In: Math
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
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