Statistics
posted by John .
Compute a oneway ANOVA  Give the source table, test null hypothesis at .05 level. Please explain the steps to solving this.
Group 1: 26, 34, 46, 48, 42, 49, 74, 61, 51, 53
EX 1 : 484
Ex 1^2 : 25,024
n = 10
Group 2: 51, 50, 33, 28, 47, 50, 48, 60, 71, 42
EX 2 : 480
EX 2^2 : 24,392
n = 10
Group 3: 52, 64, 39, 54, 58, 53, 77, 56, 63, 59
EX 3 : 575
EX 3^2 : 33,925
n = 10
Group 4: 41, 49, 56, 64, 72, 65, 63, 87, 77, 62
EX 4 : 636
EX 4^2: 42,034
n = 10

Let's use an example, and perhaps you can use this as a guideline for similar ANOVA problems.
Suppose we wish to establish if a difference exists between three different levels of something (it doesn't matter what it is...this is just for purposes of illustration).
Here are the values for each level:
Level 1: 0, 1, 1, 2, 2
Level 2: 1, 2, 1, 3, 3
Level 3: 3, 3, 2, 4, 3
Totals for each level are:
Level 1: 6 >add each value in the level for a total.
Level 2: 10
Level 3: 15
Total of squared values for each level are:
Level 1: 10 >square each value in the level, then add for total.
Level 2: 24
Level 3: 47
To calculate SS within for the ANOVA table, take (sum of total squared values) minus (sum of totals divided by number of values per level). It would look like this:
(10 + 24 + 47)  [(6^2 + 10^2 + 15^2)/5] = 8.8
SS between would be calculated this way:
(6^2 + 10^2 + 15^2)/5  (6 + 10 + 15)^2/15 = 8.13
Note: 15 = total number of values in all levels.
SS total = SS between + SS within = 16.93
To calculate df between:
k  1 = 3  1 = 2
Note: k = number of levels.
To calculate df within:
N  k = 15  3 = 12
Note: N = total number of values in all levels.
df total = df between + df within = 14
To calculate MS between:
SS between/df between = 8.13/2 = 4.065
To calculate MS within:
SS within/df within = 8.8/12 = 0.73
To calculate Fratio:
MS between/MS within = 4.065/0.73 = 5.57
Therefore, the ANOVA table would look like this:
Source......SS......df....MS......F
Between....8.13......2....4.065...5.57
Within.....8.8......12....0.73
Totals....16.93.....14
I hope this example will help. It looks like you already have the values needed to do the calculations for each of your 4 groups. Remember to check the appropriate table for your critical value to compare to your Fratio. Once you do the comparison, you will either fail to reject the null or you will reject the null. You can then form your conclusions.
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