Question

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).

Please give detail answers for A,B and C

Answer 1

(a) F-ratio = t²

(b) It is more natural to come at it the other way round, and to write down an expression for the ratio of two variance estimates for a population, and derive an expression from it which then is seen to be identical to the usual formula for t². This approach even works for the tough case of different population standard deviations, ie the Behrens-Fisher situation, so it has some power as a heuristic approach.

(c) The hypothesis being tested is:

H₀: µ₁ = µ₂

H₁: µ₁ ≠ µ₂