Question

1. You have an independent-measures study where your first sample has an SS = 36 and your second sample has an SS = 24.

a. If your sample size for both samples is n = 5, find the sample variances and compute the pooled variance.

b. On the other hand, if your samples have difference sample sizes, n1 = 5 and n2 = 13. Again, calculate the two sample variances and your pooled variance.

c. Compare your answers from part a and b. Why are there differences?

Answer 1

a)

first sample variance =SS/(n-1)=36/(5-1)=9

second sample variance =SS/(n-1)=24/(5-1)=6

pooled variance =(SS1+SS2)/(n1+n2-2)=(36+24)/(5+5-2)=7.5

b)

first sample variance =SS/(n-1)=36/(5-1)=9

second sample variance =SS/(n-1)=24/(13-1)=2

pooled variance =(SS1+SS2)/(n1+n2-2)=(36+24)/(13+5-2)=3.75

c)

here from above we can see that second sample has higher sample size and therefore has higher weigtage in pooled variance ; therefore pooled variance is nearer to second sample variance then first sample variance,