Question

In the study reported in question 2, there were 25 students in each group. Calculate and...

  1. In the study reported in question 2, there were 25 students in each group.

  1. Calculate and report the standard error of the mean.

SEx-bar = sqrt(MSe/ng)

ng is the number per group

  1. Conduct the three post-hoc Tukey HSD tests.

(mean1 – mean2) / SEx-bar

  1. Interpret the results of these tests.

(THIS WAS THE PREVIOS QUESTION)

  1. Suppose I want to know whether students from Iowa, California, and Arizona differ in their average GPA in high school. I collect my data and find the following statistics from three groups of 25 students each (total N=75):

Average GPA: Iowa = 2.10, California = 2.80, Arizona = 3.35

SSb = 4.20                       SSe= 49.25                                                                            

Set your alpha level at .05. Then…

  1. Report your degrees of freedom for between groups and for within groups;

df between = K – 1

df within = N – K

  1. Calculate and report your MSb and your MSe

MSB= SSb/K-1

MSE = SSe/N-K

  1. Calculate and report your F-ratio:

F(2, 72) = MSb/MSe

  1. Decide whether you have a statistically significant result. Give your reasoning.
  1. Interpret your results. What do you now know?

Homework Answers

Answer #1

Given N = 75, k = 3 and alpha = 0.05

a) dfbetween = K-1 = 3-1 = 2
   dfwithin = N - k = 75-3 = 72

b) MSB = SSb/k-1 = 4.20 / 2 = 2.1
   MSE = SSe/N-k = 49.25 / 72 = 0.684

c) F-Ratio = MSB / MSE = 2.1 / 0.684 = 3.0702

d) F critical value = 3.124 at 5% df and (2,72) df

since F-Ratio is less than F-Critical value so we accept H0
i.e. there is no statistically significant

e) Thus we conclude that there is no significant difference among the means of three groups

ANOVA Table:

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