Statistical Technique in Review

The independent samples t-test is a parametric statistical technique used to determine significant differences between the scores obtained from two samples or groups. Since the t-test is considered fairly easy to calculate, researchers often use it in determining differences between two groups. The t-test examines the differences between the means of the two groups in a study and adjusts that difference for the variability (computed by the standard error) among the data. When interpreting the results of t-tests, the larger the calculated t ratio, in absolute value, the greater the difference between the two groups. The significance of a t ratio can be determined by comparison with the critical values in a statistical table for the t distribution using the degrees of freedom (df) for the study (see Appendix A Critical Values for Student’s t Distribution at the back of this text). The formula for df for an independent t-test is as follows:

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df=(numberofsubjectsinsample1+numberofsubjectsinsample2)−2

Exampledf=(65insample1+67insample2)−2=132−2=130

The t-test should be conducted only once to examine differences between two groups in a study, because conducting multiple t-tests on study data can result in an inflated Type 1 error rate. A Type I error occurs when the researcher rejects the null hypothesis when it is in actuality true. Researchers need to consider other statistical analysis options for their study data rather than conducting multiple t-tests. However, if multiple t-tests are conducted, researchers can perform a Bonferroni procedure or more conservative post hoc tests like Tukey’s honestly significant difference (HSD), Student-Newman-Keuls, or Scheffé test to reduce the risk of a Type I error. Only the Bonferroni procedure is covered in this text; details about the other, more stringent post hoc tests can be found in Plichta and Kelvin (2013) and Zar (2010).