Explain when it should be appropriate to use a t test versus

Explain when it should be appropriate to use a t test versus a one-way analysis of variance.

Solution

While the t-test is limited to comparing means of two groups, one-way ANOVA can compare more than two groups. Therefore, the t-test is considered a special case of one-way ANOVA. These analyses do not, however, necessarily imply any causality (i.e., a causal relationship between the left-hand and right-hand side variables).

Table 1. Comparison between the T-test and One-way ANOVA
      T-test One-way ANOVA LHS(Dependent) Interval or ratio variable Interval or ratio variable RHS (Independent) Binary variable with only two groups Categorical variable

Null Hypothesis µ1 = µ 2 µ1 = µ 2 = µ 3 =........

Prob. Distribution T distribution F distribution

The t-test assumes that samples are randomly drawn from normally distributed populations with unknown population means. Otherwise, their means are no longer the best measures of central tendency and the t-test will not be valid. The Central Limit Theorem says, however, that the distributions of y1-bar and y2-bar are approximately normal when N is large. When n1 + n2 30 ...... in practice, you do not need to worry too much about the normality assumption.......