1 An analysis of variances produces dftotal 29 and dfwithin

1) An analysis of variances produces df_total = 29 and df_within = 27. For this analysis, how many treatment conditions are being compared?

2) A researcher reports an Fratio with df = 1, 24 for an independent-measures experiment. If all the treatments had the same number of participants, then how many individuals were in each treatment?

***Please show work for both***

Solution

(1)

dfbetween=dftotal-dfwithin =29-27=2

If n is the number of treatment, then dfbetween is n-1. So required number of treatments is

n=dfbetween +1=2+1=3

Hence, 3 treatment conditions are being compared.

(2)

Here we have df1=1

df2=24

For a F test if n is number of treatments, k is number of observations under each treatment then

df1=n-1

and

df2=n(k-1)

Therefore we have

n-1=1 which gives n=2

and

n(k-1)=24 which gives

2(k-1)=24

k=13

Hence, 13 individuals were in each treatment.