Introduction

This page includes a number of resources for statistics students. Currently, I have information and resources on Pearson's Correlation Coefficient or Pearson's r, Chi-Square, t-tests, including the One-Sample t-test, the Independent Samples t-test, and the Dependent Samples t-test, and the ANOVA, or Analysis of Variance. I will be adding a section on Linear Regression shortly.

Excel Templates

I have provided a number of Excel templates on this page which are designed to calculate these statistical tests. Unlike SPSS or Stata, my templates show how the calculation is done step-by-step, so students who need to calculate these statistics by hand can easily check their work. Blue areas are where you enter your data, green areas display your results, and orange areas are just for headers or titles. In these templates, I have already entered some data to illustrate how it works. To use the template for your own data, you can simply delete the data I entered in the blue sections and add your own. If you have any questions on how these templates are used, feel free to send me an e-mail.

Pearson's Correlation Coefficient

Pearson's Correlation Coefficient, or Pearson's r, is used to determine the strength of the relationship between two continuous variables, such as years of education completed and income. The correlation between any two variables using Pearson's r will always be between -1 and +1. A correlation coefficient of 0 means that there is no relationship, either positive or negative, between these two variables. A correlation coefficient of +1 means that there is a perfect positive correlation, or relationship, between these two variables. In the case of +1, as one variable increases, the second variable increases in exactly the same level or proportion. Likewise, as one variable decreases, the second variable would decrease in exactly the same level or proportion. A correlation coefficient of -1 means that there is a perfect negative correlation, or relationship, between two variables. In this case, as one variable increases, the second variable decreases in exactly the same level or proportion. Also, as one variable decreases, the other would increase in exactly the same level or proportion.

I have developed an Excel template (right-click and select "Save As") which can calculate Pearson's r for you. Unlike SPSS or Stata, my template takes you step by step through the calculation process - this makes it very easy to check your work when computing Pearson's r by hand. It is designed to handle up to 1,000 cases.

Chi-Square

The chi-square statistic is used to show whether or not there is a relationship between two categorical variables. It can also be used to test whether or not a number of outcomes are occurring in equal frequencies or not, or conform to a known distribution. For example, when rolling a die, there are six possible outcomes. After rolling a die hundreds of times, you could tabulate the number of times each outcome occurred, and use the chi-square statistic to test whether these outcomes were occurring in basically equal frequencies or not (for example, to test whether the die is weighted).

I have also developed an Excel template (right-click and select "Save As") which can calculate the Chi-Square statistic for you. It has two sheets, one used to calculate the Chi-Square statistic for just one variable, the second to calculate the Chi-Square statistic for two variables. Unlike SPSS or Stata, this template takes you step by step through the calculation process - this makes it very easy to check your work when computing the Chi-Square statistic by hand. With one variable, it is designed to handle up to 30 different response categories, while for two variables, it is designed to handle up to 10 response categories per variable.

T-Test

T-tests are used when you want to test the difference between two groups on some continuous variable. A good example would be the difference in yearly income between males and females. T-tests can also be used when testing the same group of people at two different times; for example, testing whether there was a significant increase or decrease in the test scores of the same group of students at two different points in time.

The equation for the t-test depends on whether we are doing an independent samples t-test (comparing two different groups) or dependent samples t-test, also called a paired t-test (comparing the same group at two different periods of time, or two different groups which have been "matched" on some important variable). There is also a one sample t-test which is used to compare a group of scores with a known population mean. Furthermore, there are separate equations for the independent samples t-test depending on whether or not our two groups have equal sample sizes (if the sample sizes are equal, the equation can be simplified).

The One-Sample T-Test

The One-Sample t-Test is used to compare a group of scores with a known population mean. For example, it can be used to determine whether a group of individuals have IQ scores significantly greater than the population mean of 100. A t-test would be preferred to a z-test in situations where the sample size is less than 30 and the population standard deviation is unknown. If either the sample is greater than 30, OR the population standard deviation is known, you would prefer the z-test over the one-sample t-test.

I have developed an Excel template (right-click and select "Save As") which can calculate a one-sample t-test for you. Unlike SPSS or Stata, my template takes you step by step through the calculation process - this makes it very easy to check your work when doing the computations by hand. It is designed to handle up to 1,000 cases.

The Independent Samples T-Test

The Independent Samples t-Test is used to compare two groups on some continuous variable, such as income or IQ score. The equation for the independent samples t-test is quite lengthy; however, when your two groups have equal sample sizes, the equation can be simplified

I have developed an Excel template (right-click and select "Save As") which can calculate an independent samples t-test for you. Unlike SPSS or Stata, my template takes you step by step through the calculation process - this makes it very easy to check your work when doing the computations by hand. It is designed to handle up to 1,000 cases.

The Dependent Samples T-Test

The Dependent Samples t-test is used to test whether scores on some variable have significantly increased or decreased comparing two different points in time. For example, you would use a dependent samples t-test to test whether there was a significant increase or decrease in the test scores of the same group of students at two different points in time.

I have developed an Excel template (right-click and select "Save As") which can calculate a dependent samples t-test for you. Unlike SPSS or Stata, my template takes you step by step through the calculation process - this makes it very easy to check your work when doing the computations by hand. It is designed to handle up to 1,000 cases.

ANOVA, or Analysis of Variance

The ANOVA, which stands for Analysis of Variance, is like a generalized version of the t-test which can be used to test the difference in a continuous variable between two or more groups, or to test the level of a continuous variable in a single group of respondents which were tested at two or more points in time. While the t-test relies upon the t-statistic, the ANOVA uses what is called the F-statistic or F-test. When comparing only two groups, either the t-test or the ANOVA may be used, as they will both give you the same result. A One-Way ANOVA is used when you have only one categorical independent or predictor variable. A Factorial ANOVA is used when you have two or more categorical independent or predictor variables. Finally, a Repeated-Measures ANOVA is used when you are looking at scores on a dependent variable across two or more points in time.

I have developed an Excel template (right-click and select "Save As") which can calculate a One-Way ANOVA for you. Unlike SPSS or Stata, my template takes you step by step through the calculation process - this makes it very easy to check your work when doing the computations by hand. It is designed to handle up to 10 groups and up to 1,000 cases.