# Independent t-test using SPSS Statistics

## Introduction

The independent-samples t-test (or independent t-test, for short) compares the means between two unrelated groups on the same continuous, dependent variable. For example, you could use an independent t-test to understand whether first year graduate salaries differed based on gender (i.e., your dependent variable would be "first year graduate salaries" and your independent variable would be "gender", which has two groups: "male" and "female"). Alternately, you could use an independent t-test to understand whether there is a difference in test anxiety based on educational level (i.e., your dependent variable would be "test anxiety" and your independent variable would be "educational level", which has two groups: "undergraduates" and "postgraduates").

This "quick start" guide shows you how to carry out an independent t-test using SPSS Statistics, as well as interpret and report the results from this test. However, before we introduce you to this procedure, you need to understand the different assumptions that your data must meet in order for an independent t-test to give you a valid result. We discuss these assumptions next.

###### SPSS Statistics

## Assumptions

When you choose to analyse your data using an independent t-test, part of the process involves checking to make sure that the data you want to analyse can actually be analysed using an independent t-test. You need to do this because it is only appropriate to use an independent t-test if your data "passes" six assumptions that are required for an independent t-test to give you a valid result. In practice, checking for these six assumptions just adds a little bit more time to your analysis, requiring you to click a few more buttons in SPSS Statistics when performing your analysis, as well as think a little bit more about your data, but it is not a difficult task.

Before we introduce you to these six assumptions, do not be surprised if, when analysing your own data using SPSS Statistics, one or more of these assumptions is violated (i.e., is not met). This is not uncommon when working with real-world data rather than textbook examples, which often only show you how to carry out an independent t-test when everything goes well! However, don't worry. Even when your data fails certain assumptions, there is often a solution to overcome this. First, let's take a look at these six assumptions:

**Assumption #1:**Your**dependent variable**should be measured on a**continuous**scale (i.e., it is measured at the**interval**or**ratio**level). Examples of variables that meet this criterion include revision time (measured in hours), intelligence (measured using IQ score), exam performance (measured from 0 to 100), weight (measured in kg), and so forth. You can learn more about continuous variables in our article: Types of Variable.**Assumption #2:**Your**independent variable**should consist of**two categorical**,**independent groups**. Example independent variables that meet this criterion include gender (2 groups: male or female), employment status (2 groups: employed or unemployed), smoker (2 groups: yes or no), and so forth.**Assumption #3:**You should have**independence of observations**, which means that there is no relationship between the observations in each group or between the groups themselves. For example, there must be different participants in each group with no participant being in more than one group. This is more of a study design issue than something you can test for, but it is an important assumption of the independent t-test. If your study fails this assumption, you will need to use another statistical test instead of the independent t-test (e.g., a paired-samples t-test). If you are unsure whether your study meets this assumption, you can use our Statistical Test Selector, which is part of our enhanced content.**Assumption #4:**There should be**no significant outliers**. Outliers are simply single data points within your data that do not follow the usual pattern (e.g., in a study of 100 students' IQ scores, where the mean score was 108 with only a small variation between students, one student had a score of 156, which is very unusual, and may even put her in the top 1% of IQ scores globally). The problem with outliers is that they can have a negative effect on the independent t-test, reducing the validity of your results. Fortunately, when using SPSS Statistics to run an independent t-test on your data, you can easily detect possible outliers. In our enhanced independent t-test guide, we: (a) show you how to detect outliers using SPSS Statistics; and (b) discuss some of the options you have in order to deal with outliers. You can learn more about our enhanced independent t-test guide here.**Assumption #5:**Your**dependent variable**should be**approximately normally distributed for each group of the independent variable**. We talk about the independent t-test only requiring**approximately**normal data because it is quite "robust" to violations of normality, meaning that this assumption can be a little violated and still provide valid results. You can test for normality using the Shapiro-Wilk test of normality, which is easily tested for using SPSS Statistics. In addition to showing you how to do this in our enhanced independent t-test guide, we also explain what you can do if your data fails this assumption (i.e., if it fails it more than a little bit). Again, you can learn more here.**Assumption #6:**There needs to be**homogeneity of variances**. You can test this assumption in SPSS Statistics using Levene’s test for homogeneity of variances. In our enhanced independent t-test guide, we (a) show you how to perform Levene’s test for homogeneity of variances in SPSS Statistics, (b) explain some of the things you will need to consider when interpreting your data, and (c) present possible ways to continue with your analysis if your data fails to meet this assumption (learn more here).

You can check assumptions #4, #5 and #6 using SPSS Statistics. Before doing this, you should make sure that your data meets assumptions #1, #2 and #3, although you don't need SPSS Statistics to do this. When moving on to assumptions #4, #5 and #6, we suggest testing them in this order because it represents an order where, if a violation to the assumption is not correctable, you will no longer be able to use an independent t-test (although you may be able to run another statistical test on your data instead). Just remember that if you do not run the statistical tests on these assumptions correctly, the results you get when running an independent t-test might not be valid. This is why we dedicate a number of sections of our enhanced independent t-test guide to help you get this right. You can find out about our enhanced independent t-test guide here, or more generally, our enhanced content as a whole here.

In the section, Test Procedure in SPSS Statistics, we illustrate the SPSS Statistics procedure required to perform an independent t-test assuming that no assumptions have been violated. First, we set out the example we use to explain the independent t-test procedure in SPSS Statistics.