,000 residents for each of the cities or countries represented in our sample..

This type of research paper writing can also be based only on means (instead of relationships). Consider two more examples: If a psychologist wants to see if age is related to memory loss, but doesn’t care whether this relationship is positive or negative (i.e., she simply wants to know if older people tend to have better memories than younger people), all she cares about are the mean memory scores for groups defined by age.

On the other hand, if the psychologist wants to know if older people tend to have better memories than younger, but she also cares about how large this difference is (e.g.. their mean score is 10 points higher), then her research project will include calculations of relationships between age and memory scores.

How to write a statistics research paper

Getting started with your research paper is a difficult task. All you need to do is hop online and search for some information on how to write it but what are the necessary steps?

You can learn them by following this short guide:

Start by proper research:

Write an introduction, transition into your thesis statement, and finish off with a conclusion of sorts – this structure will not only help you produce a strong foundation, but also provide the reader with clues regarding where you’re going in particular when writing statistics essay.

The introduction should be broad enough to capture attention of the reader and yet narrow enough to indicate that it’s about something specific.

It can also serve as a springboard for later argumentation or present the central idea.

What makes a good research paper introduction , however, is a little bit of mystery or enigma that makes the reader go “I want to know more about this, why do they think so?”

Finding journal articles on statistics research paper

The next step is to locate journals and magazines. It’s best if you have some knowledge about what kind of scholarly work this will entail – statistics papers are not often found in tabloids but rather in peer reviewed sources.

If you’re struggling with compiling a comprehensive essay list of online sources, try asking for help at your school’s librarian or library.

There are also other options such as using one of those article databases which contain articles from all over the world and sorted by category: perhaps there’s something there – it doesn’t even have to be a journal article.

There are also books out there that have statistics papers in them – in case you want to go a little bit old school.

Writing body paragraphs

The next step is writing your body or main part of the statistics research paper, so it makes sense first to decide on what kind of statistical test you’ll use and then look up relevant information about it.

Use this information as the building blocks for paragraphs going into details: why did the statistician choose it?

What are some common criticisms/counterpoints?

Which should be supported by specific examples and further justification of why they’re relevant. The next section will deal with interpreting numerical results and drawing conclusions – this involves taking those numbers and making something meaningful out of them beyond just comparing them to each other. It could be a lot to take in, so it’s best if you break this down and look up specific information for different parts of it.

Write your paper

Now that you have collected all the necessary material, statistics research paper writing shouldn’t be hard – remember not to simply copy/paste the information from somewhere else without citing your sources and making sure that your work is better than what you’ve copied.

The final step will involve polishing and proofreading your work – make sure there are no mistakes when submitting or publishing online.

You should always use correct grammar, spelling and punctuation as well as consistent referencing/citation style (MLA, APA etc.).

And there you have it: statistics research paper.

Write perfect conclusion

The next step is writing your conclusions. You’ve already done a lot of the work for this during the body part so it shouldn’t be anything out of the ordinary.

Make sure you reiterate what you said in the introduction and sometimes add some more commentary on particular things that could/can serve as relevant examples for future research or topics to investigate further.

One thing which is especially important here is presenting results/data clearly and making them easy to understand even for people who aren’t statisticians themselves. This can help greatly with potential critics.

A statistics research paper, then, should include a summary of the methods used to gather and analyze your data (usually presented in sections 2 & 3), followed by your findings (usually presented in sections 4 – 7). All of this material must be contained within a single document.

Your paper is organized differently from other types of research reports. The most common order has been presented here so as to make it easier for you to adapt these sections back into your own planning:

Note: The examples provided above are not intended to represent all possible formats that could be used but rather they provide information about what most researchers tend to do.

Also note: Depending on your course or assignment, you might be required to use certain formatting styles or these requirements may vary from one class or professor to another. But it’s always important to know how and when to cite (reference) sources within your paper.

The last few sections are optional, depending on the format guidelines established by the instructor for your assignment..

Good luck with this paper!

Statistics research paper outline template

The following is the general format and structure of a statistics research paper: introduction/background, problem statement, objectives, materials & methods, results and discussion sections. Use this table of contents as an outline when you are beginning your research.

Statistics research paper outline template

As you begin each portion make sure to refer back to this outline.

Writing an idealized outline for a statistics research paper. Each of the research paper outline item above has been discussed below in depth.

Statistics research writing tips:

Make sure to explain your purpose for the study and also give some background information on the problem. This background information should be used as a way of showing why your statistics research paper is important and significant to your field.  Here are some ways to say it without coming off as too boring or unprofessional. They’re quite general but good enough:

State what your hypothesis was; how you came up with it and any problems you faced trying to prove it.

This is how simple it is to write a great statistics term paper or research paper. If you get stuck, you can ask for research paper writing help from expert tutors.

Statistics Research Topics

Wondering what to write a research paper on statistics and probability about?

Statistics is a branch of mathematics dealing with the collection, analysis and interpretation or data.

Statistics is used in many fields, including natural science , social sciences, business and engineering.

A statistician collects, computes and analyzes numerical data to summarize information.

If you are looking for a statistics research paper topic ideas you’ve come to the right place!

statistics research paper topics

Check out this list below of major research paper topics in statistics and probability for college students:

Statistics Research Topics – Probability

Description: Probability deals with events that have uncertain outcomes..  It involves mathematical calculations using formulas involving random variables such as probability density functions (pdf), probability distributions , expected values or moments E(x), variance V(X).. In other words a probability distribution summarizes all possible outcomes in terms of probabilities based on theoretical assumptions or data collection.

A specific probability distribution can be constructed from a collection of frequencies of events in the long run.

This is known as the Central Limit Theorem  which says that if we take averages of random variables over very large numbers, their distributions will approach normal (i.e. bell-shaped curve) regardless of the shape or other details about them.

It’s also a probability measure used to find out how likely it is that one event A happens given that another event B happened first.

Statistics Research Topics – Descriptive statistics

Description: descriptive statistics collects and interprets numerical data in terms of distributions, graphs, measures and relationships among variables.

For example mean, median and mode are measures of central tendency and dispersion.

On the other hand, standard deviation measures dispersion. This is a statistical technique used to summarize data in terms of its most important features.

Descriptive statistics is also necessary for analyzing real-life situations.

It provides information that’s useful for making business decisions.

Statistics Research Topics – Testing significance of relationships (correlation)

Description: correlation deals with measuring the strength , direction and stability of relationship between two or more variables.

A positive correlation indicates that as the value of one variable increases , so does the value of another variable.

For example, if employees in a call center perform better at work when they are seated close to their supervisors, this would be an example of positive correlation because it that shows that as one variable (seating arrangements) increases the other variable (performance) also increases.

On the other hand, if two variables are negatively correlated which means that as one variable increases, the other decreases.

For example, if some countries have a high GDP per capita and low population growth rate then this would be an example of negative correlation because it shows that as your income rises your population falls.

Statistics – Research Paper – Sampling

Description: sampling deals with determining appropriate sample size s for a study based on specific requirements.

Like when you decide to choose five people out of hundreds in order to conduct surveys or research studies.

The main idea behind sampling is to reduce information loss by minimizing unnecessary information.

Also, sampling is also used to make inferences about a population or to study it indirectly by studying a representative sample (group of people) which is expected to be close enough.

Statistics Research Topics – Hypothesis testing

Description: hypothesis testing deals with conducting statistical tests that determine whether or not the data provided supports certain claim or statistically significant conclusion.

For example if you want to test whether the data shows that girls earn higher grades than boys in math classes.

This would be done using a formal statistical procedure called the t-test. By calculating two values and comparing them we can see if there’s a difference between their means.

If it turns out that one group has an average significantly different from the other, then it’s considered significant.

Statistics – Research Paper – Analysis of variance (ANOVA)

Description: analysis of variance (ANOVA) deals with comparing means between at least three or more groups to determine if they’re similar within a certain margin.

It can also be used for determining whether an overall mean is different than another overall mean across several groups.

ANOVA helps determine if there are significant differences in values that would affect results and conclusions drawn from two or more related populations.

For example, you want to know if there’s any difference among four brands of your favorite soft drink so you conduct an experiment by taking 10 people who all like this particular kind and have them taste each of the brands and see which one they prefer.

Statistics Research Topics – Confidence intervals

Description: confidence intervals are used when conducting statistical studies dealing with hypothesis testing which involves making observations about a population based on data collected.

