Question

come up with a study (something you are interested in learning more about) that would require the use of an ANOVA and calculation of the f-statistic. What I'm lookin' for here is that you would be able to identify a study that would require this statistical procedure vs. the procedures we've learned previously (t and z).

Walk us through the steps in the process of calculating the f-stat

Answer 1

Dear student, please comment in the case of any doubt and I would love to clarify it. Here, I have taken the example and tried to show the step involved in ANOVA test.

Using the following summary data, perform a one-way analysis of variance using α=.01.

Var1=[10.45]**2=109.2

Var2=[12.76]**2=162.82

Var3=[11.47]**2=131.56

MSerror=(109.2+162.82+131.56) / 3= 134.53

Calculating the remaining error (or within) terms for the ANOVA table:

df(error) = 90−3 = 87

SS(error) =(134.53)(90−3) =11703.82

Intermediate steps in calculating the variance of the sample means:

Grand mean = (50.26+45.32+53.67) / 3=49.75

Sum of squares (SS(means)) = 35.25

Var(means) = 35.253−1 = 17.62

MS(between) = (17.62)(30) = 528.75

Calculating the remaining between (or group) terms of the ANOVA table:

df(groups) = 3−1 = 2

SS(group) = (528.75)(3−1) = 1057.5

Test statistic and critical value

F = 528.75 / 134.53 = 3.93

F(critical)(2,87) = 4.86

Decision: fail to reject H0