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
SS_b = 4.20 SS_e= 49.25
Set your alpha level at .05. Then…
_a)Report your degrees of freedom for between groups and for within groups;
b) Calculate and report your MS_b and your MS_e
c) Calculate and report your F-ratio:
d) Decide whether you have a statistically significant result. Give your reasoning.
e) Interpret your results. What do you now know?

Question

Quizplus · Accepted Answer

The Answer is a. df between = 3 - 1 = 2; df within = 75 - 3 = 72.
b. MS_B= 4.20/2

\rightarrow

2.10
MS_E = 49.25/72

\rightarrow

.68
c. F₍_{2, 72)} = 2.10/.68

\rightarrow

F_{(2, 72)} = 3.09
d. Well, for an alpha level of .05 with 2 and 70 degrees of freedom (this is the closest we can get to df + 72 in Appendix C), my critical F value from Appendix C will be 3.13. Because my observed F value < than my critical F value, I conclude that my population means are NOT different, and the differences in my sample means was TOO LIKELY due to chance (or random sampling error) for me to rule chance out.
e. I know the population means are NOT significantly different from each other, so I conclude that, on average, children in CA, Iowa, and Arizona have the same GPA in high school. Any observed differences between the sample means is considered to have been caused by random sampling error, or chance.

Suppose I Want to Know Whether Students from Iowa, California