It is essentially ranges of values meant to indicate variability between certain estimated parameters within a group or group of people.

It helps shows how much uncertainty exists within estimates for a single population parameter.

This is done by adding and subtracting margins of error to the original estimation..

Statistics – Research Topics – Non-parametric tests

Description: non-parametric tests are used when conducting statistical studies to make comparisons between two or more samples using data that’s not completely numerical.

This is usually done by converting scores (e.g., number grades, percentages) into ranks so that you’re able to compare between them easier.

Some examples of these tests includes 1 rank sum test, sign test etc…

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Yes, we can provide an example of a probability and statistics research paper. It might be required for students who face difficulty in writing their own term papers or essays. We will not only provide a sample essay but also supply you with relevant instructions that are necessary to carry out the process of academic writing.

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Research Paper

Statistics research paper.

research paper in statistics example

This sample Statistics Research Paper is published for educational and informational purposes only. If you need help writing your assignment, please use our research paper writing service and buy a paper on any topic at affordable price. Also check our tips on how to write a research paper , see the lists of research paper topics , and browse research paper examples .

Statistics is a discipline that deals with data: summarizing them, organizing them, finding patterns, and making inferences. Prior to 1850 the word statistics simply referred to sets of facts, usually numerical, that described aspects of the state; that meaning is still seen in the various sets of government statistics, for example the monthly report on the nation’s unemployment rate and the voluminous tables produced in the wake of each decennial census. During the twentieth century, as a result of the work of Karl Pearson, Ronald Fisher, Jerzy Neyman, Egon Pearson, John Tukey, and others, the term came to be used much more broadly to include theories and techniques for the presentation and analyses of such data and for drawing inferences from them. Two works by Stephen Stigler, The History of Statistics: The Measurement of Uncertainty before 1900 (1986) and Statistics on the Table: The History of Statistical Concepts and Methods (1999) offer broad and readable accounts of the history of statistics.

Although often taught in departments of mathematics, statistics is much more than a branch of applied mathematics. It uses the mathematics of probability theory in many of its applications and finite mathematics and the calculus to derive many of its basic theoretical concepts, but it is a separate discipline that requires its practitioners to understand data as well as mathematics.


In a sense, statistics is mainly concerned with variability. If every object of the same class were the same, we would have no need for statistics. If all peas were indeed alike, we could measure just one and know all about peas. If all families reacted similarly to an income supplement, we would have no need to mount a large scale negative income tax experiment. If all individuals held the same opinion on an issue of the day, we would only need to ask one person’s opinion and we would need to take no particular care in how we chose that person. Variability, however, is a fact of life and so statistics is needed to help reveal patterns in the face of variability.

Statistics is used in the collection of data in several ways. If the data are to be collected via an experiment, statistical theory directs how to design that experiment in such a way that it will yield maximum information. The principles of replication (to allow the measurement of variability), control (to eliminate known sources of extraneous variability), and randomization (to “even out” unknown sources of variation) as enunciated by Fisher in his 1935 book The Design of Experiments help ensure that if differences are found between those receiving experimental treatment(s) and those in control group(s), those differences can be attributed to the treatment(s) rather than to preexisting differences between the groups or to experimental error. If the data are to be collected via a sample survey, the principles of probability sampling ensure that the findings can be generalized to the population from which the sample was drawn. Variations on simple random sampling (which is analogous to drawing numbers out of a hat) take advantage of known properties of a population in order to make the sampling more efficient. The technique of stratified sampling is analogous to blocking in experimental design and takes advantage of similarities in units of the population to control variability.

Once data are collected, via experiments, sample surveys, censuses, or other means, they rarely speak for themselves. There is variability, owing to the intrinsic variability of the units themselves or to their reactions to the experimental treatments, or to errors made in the measuring process itself. Statistical techniques for measuring the central tendency of a variable (e.g., means, medians) clear away variability and make it possible to view patterns and make comparisons across groups. Measures of the variability of a variable (e.g., ranges and standard deviations) give information on the spread of the data— within a group and in comparisons between groups. There are also summarization techniques of correlation and regression to display the patterns of relations between variables—for example, how does a nation’s GDP per capita relate to its literacy rate? These numerical techniques work hand in hand with graphical techniques (e.g., histograms, scattergrams) to reveal patterns in the data. Indeed, using numerical summaries without examining graphical representations of the data can often be misleading. Of course, there are many more complicated and sophisticated summary measures (e.g., multiple regression) and graphical techniques (e.g., residual plots) that aid in the summarization of data. Much of modern data analysis, especially as developed by John Tukey, relies on less conventional measures, on transformations of data, and on novel graphical techniques. Such procedures as correspondence analysis and data mining harness the power of modern computing to search for patterns in very large datasets.

Frequentist And Bayesian Inference

Perhaps the most important use of statistics, however, is in making inferences. One is rarely interested merely in reactions of subjects in an experiment or the answers from members of a sample; instead one wishes to make generalizations to people who are like the experimental subjects or inferences about the population from which the sample was drawn. There are two major modes of making such inference.

research paper in statistics example

Classical or frequentist inference (the mode that has been most often taught and used in the social sciences) conceptualizes the current experiment or sample as one from an infinite number of such procedures carried out in the same way. It then uses the principles codified by Fisher and refined by Neyman and Pearson to ask whether the differences found in an experiment or from a sample survey are sufficiently large to be unlikely to have happened by mere chance. Specifically it takes the stance of positing a null hypothesis that is the opposite of what the investigator believes to be true and has set out to prove. If the outcome of the experiment (or the sample quantity) or one more extreme is unlikely to have occurred if the null hypothesis is true, then the null hypothesis is rejected. Conventionally if the probability of the outcome (or one more extreme) occurring when the null hypothesis is true is less than .05 (or sometimes .01), then the result is declared “statistically significant.”

Frequentists also carry out estimation by putting a confidence interval around a quantity measured from the sample to infer what the corresponding quantity in the population is. For example, if a sample survey reports the percentage in the sample who favor a particular candidate to be 55 percent and gives a 95 percent confidence interval as 52 to 58 percent, the meaning is that a procedure has been followed that gives an interval that covers the true population percent 95 percent of the time. The frequentist does not know (and is not able to put a probability on) whether in any particular case the interval covers the true population percent—the confidence is in the procedure, not in the interval itself. Further, the interval takes into account only what is known as sampling error, the variation among the conceptually infinite number of replications of the current procedure. It does not take into account non-sampling error arising from such problems in data collection as poorly worded questions, nonre-sponse, and attrition from a sample.

In order for these mechanisms of classical statistics to be used appropriately, a probability mechanism (probability sampling or randomization) must have been used to collect the data. In the social sciences this caution is often ignored; statistical inference is performed on data collected via non-probabilistic means and even on complete enumerations. There is little statistical theory to justify such applications, although superpopulation models are sometimes invoked to justify them and social scientists often argue that the means by which the data were accumulated resemble a random process.

Since the 1970s there has been a major renewal of interest in what was historically called inverse probability and is currently called Bayesian inference (after the English nonconformist minister and—during his lifetime— unpublished mathematician Thomas Bayes [1701?— 1761]). Admitting the experimenter’s or analyst’s subjective prior distribution formally into the analysis, Bayesian inference uses Bayes’ theorem (which is an accepted theorem of probability for both frequentists and Bayesians) to combine the prior distribution with the data from the current investigation to update the probability that the hypotheses being investigated is true. Note that Bayesians do speak of the probability of a hypothesis being true while frequentists must phrase their conclusions in terms of the probability of outcomes when the null hypothesis is true. Further, Bayesians construct credibility intervals, for which, unlike the frequentists’ confidence intervals, it is proper to speak of the probability that the population quantity falls in the interval, because in the Bayesian stance population parameters are viewed as having probability distributions. For a frequentist, a population parameter is a fixed, albeit usually unknown, constant. Much of the revival of interest in Bayesian analysis has happened in the wake of advances in computing that make it possible to use approximations of previously intractable models.

While the distinction between Bayesians and frequentists has been fairly sharp, as Stephen E. Fienberg and Joseph B. Kadane (2001) note the two schools are coming together, with Bayesians paying increasing attention to frequentist properties of Bayesian procedures and frequen-tists increasingly using hierarchical models.

Two much more detailed descriptions of the field of statistics and its ramifications than is possible here are given by William H. Kruskal (1968) and Fienberg and Kadane (2001).


