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#1
I too am having trouble with ANOVA. I have 2 questions that I need assistance with.

Question 1:

Test the claim that the samples come from populations with the same mean. Assume that the populations are normally distributed with the same variance.

Given the sample data below, test the claim that the populations have the same mean. Use a significance level of 0.05.

Brand A Brand B Brand C
n = 10 n = 10 n = 10
x-bar = 32.4 x-bar = 32.0 x-bar = 27.2
s2 = 4.12 s2 = 3.06 s2 = 4.88

Find the test statistic F. Use three decimal places.


Question 2

Test the claim that the samples come from populations with the same mean. Assume that the populations are normally distributed with the same variance.

Given the sample data below, test the claim that the populations have the same mean. Use a significance level of 0.05.

Brand A Brand B Brand C
n = 10 n = 10 n = 10
x-bar = 32.4 x-bar = 32.0 x-bar = 27.2
s2 = 4.12 s2 = 3.06 s2 = 4.88

Find the critical value F. Use two decimal places.

I'm lost. I know that the test statistic for a One-Way ANOVA is: F = variance between samples/variance within samples. However, I don't understand the formulas. Please advise
 

JohnM

TS Contributor
#2
Both of these problems are the same. The F statistic is compared to the critical value to see if the variance between the groups is significantly larger than the variability inherent within the groups.

The variance between the groups is found by computing the variance between the group means and the grand mean. The variance within the groups is basically the pooled (or " weighted average") variance within the groups.

The critical value of F is found by determining the degrees of freedom for the

numerator (# groups - 1) and the
denominator [ (#groups * sample size in each group) - #groups ]

Try looking at some of the links provided in the post "Online Statistics Resources" in our Examples section. If they don't help clear it up, let us know.....
 
#3
I looked at some examples but I still have some questions. I don't understand the forulma for F. For example, I don't know if the variance between samples is: ns^2/(mean of x) or if it is n(s^2)/mean of x.
And I don't know if th variance within samples is: s^2/p or something else. I guess I just can't read the actual formula and understand what each one means. I hope I'm not confusing you.
I know n = number. However, I'm not sure what "s" or "p" or any of the rest of it means.
 

JohnM

TS Contributor
#4
For Question 1:

F = MSb/MSw --> mean-square between / mean-square within

MSb = SSb/df(b) --> sum of squares between / dof between
MSw = SSw/df(w) --> sum of squares within / dof within

df(b) = #groups - 1 = 2
df(w) = (#groups * sample size) - #groups = (3*10)-3 = 27

SSb = summation of [ n * (group mean - grand mean)^2 ]
= 10*(32.4-30.53)^2 + 10*(32-30.53)^2 + 10*(27.2-30.53)^2
= 167.467

SSw = summation of [ (n-1) * group variance ]
= (9*4.12) + (9*3.06) + (9*4.88)
= 108.54

then:
MSb = 167.467/2 = 83.73
MSw = 108.54/27 = 4.02

then:
F = 83.73/4.02 = 20.829
F(crit) = 3.354
therefore - reject Ho


For Question 2, I believe F(crit) is the same as in Question 1