Question

 Differentiating pooled variance and the estimated standard error of the difference in sample means 

For the independent-measures t test, which of the following describes the pooled variance (whose symbol is sp2 )? 

The difference between the standard deviations of the two samples 

The variance across all the data values when both samples are pooled together 

A weighted average of the two sample variances (weighted by the sample sizes) 

An estimate of the standard distance between the difference in sample means (M1 - M2) and the difference in the corresponding population means (μ1 - μ2) 

For the independent-measures t test, which of the following describes the estimated standard error of M1 - M2 (whose symbol is S(M1 - M2)_)? 

The difference between the standard deviations of the two samples 

A weighted average of the two sample variances (weighted by the sample sizes) 

An estimate of the standard distance between the difference in sample means (M1 - M2) and the difference in the corresponding population means (μ1 - μ2) 

The variance across all the data values when both samples are pooled together

Answer 1

Result:

In calculating the test statistic, you typically first need to calculate the standard error . The standard error is the value used in the denominator of the t statistic for the independent measure t test.

	size	DF	mean	sd	sum of squares
sample 1	21	20	27.6	4.5	405
sample 2	11	10	21.5	5.5	302.5

SS1 = 20*4.5^2 =405

Sd2 = sqrt(302.5/10) =5.5

Pooled variance = (405+302.5)/30 = 23.5833

Standard error of M1-M2 = sqrt(23.5833*(1/21+1/11)) = 1.8075

t statistic = ( 27.6-21.5)/1.8075 = 3.3748

Degrees of Freedom = 30