Which is NOT an assumption underlying t-tests?

Question

BlackTom AI · Accepted Answer

The question asks which option is NOT an assumption underlying t-tests, so we will evaluate each choice in turn.
Option a) Observations must be independent. This is indeed an assumption of both independent-samples and paired-samples t-tests, because dependence among observations would distort standard error estimates and test statistics.
Option b) Normality. T-tests rely on the assumption that the sampling distribution of the test statistic is approximately normal, which is typically satisfied when the underlying populations are normal or when sample sizes are large by the central limit theorem. Thus, normality is a valid assumption to consider.
Option c) Sphericity. Sphericity is a specific assumption associated with repeated measures ANOVA rather than with t-tests. It concerns the equality of variances of the differences between all combinations of related measurements, which does not arise in standard t-tests for comparing means between two groups or paired observations. Therefore, this requirement is not an assumption of t-tests.
Option d) Equality of variances. For the independent-samples t-test, homogeneity of variances (equal variances) between groups is an assumption that can affect the validity of the test; when variances are unequal, choices like Welch's t-test are often recommended. Hence, this is indeed a t-test assumption, though its strictness depends on the version of the test used.

In summary, the idea of sphericity does not apply to t-tests, whereas independence, normality, and equality of variances are relevant considerations for various t-test scenarios. The contrast with sphericity helps distinguish between t-tests and other ANOVA families that involve repeated measures.

Which is NOT an assumption underlying t-tests?Single choice

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