Question

I have an assignment that I don't fully understand. I'm working on it, but I'd like some help.

I was given the following information:

-20 Subjects, randomly and evenly assigned to assigned to 4 groups. Each group was given an amount of time to master a certain task(4 hours, 8 hours, 24 hours, 40 hours).

The mean of their errors after 200 hours were: Group 1, 42 errors. group 2 40, group 3 34, group 4 33.

I was then given the following table:

Source SS df MS F

Between 294

Within 36

Total 330

I was then asked to find the value of F and complete the table. My questions are:

1) How would I find the value of F?

2) How were 294 and 36 obtained from the above information?

Thank you for your time.

Answer 1

Given Summary data

20 subjects we evenly distributed in to 4 groups which means each group will have 5 subjects

Groups	Count (n)	Average ()	Sum ( n*)	Sum square
1	5	42	210	44100
2	5	40	200	40000
3	5	34	170	28900
4	5	33	165	27225
	N = 20	Grand Total	X = 745	(X)2 = 140225

SS_Between = (X)²/n - (X)²/N = 140225/5 - 745²/20 = 293.75 = 294

Within = Total - Between = 330 - 294 = 36

df between = number of groups - 1 = 4 - 1 = 3

df error = N - number of groups = 20 - 4 = 16

df total = N -1 = 19

Mean square = Sumsquare/df

F = (Mean square between) / (Mean square within)

ANOVA table

Source	SS	df	MS	F
Between	294	3	98	43.56
Within	36	16	2.25
Total	330	19