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research paper in statistics example

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View sample Time Series Research Paper. Browse other statistics research paper examples and check the list of research paper topics for more inspiration. If you need a religion research paper written according to all the academic standards, you can always turn to our experienced writers for help. This is how your paper can get an A! Feel free to contact our research paper writing service for professional assistance. We offer high-quality assignments for reasonable rates.

A time series is a stretch of values on the same scale indexed by a time-like parameter. The basic data and parameters are functions.

Time Series Research Paper

Time series take on a dazzling variety of shapes and forms, indeed there are as many time series as there are functions of real numbers. Some common examples of time series forms are provided in Fig. 1. One notes periods, trends, wandering and integer-values. The time series such as those in the figure may be contemporaneous and a goal may be to understand the interrelationships.

Concepts and fields related to time series include: logitudinal data, growth curves, repeated measures, econometric models, multivariate analysis, signal processing, and systems analysis.

The field, time series analysis, consists of the techniques which when applied to time series lead to improved knowledge. The purposes include summary, decision, description, prediction.

The field has a theoretical side and an applied side. The former is part of the theory of stochastic processes (e.g., representations, prediction, information, limit theorems) while applications often involve extensions of techniques of ‘ordinary’ statistics, for example, regression, analysis of variance, multivariate analysis, sampling. The field is renowned for jargon and acronyms—white noise, cepstrum, ARMA, ARCH (see Granger 1982).

1. Importance

‘… but time and chance happeneth to them all’ (Ecclesiastes).

Time series ideas appear basic to virtually all activities. Time series are used by nature and humans alike for communication, description, and visualization. Because time is a physical concept, parameters and other characteristics is mathematical models for time series can have real-world interpretations. This is of great assistance in the analysis and synthesis of time series.

Time series are basic to scientific investigations. There are: circadian rhythms, seasonal behaviors, trends, changes, and evolving behavior to be studied and understood. Basic questions of scientific concern are formulated in terms of time series concepts— Predicted value? Leading? Lagging? Causal connection? Description? Association? Autocorrelation? Signal? Seasonal effect? New phenomenon? Control? Periodic? Changing? Trending? Hidden period? Cycles?

Because of the tremendous variety of possibilities, substantial simplifications are needed in many time series analyses. These may include assumptions of stationarity, mixing or asymptotic independence, normality, linearity. Luckily such assumptions often appear plausible in practice.

The subject of time series analysis would be important if for no other reason than that it provides means of examining the basic assumption of statistical independence invariably made in ordinary statistics. One of the first commonly used procedures for this problem was the Durbin–Watson test (Durbin and Watson 1950). The autocovariance and spectrum functions, see below, are now often used in this context.

Figure 2 The dashed lines provide 95 percent bounds about a central curve

Contemporary time series analysis has substantial beginnings in both the physical and social sciences. Basic concepts have appeared in each subject and made their way to the other with consequent transfer of technology. Historical researchers important in the development of the field include: Lauritzen (1981), Hooker (1901), Einstein (1914), Wiener (1949), Yule (1927), Fisher (1929), Tukey (1984), Whittle (1951), Bartlett (1966). Books particularly influential in the social sciences include Moore (1914) and Davis (1941). Nowadays many early analyses appear naive. For example, Beveridge in 1920 listed some 19 periods for a wheat price index running from 1500 to 1869 (Beveridge 1922). It is hard to imagine the presence of so much regular behavior in such a series. When statistical uncertainty is estimated using latter-day techniques most of these periods appear insignificant; see the periodogram with 95 percent error bounds in Fig. 2. Many historical references are included in Wold (1965).

Time Series Research Paper

Historians of science have made some surprising discoveries concerning early work with time series. An example is presented in Tufte (1983). He shows a time series plot from the tenth or eleventh century AD. This graph is speculated to provide movements of the planets and sun. It is remarkable for its cartesian type character. More generally Tufte remarks, following a study of newspapers and magazines, that ‘The timeseries plot is the most frequently used form of graphic design.’ Casual observation certainly supports Tufte’s study.

Important problems that were addressed in the twentieth century include: seasonal adjustment, leading and lagging indicators, and index numbers. Paradigms that were developed include:

series = signal + noise

series = trend seasonal + noise

series = sum of cosines + noise

series = regression function + noise

These conceptualizations have been used for forecasting, seasonal adjustment and description amongst other things. There are surprises, for example, ordinary least squares is surprisingly efficient in the time series case (see Grenander and Rosenblatt 1957). Other books from the 1950s and 1960s that proved important are Blackman and Tukey (1959), Granger and Hatanaka (1964), Box and Jenkins (1970). Important papers from the era include: Akaike (1965), Hannan (1963) and Parzen (1961).

An important development that began in the 1950s and continues today is the use of recursive computation in the state space model; see Kalman (1963), Harvey (1990), Shumway and Stoffer (2000), and Durbin and Koopman (2001).

3.1 Concepts

There are a number of concepts that recur in time series work. Already defined is the time series, a stretch of values on the same scale indexed by a time parameter. The time parameter may range over the positive and negative integers or all real numbers or subsets of these. Time series data refer to a segment of a time series. A time series is said to have a trend when there is a slowly evolving change. It has a seasonal component when some cyclic movement of period one year is present. (The period of a cyclic phenomenon is the amount of time for it to repeat itself. Its frequency is the reciprocal of the period.)

There is an algebra of mathematical operations that either nature or an analyst may apply to a time series {X(t)} to produce another series {Y(t)}. Foremost is the filter, or linear time invariant operation or system. In the case of discrete equispaced time this may be represented as

Time Series Research Paper

t, u = 0, + 1, … An example is the running mean used to smooth a series. The functions X(.), Y(.) may be vector-valued and a(.) may be matrix-valued. In the vector-valued case feedback may be present. The sequence a(u) is called the impulse response function. The operation has the surprising property of taking a series of period P into a series of the same period P. The filter is called realizable when a(u) = 0 for u < 0. Such filters appear in causal systems and when the goal is prediction.

The above ideas concern both deterministic and random series. The latter prove to be important in developing solutions to important problems. Specifically it often proves useful to view the subject of time series as part of the general theory of stochastic processes, that is, indexed families of random variables. One writes {Y(t, ω), t in V}, with ω a random variable and V a set of times. Time series data are then viewed as a segment, {Y(t, ω 0 ), t = 0,…, T – 1} of the realization labeled by ω , the obtained value of ω. Stochastic time series {Y(t), t = 0, + 1, + 2, …} sometimes are conveniently described by finite dimensional distributions such as

Time Series Research Paper

This is particularly the case for time series values with joint normal distributions.

Time series may also be usefully described or generated by stochastic models involving the independent identically distributed random variables of ordinary statistics.

Stochastic models may be distinguished as parametric or nonparametric. Basic parameters of the nonparametric approach include: moments, joint probability and density functions, mean functions, auto-covariance and cross-covariance functions, power spectra.

One basic assumption of time series analysis is that of stationarity. Here the choice of time origin does not affect the statistical properties of the process. For example, the mean level of a stationary series is constant. Basic to time series analysis is handling temporal dependence. To this end one can define the cross-covariance function of the series X and Y at lag u as the covariance of the values X(t + u) and Y(t). In the stationary case this function does not depend on t. In an early paper, Hooker (1901) computed an estimate of this quantity. Another useful parameter is the power spectrum, a display of the intensity or variability of the phenomenon vs. period or frequency. It may be defined as the Fourier transform of the auto-covariance function. The power spectrum proves useful in displaying the serial dependence present, in discovering periodic phenomena and in diagnosing possible models for a series.

In the parametric case there are the autoregressive moving average (ARMA) series. These are regression-type models expressing the value Y(t) as a linear function of a finite number of past values Y(t – 1), Y(t – 2), … of the series and the values ε(t), ε(t – 1), … of a sequence of independent identically distributed random variables. ARMAs have proved particularly useful in problems of forecasting.

Contemporary models for time series are often based upon the idea of state. This may be defined as the smallest entity summarizing the past history of the process. There are two parts to the state space model. First, a state equation that describes how the value of the state evolves in time. This equation may contain a purely random element. Second there is an equation indicating how the available measurements at that time t come from the state value at that time. It too may involve a purely random element. The concept of the state of a system has been basic to physics for many years in classical dynamics and quantum mechanics. The idea was seized upon by control engineers, for example, Kalman (1963) in the late 1950s. The econometricians realized its usefulness in the early 1980s (see Harvey 1990).

