The independent samples t-test is used to compare two sample means from unrelated groups. This means that there are different people providing scores for each group. The purpose of this test is to determine if the samples are different from each other.
Assumptions
- The dependent variable is continuous (interval or ratio) - based on operationalization of the variable
- Categorical independent variable with only two levels - based on operationalization of the variable
- Each observation is independent of other observations - evaluated through the study's design
- No significant outliers for the dependent variable - can be assessed using boxplots, scatterplots, and other methods
- The dependent variable should be approximately normally distributed for each level of the independent variable - can be assessed using histograms, Q-Q plots, skewness, kurtosis, K-S test and/or Shapiro Wilks
- Homogeneity of variances - tested using Levene's test, which is automatically included in the output
Running a Single Sample t-test using SPSS
- Analyze > Compare Means and Proportions > Independent-Samples T Test
- Move the dependent variable into the Test Variable(s) box
- Move the independent variable into the Grouping Variable box.
- Click on Define Groups and enter the numerical code for each group (i.e., if you indicated that 1 = Treatment and 2 = Control, you would use 1 and 2 in the boxes)
- Click Continue to return to the main dialogue box.
- Review Options for missing values and confidence interval options.
- Select OK to run the analysis.
Interpreting the Output
- Group Statistics
- provides summary statistics about the dependent variable for each group including sample size, mean, standard deviation, and standard error of the mean
- Independent Samples Test
- Levene's Test for Equality of Variances
- Sig. denotes the probability that you will interpret when assessing if the assumption is met
- Note: a significance value less than .05 indicates that the variances are significantly different from each other, thus violating the assumption
- provides the results of the statistical test
- test statistic = t
- associated probability (p-value) = Sig.
- confidence interval of the difference (if elected to include)
- Note: there are two sets of statistics provided: Equal variances assumed and Equal variances not assumed. Interpret and report the statistics that align with the results of the Levene's test.
Reporting Results in APA Style
When reporting the results of the independent samples t-test, APA Style has vague requirements on what information should be included. Below is the key information you should anticipate reporting when presenting the results of the test. You want to replace the red text with the appropriate values from your output.
t(degrees of freedom) = the t statistic, p = p value.
Example:
An independent-samples t-test was run to determine if the Mind Over Matter coping strategy was more effective at reducing anxiety than deep breathing exercises. The results showed that the participants using the Mind Over Matter strategy (M = 21, SD = 2.2) reported lower levels of anxiety than participants using deep breathing exercises (M = 28, SD = 2.7). This difference was significant (t(19) = 4.37, p < .01).
Notes:
- When reporting the p-value, there are two ways to approach it. One is when the results are not significant. In that case, you want to report the p-value exactly: p = .247. The other is when the results are significant. In this case, you can report the p-value as being less than the level of significance: p < .05. If SPSS reports the p-value as < .001, you would report it the same way: p < .001.
- The t statistic should be reported to two decimal places with a 0 before the decimal point if needed: t = 0.36 or t = 2.71.
- Degrees of freedom for this test are (n1 - 1) + (n2 - 1) or (n1 + n2) - 2, where "n1" represents the number of people in one group and "n2" represents the number of people in the other group. The n for each group can be found in the SPSS output.
