Question

Two species of rat were grown under controlled conditions for 16 days and the following weight gains (in grams) were obtained. If the number is negative, it means the rat lost weight.

Species A -23 4 0 -18 7 32 -4 -2 Species B 21 38 20 24 24 58 16 -16 14 28 -5 25

Species A	-23	4	0	-18	7	32	-4	-2
Species B	21	38	20	24	24	58	16	-16	14	28	-5	25

Using both a student’s t-test and a one-factor ANOVA (Hint, in JMP, use the fit y by x option, then pooled t/ANOVA).

a. What is the mathematical relationship between the value of F you obtain in the ANOVA and the value of “t” you obtain in the t-test ?

b. In this example, is there any advantage to using a t-test or an ANOVA? Is there a scenario where you may have an advantage using one test over the other?

Answer 1

Answer:

Excel Output:

В t-Test: Two-Sample Assuming Equal Variances -23 21 38 Variable 1 Variable 2 20 Mean -0.5 20.58333 -18 24 Variance 280 350.8106 7 Observations 24 8 12 32 Pooled Variance 58 323.2731 -4 16 Hypothesized Mean Difference 0 -2 -16 df 18 t Stat 14 -2.56906 P(T<=t) one-tail 28 0.009657 -5 t Critical one-tail 1.734064 P(T<t) two-tail 25 0.019314 t Critical two-tail Scanned with CamScanner 2.100922 A .

H G K M N Anova: Single Factor SUMMARY Groups Count Sum Average Variance Column 1 -0.5 280 -4 Column 2 247 20.58333 350.8106 12 ANOVA F crit df 1 2133.633 6.600095 0.019314 4.413873 P-value SS MS Source of Variation Between Groups 2133.633 Within Groups 18 323.2731 5818.917 with CS 19 7952.55 Totai

Explanation:

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