Tagged: two sample t-test

Introduction

A t-test for independent groups is useful when the same variable has been measured in two independent groups and the researcher wants to know whether the difference between group means is statistically significant. “Independent groups” means that the groups have different people in them and that the people in the different groups have not been matched or paired in any way.

Objectives

The independent t-test compares the means of two unrelated/independent groups measured on the Interval or ratio scale. The SPSS t-test procedure allows the testing of the hypothesis when variances are assumed to be equal or when are not equal and also provides the t-value for both assumptions. This test also provides the relevant descriptive statistics for both of the groups.

Assumptions

• Variable can be classified in two groups independent of each other.
• Variable is Measured on interval or ratio scale.
• Measured variable is approximately normally distributed
• Both groups have similar variances  (variances are homogeneity)

Data

Suppose a researcher wants to discover whether left and right-handed telephone operators differed in the time it took them to answer calls. The data for reaction time were obtained (RT’s measured in seconds):

The mean reaction times suggest that the left-handers were slower but do a t-test confirm this?

Independent Sample t Test using SPSS

Perform the following step by running the SPSS and entering the data set in the SPSS data view

1. Click Analyze > Compare Means > Independent-Samples T Test… on the top menu as shown below.

Select continuous variables that you want to test from the list.

Click on the arrow to send the variable in the “Test Variable(s)” box. You can also double click the variable to send it in “Test Variable” Box.

Select the categorical/grouping variable so that group comparison can be made and send it to the “Grouping Variable” box.

Click on the “Define Groups” button. A small dialog box will appear asking about the name/code used in variable view for the groups. We used 1 for males and 2 for females. Click Continue button when you’re done. Then click OK when you’re ready to get the output.  See the Pictures for Visual view.

Output

First Table in output is about descriptive statistics concerning your variables. Number of observations, mean, variance, and standard error is available for both of the groups (male and female)

The second Table in output is an important one concerning the testing of the hypothesis. You will see that there are two t-tests. You have to know which one to use. When comparing groups having approximately similar variances use the first t-test. Levene’s test checks for this. If the significance for Levene’s test is 0.05 or below, then it means that the “Equal Variances Not Assumed” test should be used (the second one), Otherwise use the “Equal Variances Assumed” test (first one).  Here the significance is 0.287, so we’ll be using the “Equal Variances” first row in the second table.

In the output table “t” is calculated t-value from test statistics, from example, t-value is 1.401

df stands for degrees of freedom, in the example, we have 18 degrees of freedom

Sig (two-tailed) means two-tailed significance value (P-Value), for example, sig value is greater than 0.05 (significance level).

Decision

As the P-value of 0.178 is greater than our 0.05 significance level we fail to reject the null hypothesis. (two-tailed case)

As the P-value of 0.089 is greater than our 0.05 significance level we fail to reject the null hypothesis. (one tail case with 0.05 significance level)

As the P-value of 0.089 is smaller than our 0.10 significance level we reject the null hypothesis and accept the alternative hypothesis. (one tail case with 0.10 significance level). In this case, it means that the left handler has a slower reaction time as compared to the right handler on average.

Other links to study Independent Sample t test using SPSS

• http://libguides.library.kent.edu/SPSS/IndependentTTest
• https://statistics.laerd.com/spss-tutorials/independent-t-test-using-spss-statistics.php