A number of specific probability models have been

 studied in depth, including the Gaussian, the ARMA, the bilinear (Granger 1978), various other nonlinear (Tong 1990), long and short memory, ARMAX, ARCH (Einstein 1914), hidden Markov (MacDonald and Zucchini 1997), random walk, stochastic differential equations (Guttorp 1995, Prakasa Rao 1999), and the periodically stationary.

A list of journals where these processes are often discussed is included at the end of this research paper.

3.2 Problems

There are scientific problems and there are associated statistical problems that arise. Methods have been devised for handling many of these. The scientific problems include: smoothing, prediction, association, index numbers, feedback, and control. Specific statistical problems arise directly. Among these are including explanatories in a model, estimation of parameters such as hidden frequencies, uncertainty computation, goodness of fit, and testing.

Special difficulties arise. These include: missing values, censoring, measurement error, irregular sampling, feedback, outliers, shocks, signal-generated noise, trading days, festivals, changing seasonal pattern, aliasing, data observed in two series at different time points.

Particularly important are the problems of association and prediction. The former asks the questions of whether two series are somehow related and what is the strength of any association. Measures of association include: the cross-correlation and the coherence functions. The prediction problem concerns the forecasting of future values. There are useful mathematical formulations of this problem but because of unpredictable human intervention there are situations where guesswork seems just as good.

Theoretical tools employed to address the problems of time series analysis include: mathematical models, asymptotic methods, functional analysis, and transforms.

4.1 Descriptive

Descriptive methods are particularly useful for exploratory and summary purposes. They involve graphs and other displays, simple statistics such as means, medians and percentiles, and the techniques of exploratory data analysis (Tukey 1977).

The most common method of describing a time series is by presenting a graph, see Fig. 1. Such graphs are basic for communication and assessing a situation. There are different types. Cleveland (1985) mentions the connected, symbol, connected-symbol and verticalline displays in particular. Figure 1 presents connected graphs.

Descriptive values derived from time series data include extremes, turning points, level crossings and the periodogram (see Fig. 2 for an example of the latter). Descriptive methods typically involve generating displays using manipulations of time series data via operations such as differencing, smoothing and narrow band filtering.

A display with a long history (Laplace 1825, Wold 1965) is the Buys–Ballot table. Among other things it is useful for studying the presence and character of a phenomenon of period P such as a circadian rhythm. One creates a matrix with entry Y((i – 1)P + j) in row i, column j = 1, …, P and then, for example, one computes column averages. These values provide an estimate of the effect of period P. The graphs of the individual rows may be stacked beneath each other in

 a display. This is useful for discerning slowly evolving behavior.

Descriptive methods may be time-side (as when a running mean is computed), frequency-side (as when a periodogram is computed) or hybrid (as when a sliding window periodogram analysis is employed).

4.2 Parameter Estimation

The way to a solution of many time series problems is via the setting down of a stochastic model. Parameters are constants of unknown values included in the model. They are important because substantial advantages arise when one works within the context of a model. These advantages include: estimated standard errors, efficiency, and communication of results. Often parameter estimates are important because they are fed into later procedures, for example, formulas for forecasting.

General methods of estimating parameters include: method of moments, least squares and maximum likelihood. An important time series case is that of harmonic regression. It was developed in Fisher (1929) and Whittle (1951).

There are parametric and nonparametric approaches to estimation. The parametric has the advantage that if the model is correct, then the estimated coefficients have considerably smaller standard errors.

4.3 Uncertainty Estimation

Estimates without some indication of their uncertainty are not particularly useful in practice. There are a variety of methods used in time series analysis to develop uncertainty measures. If maximum likelihood estimation has been used there are classic (asymptotic) formulas. The delta-method or method of linearization is useful if the quantity of interest can be recognized to be a smooth function of other quantities whose variability can be estimated directly. Methods of splitting the data into segments, such as the jackknife, can have time series variants. A method currently enjoying considerable investigation is the bootstrap (Davison and Hinkley 1997). The assumptions made in validating these methods are typically that the series involved is stationary and mixing.

4.4 Seasonal Adjustment

Seasonal adjustment may be defined as the attempted removal of obscuring unobservable annual components. There are many methods of seasonal adjustment (National Bureau of Economic Research 1976), including state space approaches (Hannan 1963).

The power spectrum provides one means of assessing the effects of various suggested adjustment procedures.

4.5 System Identification

System identification refers to the problem of obtaining a description or model of a system on the basis of a stretch of input to and the corresponding output from a system of interest. The system may be assumed to be linear time invariant as defined above.

In designed experiments the input may be a series of pulses, a sinusoid or white noise. In a natural experiment the input is not under the control of the investigator and this leads to complications in the interpretation of the results. System identification relates to the issue of causality. In some systems one can turn the input off and on and things are clearer.

4.6 Computing

Important computer packages for time series analysis include: Splus, Matlab, Mathematica, SAS, SPSS, TSP, STAMP. Some surprising algorithms have been found: the fast Fourier transform (FFT), fast algorithms from computational geometry, Monte Carlo methods, and the Kalman–Bucy filter. Amazingly a variant of the latter was employed by Thiele in 1880 Lauritzen 1981), while the FFT was known to Gauss in the early 1800s (Heideman et al. 1984).

5. Current Theory And Research

Much of what is being developed in current theory and research is driven by what goes on in practice in time series analyses. What is involved in a time series analysis? The elements include: the question, the experiment, the data, plotting the data, the model, model validation, and model use. The importance of recognizing and assessing the basic assumptions is fundamental.

The approach adopted in practice often depends on how much data are available. In the case that there are a lot of data even procedures that are in some sense inefficient are often used effectively. A change from the past is that contemporary analysis often results from the appearance of very large fine data sets. The amount of data can seem limitless as, for example, in the case of records of computer tasks. There are many hot research topics. One can mention: exploratory data analysis techniques for very large data sets, so-called improved estimates, testing (association? cycle present?), goodness of fit diagnostics. There are the classical and Bayesian approaches, the parametric, semi-parametric, and nonparametric analyses, the problem of dimension estimation and that of reexpression of variables.

Current efforts include research into: bootstrap variants, long-memory processes, long-tailed distributions, nonGaussian processes, unit roots, nonlinearities, better approximations to distributions, demonstrations of efficiency, self-similar processes, scaling relationships, irregularly observed data, doubly stochastic processes as in hidden Markov, cointegration, disaggregation, cyclic stationarity, wavelets, and particularly inference for stochastic differential equations.

Today’s time series data values may be general linear model type (Fahrmein and Tutz 1994), for example, ordinal, state-valued, counts, proportions, angles, ranks. They may be vectors. They may be functions. The time label t may be location in space or even a function. The series may be vector-valued. The data may have been collected in an experimental design.

There are some surprises: the necessity of tapering and prewhitening to reduce bias, the occurrence of aliasing, the high efficiency of ordinary least squares estimates in the correlated case, and the approximate independence of empirical Fourier transform values at different frequencies (Brillinger 1975).

6. Future Directions

It seems clear that time series research will continue on all the existing topics as the assumptions on which any existing problem solution has been based appear inadequate. Further, it can be anticipated that more researchers from nontraditional areas will become interested in the area of time series as they realize that the data they have collected, or will be collecting, are correlated in time.

Researchers can be expected to be even more concerned with the topics of nonlinearity, conditional heteroscedasticity, inverse problems, long memory, long tails, uncertainty estimation, inclusion of explanatories, new analytic models, and properties of the estimates when the model is not true. The motivation for the latter is that time series with unusual structure seem to appear steadily. An example is the data being collected automatically via the World Wide Web. Researchers can be anticipated to be seeking extensions of existing time series methods to processes with more general definitions of the time label— spatial, spatial-temporal, functional, angular. At the same time they will work on processes whose values are more general, even abstract.

More efficient, more robust, and more applicable solutions will be found for existing problems. Techniques will be developed for dealing with special difficulties such as missing data, nonstationarity, outliers. Better approximations to the distributions of time series based statistics will be developed.

Many have stressed the advantages of linear system identification via white noise input. Wiener (1958) stressed the benefits of using Gaussian white noise input. This idea has not been fully developed. Indeed data sets obtained with this input will continually yield to novel analytic methods as they make their appearance.

