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F-ratio and t statistic Questions

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1. Describe the similarities between an F-ratio and a t statistic.
a. The basic relationship between t statistic and F-ratios can be stated in an equation. What is that equation?
b. These two methods are very similar in calculation (t and F). If you have data from an independent-measures experiment, with only two treatment conditions, you can use either a t test or an independent-measures ANOVA and expect the same results. Provide evidence of why this formula (answer from part a) works. Hint: you can show the t and F formulas in terms of what each measures (words, not numbers) including numerator and denominator values.
c. If you are testing the same hypothesis, with only two treatments, what would the null hypothesis read for each (show in terms of symbols)?

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Solution Summary

F-ratio and t statistic questions are examined.

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1.) Both the t-test and the F-ratio test differences between means of groups.
The t test is applied when there are only two groups. The analysis of variance,
with its F ratio, is performed only when there are more than two groups. However,
the analysis of variance may be used with just two groups. In instances where there are only two groups, the t-test and the F-ratio test give identical conclusions. Other similarities between these tests include the same assumptions on normal distribution of the sample and the ...

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