Explain in your own words what pooled variance is. If you have two different samples of different sizes (the n for each group is different_, explain wether the value of the pooled variance will be closer to the larger sample or smaller sample.

kislotd

kislotd

Answered question

2022-07-16

Explain in your own words what pooled variance is. If you have two different samples of different sizes (the n for each group is different_, explain wether the value of the pooled variance will be closer to the larger sample or smaller sample.

Answer & Explanation

Ryan Hahn

Ryan Hahn

Beginner2022-07-17Added 11 answers

Pooled Variance: In statistics, pooled variance is a method for estimating variance of several different populations when the mean of each of the population may be different, but one believe that the variance of the two population is same. So, we can estimate the common variance by pooling the information from samples from first population and second population. Pooled variance is also known as common variance. The square root of pooled variance is called pooled standard deviation.
Then the common standard deviation can be estimated by the pooled standard deviation:
s p = ( n 1 1 ) s 1 2 + ( n 2 1 ) s 2 2 n 1 + n 2 - 2
be the sample size from first population
be the sample size from second population
be the sample standard deviation of first population
be the sample standard deviation of second population and
n 1 + n 2 2 is the corresponding degrees of freedom.
Suppose assume that the two population variances are equal then first we have calculate the pooled standard deviation
Case(i) : Let for large sample sizes n 1 = 35 , n 2 = 40 , s 1 = 0.68  and  s 2 = 0.75
then pooled standard deviation is given by
s p = ( 35 1 ) ( 0.68 ) 2 + ( 40 1 ) ( 0.75 ) 2 35 + 40 2
s p 2 = 0.5159
Case(ii) : Let for small sample sizes n 1 = 10 , n 2 = 12 , s 1 = 0.68  and  s 2 = 0.75
then pooled standard deviation is given by
From the above calculations, there is no change in the pooled variances for large sample sizes and small sample sizes almost they are equal when we assume standard deviations are same for both the cases.

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