The principal journals in which newly developed statistical methods for time series are presented and studied include: Journal of Time Series Analysis, Annals of Statistics, Stochastic Processes and their Applications, Journal of the American Statistical Association, Econometrica, IEEE Transactions in Signal Processing.



research paper in statistics example

Research Papers on Statistics

Statistics is often termed as a science which requires learning from a set of collected data. Research papers on statistics involve great focus on analysis, proportional inference and interpretation. This section of Researchomatic is therefore focused on bringing to its customers some of the most carefully selected and compiled research papers on statistics that will help students to better understand the subject.

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research paper in statistics example

How To Write A Statistics Research Paper?

Haiden Malecot

Table of Contents

Statistics Research Paper

Naturally, all-encompassing information about the slightest details of the statistical paper writing cannot be stuffed into one guideline. Still, we will provide a glimpse of the basics of the stats research paper.

What is a stats research paper?

One of the main problems of stats academic research papers is that not all students understand what it is. Put it bluntly, it is an essay that provides an analysis of the gathered statistical data to induce the key points of a specified research issue. Thus, the author of the paper creates a construct of the topic by explaining the statistical data.

Writing a statistics research paper is quite challenging because the sources of data for statistical analysis are quite numerous. These are data mining, biostatistics, quality control, surveys, statistical modelling, etc.

Collecting data for the college research paper analysis is another headache. Research papers of this type call for the data taken from the most reliable and relevant sources because no indeterminate information is inadmissible here.

How to create the perfect statistics research paper example?

If you want to create the paper that can serve as a research paper writing example of well-written statistics research paper example, then here is a guideline that will help you to master this task.

Select the topic

Obviously, work can’t be written without a topic. Therefore, it is essential to come up with the theme that promises interesting statistics, and a possibility to gather enough data for the research. Access to the reliable sources of the research data is also a must.

If you are not confident about the availability of several sources concerning the chosen topic, you’d better choose something else.

Remember to jot down all the needed information for the proper referencing when you use a resource

Data collection

The duration of this stage depends on the number of data sources and the chosen methodology of the data collection. Mind that once you have chosen the method, you should stick to it. Naturally, it is essential to explain your choice of the methodology in your statistics research paper.

Outlining the paper

Creating a rough draft of the paper is your chance to save some time and nerves. Once you’ve done it, you get a clear picture of what to write about and what points should be worked through.

The intro section

This is, perhaps, the most important part of the paper. As this is the most scientific paper from all the papers you will have to write in your studies, it calls for the most logical and clear approach. Thus, your intro should consist of:

The body of the text (research report, as they say in statistics)

Believe it or not, but many professional writers start such papers from the body. Here you have to place the Methodology Section where you establish the methods of data collection and the results of it. Usually, all main graphs or charts are placed here as a way to convey the results. All additional materials are gathered in the appendices.

The next paragraph of the paper will be the Evaluation of the gathered data . And that’s where the knowledge on how to read statistics in a research paper can come in handy. If you have no clue how to do it, you’re in trouble, to be honest. At least, you should know three concepts: odds ratios, confidence intervals, and p values. You can start searching for them on the web or in B.S.Everitt’s Dictionary of Statistics.

And the last section of the body is Discussion . Here, as the name suggests, you have to discuss the analysis and the results of the research.

The conclusion

This section requires only several sentences where you summarise the findings and highlight the importance of the research. You may also include a suggestion on how to continue or deepen the research of the issue.

Tips on how to write a statistics paper example

Here are some life hacks and shortcuts that you may use to boost your paper:

…Final thoughts

We hope that our guideline on how to write a statistics paper example unveiled the mystery of writing such papers.

But, in the case you still dread stats essays, here is a sound solution: entrust your task to the professionals! Order a paper at trustworthy writing service and enjoy saved time and the great result.

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How to Write a Statistics Research Paper: A Complete Guide

A statistics research paper is a piece of original research in written form, primarily aimed to be published in an academic journal or magazine and reviewed by the author’s peers. There are no strict requirements as to the assignment’s size, format, number of sources to be used and other characteristics – it is an extremely versatile kind of work, and you should always consult the guidelines of your particular college and ask your instructor about the specifications required in your case.

Research papers in statistics are the main method of moving the research in this discipline forward. They are presented for peer review and don’t exist by themselves, but are intended for discussion and criticism. Although your research paper is just a college assignment, it should fully meet the requirements of this standard. For you, this means that you should carefully prepare your writing for potential counter-arguments and refutations. The quality of your writing depends to a very significant degree on how well you manage to prepare to potential opposition to your point of view. To be fully ready for this, you have to study not just the data sets dealing with the primary subject of your paper, but with all the significant texts about it written before you as well.

In this statistics research paper writing guide, we will cover all the factors that define whether your research paper succeeds or fails.

Choice of Topic

This is, unmistakably, one of the most important stages of your work – a poorly chosen topic means harder work and worse results. That’s why you cannot approach this step carelessly.

In the end, the topic you choose should at the same time leave you enough space for independent data collection and analysis and provide sufficient background information to build your argument upon.

Try a quicker way

Here are some examples of good topics you may find helpful in your work:

As you can see from this list of topics, statistical analysis can be applied equally effectively to almost any area of human knowledge.

Data Collection

There are three types of sources to be used when writing statistics papers:

Probably more than any other types of academic assignments, statistics research papers are dependent on the information gathered by students themselves and not found in published sources. That is why methods of your data collection occupy a significant portion of your assignment.

Be very careful when selecting data collection methods. You may be given some recommendations by your instructor – if so, follow them and don’t try to be original, for they know what works for your particular case and what doesn’t. If there are no recommendations, try to obtain them – if you ask intelligent questions, instructors usually don’t refuse to answer them. You should be as careful as possible when collecting your data. Once the information is collected, it is impossible to correct the mistakes that have been made in the process of gathering it, and the trustworthiness of your entire paper can easily be compromised.

Make sure you provide sufficient information about your data collection methods for your readers to be able to reconstruct your results. Experiments that cannot be repeated aren’t given much value in the academic community.


Your introduction should be, on the one hand, based on facts and, on the other hand, be fascinating and thought-provoking, so that the reader becomes interested in the contents of your paper upon reading just a few lines. In addition to that, it should explain the purpose of your work and smoothly lead to the main content of the paper.

Begin with the so-called a hook – a sentence aimed at grabbing the reader’s attention right off the bat. It may be some interesting statistical information, unexpected piece of data, not a very well-known fact – anything that can pique the audience’s interest and motivate them to read on.

Then move to the thesis statement – a short (no longer than a couple of sentences, and just one if possible) summary of your primary idea behind the entire paper. It is important to understand that a thesis statement is not identical to the topic. A topic simply limits the scope of your research. Thesis statement actively declares what your hypothesis is, and the rest of the paper is dedicated to finding out whether your idea about the subject matter is right or wrong. For example, “Statistical Analysis of Health Benefits of Weight Training vs. Aerobics” is a topic. “Aerobic exercises possess much higher relative health benefits for non-professional sportsmen than weight training” can be a thesis statement for a paper on this topic.

Body Paragraphs

What the body of your paper should contain:

General Style and Writing Tips: Secrets of Our Best Academic Writers

A conclusion is a part where you sum up everything you’ve found out by this point, repeat your thesis statement and decide if your original hypothesis turned out to be true or not. There is not a lot to say about this part: you simply sum up your evidence, explain why you believe the research you’ve carried out to be important, make suggestions for further research in the same area and more or less repeat everything you’ve written up to this moment in short.

Post-Writing Tips: Revising and Proofreading Your Research Paper

You can simply reread your entire paper, trying to notice all the mistakes and flaws in your writing as you go along, but a much more efficient approach to the task of proofreading is using a checklist. You may prepare your own based on the blunders you most often make, or use a ready-made list, like this one:

Writing a statistics research paper is a long, hard and complicated job, but following the right work process, you can make your task considerably easier – we hope that these statistics research paper writing tips will be of help the next time you encounter such an assignment.

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research paper in statistics example

Writing with Descriptive Statistics

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This handout explains how to write with statistics including quick tips, writing descriptive statistics, writing inferential statistics, and using visuals with statistics.

Usually there is no good way to write a statistic. It rarely sounds good, and often interrupts the structure or flow of your writing. Oftentimes the best way to write descriptive statistics is to be direct. If you are citing several statistics about the same topic, it may be best to include them all in the same paragraph or section.

The mean of exam two is 77.7. The median is 75, and the mode is 79. Exam two had a standard deviation of 11.6.

