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The following is a partial ANOVA table for a single factor ANOVA analysis we want to fill out the remaining parts of the table and answer the questions below so the first part is we can see that the degrees of freedom for the treatment group is 5 and the degrees of freedom for the error is missing but the total degrees of freedom is 35 well something that we know is that the total degrees of freedom is simply just the sum of the treatment degrees of freedom and the Air degrees of freedom so that means that this should be equal to 30 and if we want to know how many treatments there are we know that I minus 1 is equal to 5 from the table and so I is the number of treatments which implies that I is equal to 6 so there are 6 treatments in this example and then we want to know how many observations are in each group well we know that I times J J minus 1 that is is equal to 30 the error degrees of freedom so if I is equal to 6 this implies that this is equal to 6 times J minus 1 which would imply that this must be equal to 5 all right so if this is equal to 5 that means that J is equal to 6 as well so the number of observations in each group is equal to 6 and so the total number of observations would be equal to 36 and that makes sense because the total degrees of freedom happen to be n minus 1 the number of observations the total number of observations in the group minus 1 so this makes sense now the next thing that we want to know is we want to find SSE the sums of squares for this so so SS e is something we want to know well we know that SST the total sums of squares is equal to SS TR + SSE so if we add the two sums of squares together we'll get this so if we want to find just SS II then we can simply take the total sum of squares subtract off the sum of square treatment and it's left should be our sums of squares for error so in other words four thousand fifty six point eight minus two hundred and fourteen point one is equal to our sums of squared error which is forty or three thousand eight hundred and forty two point seven three thousand eight hundred and forty two point seven and so now to find the mean squares this is really pretty straightforward because the mean squares are simply just the sums of squares divided by their corresponding degrees of freedom so sum of the squares divided by their corresponding degrees of freedom and so we'll find that the mean square for the treatment is equal to s STR divided by
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