Which statistical test uses the t-statistic to determine whether the means of two independent samples differ significantly?

Which statistical test uses the t-statistic to determine whether the means of two independent samples differ significantly?

• A. Independent t-test
• B. Paired t-test
• C. ANOVA
• D. Chi-square test

Answer: (A)

Testing whether two independent groups have different means is done with the independent samples t-test. It relies on a t-statistic that compares the observed difference between the group means to the variability within the groups. If the difference is large relative to this variability, the t-statistic is large in magnitude and the p-value is small, leading to rejection of the null hypothesis that the means are equal. This situation applies when you have two separate groups and a continuous outcome. The other tests fit different situations: a paired t-test is for related or matched samples, where you compare differences within pairs rather than two independent means; ANOVA is used when comparing means across three or more groups (the two-group case is mathematically a special case of ANOVA but is typically reported as a t-test); and the chi-square test handles categorical data, not means. If variances between the two groups are assumed equal, you use the pooled version; if not, Welch’s t-test is used. In practice, SPSS will often report Levene’s test to guide which version to use.

Testing whether two independent groups have different means is done with the independent samples t-test. It relies on a t-statistic that compares the observed difference between the group means to the variability within the groups. If the difference is large relative to this variability, the t-statistic is large in magnitude and the p-value is small, leading to rejection of the null hypothesis that the means are equal. This situation applies when you have two separate groups and a continuous outcome.

The other tests fit different situations: a paired t-test is for related or matched samples, where you compare differences within pairs rather than two independent means; ANOVA is used when comparing means across three or more groups (the two-group case is mathematically a special case of ANOVA but is typically reported as a t-test); and the chi-square test handles categorical data, not means. If variances between the two groups are assumed equal, you use the pooled version; if not, Welch’s t-test is used. In practice, SPSS will often report Levene’s test to guide which version to use.