Overall the company had another excellent year. We shipped 14.3 tons of fertilizer for the year, and averaged 1.7 tons of fertilizer during the summer months. This is an increase over last year, where we shipped only 13.1 tons of fertilizer, and averaged only 1.4 tons during the summer months. (Standard deviations were as followed: this summer .3 tons, last summer .4 tons).

Some fields prefer to put means and standard deviations in parentheses like this:

If you have lots of statistics to report, you should strongly consider presenting them in tables or some other visual form. You would then highlight statistics of interest in your text, but would not report all of the statistics. See the section on statistics and visuals for more details.

If you have a data set that you are using (such as all the scores from an exam) it would be unusual to include all of the scores in a paper or article. One of the reasons to use statistics is to condense large amounts of information into more manageable chunks; presenting your entire data set defeats this purpose.

At the bare minimum, if you are presenting statistics on a data set, it should include the mean and probably the standard deviation. This is the minimum information needed to get an idea of what the distribution of your data set might look like. How much additional information you include is entirely up to you. In general, don't include information if it is irrelevant to your argument or purpose. If you include statistics that many of your readers would not understand, consider adding the statistics in a footnote or appendix that explains it in more detail.

Free Statistics Research Paper Sample for You

Type of paper: Research Paper

Topic: Sports , Time , Gender , Gym , Education , Information , Physical Exercise , Difference

Words: 1100

Published: 2020/12/25


We all know that exercise brings great benefit to the lives of everyone. Playing sports, you strengthen your immune system, strengthen the muscles have a greater impact on cardiac system of the body. Due to physical exercise each person develops, reinforcing its character. Regular exercise is important for the health of men of any age - they protect from diseases and, as evidenced by various studies, slow the aging process. Exercise helps increase strength and endurance. Aerobics, cycling, tennis, basketball, jogging and skiing develop endurance, burning a lot of calories. They significantly strengthen the cardiovascular system, the foundation of good health. Exercises that produce power form the body and build muscle. Through the power of the body can be carried out a wide variety of actions that will get more out of life. In this case study I would like to investigate the average time spent on sports by males and females and check if there is a significant difference in time spent on sport by gender.

Data Gathering

For the purpose to gather the data I found a gym near my home and spent there a day. During all the day I asked each sportsman how many hours he or she spends on training per week (on average). I recorded the answer and the gender of respondent. That day there were 83 visitors in the gym. My sample consists of 83 observations.

I’m given with the data of 83 observations of two variables: Time – the number of hours spent in gym averagely per week. Gender – the gender of respondent (0 – male, 1 – female). The gathered data is in a table below: Summarizing the Data I begin with a descriptive statistics for hours spent on sport by the factor of gender. Descriptive statistics helps me to understand the distribution of the variables:

Descriptive Statistics: Time

Variable Gender N N* Mean SE Mean StDev Minimum Q1 Median Q3 Time 0 46 0 6,761 0,561 3,808 1,000 3,000 6,500 10,000 1 37 0 6,919 0,567 3,451 1,000 4,500 7,000 9,500

Variable Gender Maximum Mode Mode Time 0 13,000 3 5 1 13,000 6; 7; 8 5 According to the descriptive statistics the typical time spent on sports is 5 hours per week for both males and females (Mode = 5). The average time spent on sports is 6.761h for men and 6.919h for women. The men’s data is more dispersed than women’s (standard deviations are 3.808 and 3.451 respectively).

Graphical visualization of the frequency distribution for each gender is given below:

Statistical Inference In this section I will perform a hypothesis testing to check the claim mentioned in introduction part of the paper. Null hypothesis: There is no significant difference in time spent on sports between the genders Alternative hypothesis: There is a significant difference in time spent on sports between the genders. I test this hypothesis using independent samples Student’s t-test.

Set level of significance alpha:

Perform testing:.

Two-Sample T-Test and CI: Time; Gender Two-sample T for Time Gender N Mean StDev SE Mean 0 46 6,76 3,81 0,56 1 37 6,92 3,45 0,57 Difference = mu (0) - mu (1)

Estimate for difference: -0,158

95% CI for difference: (-1,763; 1,447) T-Test of difference = 0 (vs not =): T-Value = -0,20 P-Value = 0,845 DF = 81 Both use Pooled StDev = 3,6534 Since p-value of the test is 0.845>0.05, I failed to reject the null hypothesis. I have no evidence to say that there is a significant difference in time spent on sports between the genders (at 5% level of significance).

The analysis shows that there is no difference in time spent on sports between women and men. Both genders are spend approximately equal time on gym per week. However, there is a number of factors which could bias my results. The first factor is that the answers of sportsmen were subjective. Each individual reported his or her own opinion about how many hours is being spent on gym. But this estimation is not accurate. Some people feel time better, some feel it worse. Somebody like to lie to make an impression of a great sportsman. It would be better if I could check their indications by my own – if I’d be able to spend a week in a gym observing each sportsman, for how many hours he or she visited the gym. The second factor is that the men’s data is not seems to be normally distributed. It may affect the result of t-test, because the normality of distribution is the basic assumption of the test. This issue may be resolved if I increase my sample (remember Central Limit Theorem). The third factor is that I observe the data only during one day. May be the other days of the week (or even of the year) are characterized with another content of sportsmen and the data may report a significantly different result. The fourth factor is that I have observed only 1 gym. This gym may have preferences for one gender, which bias the number of visitors by gender. It may have more exercise machines for males (for example) and less for females or vice versa. It also could affect the visitors and their attitude to the time spent on gym. This issue could be resolved if I perform my study in different gyms.

Boneau, C. Alan. "The Effects of Violations of Assumptions Underlying the T Test."Psychological Bulletin: 49-64.

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How to Find Statistics for a Research Paper

Last Updated: March 29, 2019 References

This article was co-authored by wikiHow staff writer, Jennifer Mueller, JD . Jennifer Mueller is a wikiHow Content Creator. She specializes in reviewing, fact-checking, and evaluating wikiHow's content to ensure thoroughness and accuracy. Jennifer holds a JD from Indiana University Maurer School of Law in 2006. There are 9 references cited in this article, which can be found at the bottom of the page. This article has been viewed 22,038 times. Learn more...

When you're writing a research paper, particularly in social sciences such as political science or sociology, statistics can help you back up your conclusions with solid data. You typically can find relevant statistics using online sources. However, it's important to accurately assess the reliability of the source. You also need to understand whether the statistics you've found strengthen or undermine your arguments or conclusions before you incorporate them into your writing. [1] X Research source [2] X Trustworthy Source University of North Carolina Writing Center UNC's on-campus and online instructional service that provides assistance to students, faculty, and others during the writing process Go to source

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Top 99+ Trending Statistics Research Topics for Students

statistics research topics

Being a statistics student, finding the best statistics research topics is quite challenging. But not anymore; find the best statistics research topics now!!!

Statistics is one of the tough subjects because it consists of lots of formulas, equations and many more. Therefore the students need to spend their time to understand these concepts. And when it comes to finding the best statistics research project for their topics, statistics students are always looking for someone to help them. 

In this blog, we will share with you the most interesting and trending statistics research topics in 2023. It will not just help you to stand out in your class but also help you to explore more about the world.

As you know, it is always suggested that you should work on interesting topics. That is why we have mentioned the most interesting research topics for college students and high school students. Here in this blog post, we will share with you the list of 99+ awesome statistics research topics.

Why Do We Need to Have Good Statistics Research Topics?

Table of Contents

Having a good research topic will not just help you score good grades, but it will also allow you to finish your project quickly. Because whenever we work on something interesting, our productivity automatically boosts. Thus, you need not invest lots of time and effort, and you can achieve the best with minimal effort and time. 

What Are Some Interesting Research Topics?

If we talk about the interesting research topics in statistics, it can vary from student to student. But here are the key topics that are quite interesting for almost every student:-

Top 99+ Trending Statistics Research Topics For 2023

Here in this section, we will tell you more than 99 trending statistics research topics:

Sports Statistics Research Topics

Psychology Research Topics for Statistics

Applied Statistics Research Topics

Personalized Medicine Statistics Research Topics

Experimental Design Statistics Research Topics

Easy Statistics Research Topics

Statistical Research Topics for High School

Survey Topics for Statistics

Statistics Research Paper Topics for Graduates

AP Statistics Topics

Good Statistics Research Topics 

Business Statistics Topics

Statistical Research Topics for College Students

How To Write Good Statistics Research Topics?

