Independent Samples t-test using SPSS

When to use an Independent Samples t-test

The independent samples t-test can be used to assess whether the mean value of some outcome variable is different between two groups.

The observations/measurements on the outcome variable must be Scale data, such as weight, where you might want to compare the mean weight of the population of two different countries.

If your measurements are:

Ordinal then consider a Mann-Whitney test instead
Nominal then consider a Chi-squared test.

If you wish to compare more than two groups then consider using ANOVA (or a Kruskal Wallis test for Ordinal data).

For more help on “What test do I need” go to the sigma website statistical worksheets resources page.

Example

Consumer Reports, a US magazine, conducted a study to compare the calorie content of beef and poultry hotdogs. They used an independent t-test to determine if there was evidence of a difference in the mean calorie content between the two types of hotdogs.

The data shown below can be downloaded in an SPSS file called hotdog.sav. The data should be set up as two columns. One column contains all the measurements/observations for calories. The other column then indicates which group the measurements came from (coded beef=1, and poultry=2):

*Data is taken from Moore DS & McCabe GP (2002) Introduction to the Practice of Statistics WH Freeman & Co. USA

Using SPSS

To perform the Paired Samples T test, from the Main Menu, click the Analyze menu then select Compare Means and then Independent-Samples T Test:

In the next dialogue window, move calories (the outcome variable) to the Test Variable(s) box. Next, move hotdog to the Grouping Variable box.

You will need to click on the Define Groups button above to choose which two groups to compare.

In the next dialogue box (shown below) select the option Use specified values and enter the numeric values (coded beef=1, and poultry=2). Then click the Continue button:

Finally, click OK:

Examining the Output

The first table Group Statistics is useful because it provides descriptive statistics for the calorie content of beef and poultry hotdogs. In our case, the mean calorie content for beef hotdogs is 156.85, which was higher than the mean calorie content for poultry hotdogs is 122.47.

But do the results provide evidence that this reflects a true difference in the mean calorie content? Or could we have observed this difference just by chance?

The Research Question is: Is there a difference in the mean calorie content in beef and poultry hotdogs?

The Independent-Samples t-test answers this by testing the hypotheses:

H0: There is no difference in the mean calorie content

H1: There is a difference in the mean calorie content

The table titled Independent Samples Test provides the main results of our test. The column labelled Two-sided p provides you with your p-value which is reported as <.001. This is less than 0.05 so there is evidence in favour of H1 that there is a difference in the mean calorie content of beef hotdogs compared to poultry hotdogs.

The table also shows that the t statistic was 4.346 on 35 degrees of freedom (df), which we often include when reporting our results. Note that we are extracting these results from the first row of the table labelled Equal variances assumed. We will come back to the choice of row later when we consider assumptions in the test.

Reporting Results

We could write the results as:

“An independent samples t-test was used to compare the mean calorie content of beef and poultry hotdogs. Beef hotdogs had a higher mean calorie content (M=156.85, SD=22.6242) compared to poultry hotdogs (M=122.47, SD=25.483), and this difference was statistically significant, t(35) = 4.346, p<0.001.”

Further Work

Effect size with Cohen’s d

You can obtain Cohen’s d via the main dialogue by making sure the option to Estimate effect sizes is ticked:

The effect size results are given in the table labelled Independent Samples Effect Sizes. The value for Cohen’s d most often reported is the one in the Point Estimate Column.

A commonly used interpretation of this value is based on benchmarks suggested by Cohen (1988). Here effect sizes are classified as follows: A value of Cohen’s d around 0.2 indicates a small effect, a value around 0.5 is a medium effect and a value around 0.8 is a large effect. In our case Cohen’s d was 1.434, so we have a very large effect.

Checking Assumptions: Homogeneity of variances

We also need to assess the assumption of homogeneity (equality) of variance. This essentially means: can we assume the amount by which the calorie content varies in beef hotdogs is about the same as the amount calories vary in poultry hotdogs?

Levene’s test is used in SPSS to evaluate the homogeneity of variance assumption. Earlier we saw this table:

The sig value or p-value from Levene’s test is shown in the second column of the table. You need the p-value to be greater than 0.05 to be able to assume homogeneity of variances. Here p=0.314 and so we can assume equal variances. Hence, we use the results for the t-test in the first row labelled Equal variances assumed.

If Levene’s test had given us a p-value below 0.05 then we the results for the t-test would come from the second row labelled Equal variances not assumed.

Checking Assumptions: Normality

For the test to be valid it should be reasonable to assume that the calorie measurements are approximately normally distributed. If we have 30 or more measurements in each group, then we can safely make that assumption and need not check this any further. Since we only had 20 measurements for beef and 17 for poultry, we need to do some further assessments:

From the SPSS main menu click Analyze then Descriptive Statistics then Explore:

In the dialogue box that opens, Place the calorie content variable in the Dependent List, and the hotdog type variable in the Factor List.

Click the Plots button. In the new dialogue box, under the Descriptive group, deselect Stem-And-Leaf and select Histogram. Then click the checkbox for Normality plots with tests. Click Continue then OK.

Normality could be judged by examining the histograms of your calorie data -see graphs below- to see if both beef and poultry display a roughly symmetric bell-shaped curve.

With small sample sizes, the differences in scores can make the histogram appear jagged, making it difficult to determine normality. It is probably better to assess normality using the Shapiro-Wilk test, which appears in the SPSS output immediately above the histogram.

You need a non-significant result in both groups, i.e. the sig values (p-values) both need to be greater than 0.05 to be able to assume normality. In our example, p = 0.283 for beef and p=0.277 for poultry, so we can assume the data in both groups is normally distributed. If this were not the case, we would need to use the non-parametric equivalent of the independent samples t-test, called the Mann-Whitney test.

For more resources, see sigma.coventry.ac.uk Adapted from material developed by Coventry University Creative Commons License