Final answer:
The statement that ANOVA produces identical results to a two-sample t-test with equal variances is false because ANOVA is designed for comparing three or more groups, whereas a t-test compares two. Both tests do share similar assumptions of normal distribution and equal variances.
Step-by-step explanation:
The statement that a one way analysis of variance (ANOVA) procedure will produce identical results as a two-sample independent t-test with equal variances is false. While it is true that when comparing two groups, the results of an ANOVA and a t-test will mathematically be equivalent, ANOVA is designed to compare means among three or more groups. Both tests assume that samples are drawn from normally distributed populations with equal variances and are independent of each other, but they are used in different circumstances. A t-test is ideal for comparing two means, whereas ANOVA is used for comparing three or more means.
One assumption that must be true to perform a test of two variances, such as the F test, is that the populations from which the samples are drawn are normally distributed. This assumption is crucial for the test to yield reliable results. Additionally, for ANOVA, all populations of interest must be normally distributed, have equal standard deviations, and samples must be randomly and independently selected from each population.