So, the main question that arises here is how you can write good statistics research topics. The trick is understanding the methodology that is used to collect and interpret statistical data. However, if you are trying to pick any topic for your statistics project, you must think about it before going any further. 

As a result, it will teach you about the data types that will be researched because the sample will be chosen correctly. On the other hand, your basic outline for choosing the correct topics is as follows:

Note:   Always include the sources from which you obtained the statistics data.

Top 3 Tips to Choose Good Statistics Research Topics

It can be quite easy for some students to pick a good statistics research topic without the help of an essay writer . But we know that it is not a common scenario for every student. That is why we will mention some of the best tips that will help you choose good statistics research topics for your next project. Either you are in a hurry or have enough time to explore. These tips will help you in every scenario.

1. Narrow down your research topic

We all start with many topics as we are not sure about our specific interests or niche. The initial step to picking up a good research topic for college or school students is to narrow down the research topic.

For this, you need to categorize the matter first. And then pick a specific category as per your interest. After that, brainstorm about the topic’s content and how you can make the points catchy, focused, directional, clear, and specific. 

2. Choose a topic that gives you curiosity

After categorizing the statistics research topics, it is time to pick one from the category. Don’t pick the most common topic because it will not help your grades and knowledge. Instead of it, please choose the best one, in which you have little information, or you are more likely to explore it.

In a statistics research paper, you always can explore something beyond your studies. By doing this, you will be more energetic to work on this project. And you will also feel glad to get them lots of information you were willing to have but didn’t get because of any reasons.

It will also make your professor happy to see your work. Ultimately it will affect your grades with a positive attitude.

3. Choose a manageable topic

Now you have decided on the topic, but you need to make sure that your research topic should be manageable. You will have limited time and resources to complete your project if you pick one of the deep statistics research topics with massive information.

Then you will struggle at the last moment and most probably not going to finish your project on time. Therefore, spend enough time exploring the topic and have a good idea about the time duration and resources you will use for the project. 

Statistics research topics are massive in numbers. Because statistics operations can be performed on anything from our psychology to our fitness. Therefore there are lots more statistics research topics to explore. But if you are not finding it challenging, then you can take the help of our statistics experts . They will help you to pick the most interesting and trending statistics research topics for your projects. 

With this help, you can also save your precious time to invest it in something else. You can also come up with a plethora of topics of your choice and we will help you to pick the best one among them. Apart from that, if you are working on a project and you are not sure whether that is the topic that excites you to work on it or not. Then we can also help you to clear all your doubts on the statistics research topic. 

Frequently Asked Questions

Q1. what are some good topics for the statistics project.

Have a look at some good topics for statistics projects:- 1. Research the average height and physics of basketball players. 2. Birth and death rate in a specific city or country. 3. Study on the obesity rate of children and adults in the USA. 4. The growth rate of China in the past few years 5. Major causes of injury in Football

Q2. What are the topics in statistics?

Statistics has lots of topics. It is hard to cover all of them in a short answer. But here are the major ones: conditional probability, variance, random variable, probability distributions, common discrete, and many more. 

Q3. What are the top 10 research topics?

Here are the top 10 research topics that you can try in 2023:

1. Plant Science 2. Mental health 3. Nutritional Immunology 4. Mood disorders 5. Aging brains 6. Infectious disease 7. Music therapy 8. Political misinformation 9. Canine Connection 10. Sustainable agriculture

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1.4 - example: descriptive statistics, example 1-5: women's health survey (descriptive statistics) section  .

Let us take a look at an example. In 1985, the USDA commissioned a study of women’s nutrition. Nutrient intake was measured for a random sample of 737 women aged 25-50 years. The following variables were measured:

Download the data file: nutrient.txt

Using Technology

Minitab icon

We will use the SAS program called to carry out the calculations that we would like to see.

The lines of this program are saved in a simple text file with a .sas file extension. If you have SAS installed on the machine on which you have download this file, it should launch SAS and open the program within the SAS application. Marking up a print out of the SAS program is also a good strategy for learning how this program is put together.

Download the SAS file: nutrient.sas

The video will walk you through the various parts of the code.

The first part of this SAS output, (download below), is the results of the Means Procedure - proc means. Because the SAS output is usually a relatively long document, printing these pages of output out and marking them with notes is highly recommended if not required!

Download the SAS Output file: nutrient2.lst

The first column of the Means Procedure table above gives the variable name. The second column reports the sample size. This is then followed by the sample means (third column) and the sample standard deviations (fourth column) for each variable. I have copied these values into the table below. I have also rounded these numbers a bit to make them easier to use for this example.

Using Minitab

Click on the graphic or the link below to walk through how to find descriptive statistics for the Women's Nutrition dataset in Minitab.

Video: Descriptive Statistics in Minitab

Descriptive Statistics

A summary of the descriptive statistics is given here for ease of reference.

Notice that the standard deviations are large relative to their respective means, especially for Vitamin A & C. This would indicate a high variability among women in nutrient intake. However, whether the standard deviations are relatively large or not, will depend on the context of the application. Skill in interpreting the statistical analysis depends very much on the researcher's subject matter knowledge.

The variance-covariance matrix is also copied into the matrix below.

\(S = \left(\begin{array}{RRRRR}157829.4 & 940.1 & 6075.8 & 102411.1 & 6701.6 \\ 940.1 & 35.8 & 114.1 & 2383.2 & 137.7 \\ 6075.8 & 114.1 & 934.9 & 7330.1 & 477.2 \\ 102411.1 & 2383.2 & 7330.1 & 2668452.4 & 22063.3 \\ 6701.6 & 137.7 & 477.2 & 22063.3 & 5416.3 \end{array}\right)\)


Because this covariance is positive, we see that calcium intake tends to increase with increasing iron intake. The strength of this positive association can only be judged by comparing s 12 to the product of the sample standard deviations for calcium and iron. This comparison is most readily accomplished by looking at the sample correlation between the two variables.

Sample Correlations

The sample correlations are included in the table below.

Here we can see that the correlation between each of the variables and themselves are all equal to one, and the off-diagonal elements give the correlation between each of the pairs of variables.

Generally, we look for the strongest correlations first. The results above suggest that protein, iron, and calcium are all positively associated. Each of these three nutrients intake increases with increasing values of the remaining two.

The coefficient of determination is another measure of association and is simply equal to the square of the correlation. For example, in this case, the coefficient of determination between protein and iron is \((0.623)^2\) or about 0.388.

\[r^2_{23} = 0.62337^2 = 0.38859\]

This says that about 39% of the variation in iron intake is explained by protein intake. Or, conversely, 39% of the protein intake is explained by the variation in the iron intake. Both interpretations are equivalent.

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Statistical Research Papers by Topic

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100 Inspiring Statistics Research Topics

Definition and importance of statistics.

The definition of statistics is always different, depending on your subject and methodology. In simple terms, it is a defined study, analysis, and manipulation of data that must be reviewed. The complex part of statistical analysis is drawing conclusions or coming up with reports. Since it all comes down to data interpretation, one must think about choosing good statistics research topics. Start by addressing various scientific, industrial, or social problems. It will make it easier to narrow things down and find the most efficient solution, be it a manual statistical interpretation or software automation. If things do not work for you, remember that you can pay for research paper and receive additional help with calculation or methodology choice. It will also help you to quote every statistical bit of data correctly if it has been taken from an outside source! 

Statistics Research Topics

How To Write Statistics Research Topics?

The trick here is to know what methodology will be used to collect and interpret statistical data. Even if you have not chosen your statistics project topic, think about it before going any further. It will help you learn about what kind of data will be researched as the sample will be picked correctly. Your basic outline for choosing the right topic should be this way:

Always provide sources for statistical data that has been referred to if it is not your first-hand obtained data! 

100 Research Topics For Statistics 

- good statistics research topics .

It must be noted that statistics are required by numerous disciplines these days, which is why choosing something good for your research can deal with anything. Starting with social media analysis to an estimation of students that have passed the exam successfully, all of it can relate to good stat research topics. 

- Statistics Topics For Research Project 

When you have to choose a specific topic that will reflect statistical methods, start by narrowing things down or determining what kind of analysis will be used. You can think about the role that statistical analysis plays in a certain field. See some examples below: 

- Ph.D. Research Topics In Statistics 

As a rule, dealing with Ph.D. is supposed to be more challenging, yet statistical methods still remain the same. It is the subject and the data sample set that go through the changes. For example, you can choose electrical engineering for your statistical method to match the Ph.D. academic level. 

- Easy Statistics Research Topics 

If you want to find an easy statistics research area, think about the real-life application of statistics. It will help you choose easier research topics for statistics. Just make sure to provide explanations of how statistical research helps, talk about why it happens, and how exactly. 

- Survey Methods Statistics Research Topics 

Not a single statistical method may go without some sort of survey method. It is one of the reasons why we have included various statistics research paper topics that are based on surveys and their practical examples. 

- Business Statistics Research Topics 

When you need something statistical for your business, think about estimation, prognosis, and analysis. In the majority of cases, you shall deal with economics and finances to provide the pros and cons of certain methodologies. See some statistical research topic examples that relate to business matters: 

- Applied Statistics Research Topics 

If your college professor asked you to deal with applied statistics for your next assignment, have no worries because applied statistics are related to practice. For example, you can provide a certain case or turn to an actual event where statistical practice can or will be used. Once you choose a case study, narrow things down and see our examples: 

- Sports Statistics Research Topics 

Regardless of whether you are making bets on sports or want to find out who might win the game by turning to scientific methods, sports statistics is what you will need. See some good statistics research topics about sports to get inspired: 

- Possible Research Topics For Statistics 

Here are the possible subjects where statistics can be researched. If you are not good with formulas and mathematical calculations, these inspiring statistical research topics will help you: 

- Psychology Research Topics for Statistics 

Psychology, Sociology, Healthcare, and Education are among those topics where statistical analysis is essential. Since psychology encompasses philosophy and the constant variables, depending on the case, these statistical psychology topics will be helpful. 

Fitting Your Statistical Research Correctly 

One of the most common challenges with statistics is knowing where to fit related data without making it look awkward. If you are in such a situation, our friendly experts are here to provide assistance. As they write research papers for money , they provide you with custom-tailored ideas and will help you avoid plagiarism as you refer to existing case studies. If you want to end up with a great statistical research project, asking for additional guidance is only natural! Take your time to research our list of inspiring statistical topics for research paper and get help when necessary! 

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About Racism

Reading through the article provided a vivid reflection on how racism becomes a serious issue in the today society. There are various types of racism the article brings out manifested in micro aggression form. The varied opinions in my mind provide a clear picture of the information relayed in the article through the following analysis. Discrimination concerning race will major in my analysis. First, let me talk about the black guy abused in the Saudi Arabia that has sparked public […]

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The article, Racial Athletic Stereotype Confirmation in College Football Recruiting, can be found in the Journal of Social Psychology and is written by Grant Thomas, Jessica J. Good, and Alexi R. Gross. This article was published in 2015 and it explores the topic of racial stereotypes in the context of college athletic recruitment. They were basically studying if a racial bias could play a role in college athletic recruitment. The researchers’ first hypothesis was that coaches would rate black players […]

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Statistical Papers

Statistical Papers provides a forum for the presentation and critical assessment of statistical methods. In particular, the journal encourages the discussion of methodological foundations as well as potential applications.

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Photorealism: A Research Paper

Photography was invented and observed in the year 1839. Photorealism might also could have been a style manner of artwork that usually enclosed on portray drawings and exceptional photographs platform all through artists research an image, and so makes an attempt to create the photo as in any other medium although the time period can be used loosely to provide an explanation for layout in lots of diverse media it’s conjointly accustomed refer in particular to plenty of art work and painters of the social movement that started out within the overdue 1960s and early 1970s. As a full-scale social movement, photorealism emerged from Pop Art, and as a counter to the maximalist other creative movement, similar to the minimalist art movements of the late 1960s and early 1970s. Photorealists use a photograph or many photos to collect the statistics to form their art works. They argued that the utilization of a camera and picture is a recognition of modernism.

However, admittance to the utilization of images in photorealism become met with severe grievance once the motion commenced to acquire momentum in the past due 1960s, regardless of the actual reality that visual devices were used because the fifteenth century to assist artists with their work. The creation of images inside the nineteenth century had three fundamental effects on art portrait and scenic artists had been tested significance to images and artists turned to photography as careers amongst 19th and 20th-century art moves. It’s far nicely recounted that artists used the photo as deliver fabric and as a useful resource, however, they visited nice lengths to disclaim the very fact fearing that their paintings might be misunderstood as imitations and via the photo’s invention artists had been hospitable a good buy of latest experimentation.

Thus, the end result of the discovery of the photograph became an event in art’s records in the direction of the assignment going through the artist because the earliest acknowledged cave drawings making a try to reproduction the scenes they considered. By the time the photorealists started production their bodies of labor the photo became the main definition of recreating fact and abstraction turned into the primary awareness of the art international. Realism continuing as a present day the front, even experiencing a reemergence within the 1930s, however with the aid of the fifties modernist critics and artistic movement had mineralized realism as a significant art undertaking.

Photorealists, as an alternative, were more inspired by using the paintings of pop artists, and reacted against the creative motion. Pop art and photorealism were reactionary moves, stemming from the increasing and in very extremely good quantity abundance of photographic media, that by means of the middle 20th century had adult into such a big improvement that it certainly turned into threatening to reduce the worth of images in artwork. However, while the pop artists have been primarily commenting at the absurdity of loads of the representational manner, photorealists have been trying to reclaim and exalt the worth of a photo.

In photorealism, change and motion ought to be frozen in time that must then be as it should be painted by means of the creator. Photorealists acquire their intellectual imagery and information with the digital camera and picture. Once the photo is developed the author can consistently transfer the picture from the photographic slide onto canvases.

research paper in statistics example

Commonly that is regularly performed either through sticking out the slide onto the canvas or by way of victimization historic grid strategies. The resulting snap shots are typically direct copies of the primary image however are normally larger than the first picture or slide. This ends in photorealist vogue being tight and specific, generally with a strain on mental imagery that wishes an excessive level of technical artwork and technology to simulate, like reflections in a reflect like surfaces and therefore the geometric rigor of synthetic surround.

By the 1970s, the accepted acknowledgement approximately the genesis of photorealism had driven ahead for step one to the discovery of the camera within the nineteenth century, with the new device displacing painting by using its realism and velocity. Then, approximately a century and a half later, painters started projecting digital camera producing photographs onto canvas and tracing the imagery, growing the primary works of called photorealism. Photorealists normally display a photographed picture on to many sizes canvas and then used an airbrush to recreate the results of a photo revealed on smooth photographic paper.

The concept of the portray become complicated in most cases with the photograph and that the painting was fair-minded with the method of finishing it up. To conceal the painterliness of panorama/portrait scenes with the appearance of images. To are looking for out a way to capture a crisp floor by means of the usage of an airbrush strategies in their many pictures of the well-known American culture.

Photorealist artists try and make paintings that undergo a resemblance to snap shots as near practical. Photorealist creations are as well frequently called via many names as superrealism and hyperrealism. Each of those names normally could pass under their personal particle genre. They are commonly all in generally taken into consideration to be aspect shoots of photo realism raising upon later with their very own precise surroundings of attention. Numerous specialists do speedier, littler scale watercolor investigations of the photo to work out the subtleties of shading and arrangement, before setting out on the strongly point by point generation of an enormous scale photorealist painting. So, as to precisely move the picture from the photo to the canvas, photorealist craftsmen utilize a mechanical or semi-mechanical methods for move, for example, a projector or the matrix framework.

Despite the fact that recently kept for the most part to the jargon of workmanship fans, the terms ‘photorealism’ and ‘photorealistic’ have abruptly become substantially more unmistakable on the grounds that they’ve been applied in the enormously well-known area of PC gaming. Over numerous decades now, every specialized and graphical development in the gaming scene has been one little advance towards what is in actuality the genuine ultimate objective for most of game planners – an ongoing, 3D world that is genuinely unclear from a true scene. Consequently, the utilization of descriptors photorealistic, and now and again photoreal, to depict games with always improved illustrations.

Ways to deal with games structure that evade this pattern, supporting rather a masterful style in which scenes purposely look like works of art or drawings, are correspondingly depicted as non-photorealistic. With many artists that worked within the photorealism era took a deeper meaning to paintings that not only tricked the viewers as in to thinking the painting is a realistic photograph showing the long process of the patient mind recreating a real still life image on to a canvas.

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