t-Test: Independent or Correlated Samples

t-Test for Independent or Correlated Samples

The logic and computational details of two-sample t-tests are described in Chapters 9-12 of the online text Concepts & Applications of Inferential Statistics. For the independent-samples t-test, this unit will perform both the "usual" t-test, which assumes that the two samples have equal variances, and the alternative t-test, which assumes that the two samples have unequal variances. (A good formulaic summary of the unequal-variances t-test can be found on the StatsDirect web site. A more thorough account appears in the online journal Behavioral Ecology.)

Setup		Procedure
Independent Samples Correlated Samples
Data Entry
Sample A	Sample B

Please be sure to perform the Data Check procedure.
Reset Calculate

Data Summary
	A	B	Total
n
-X
-X²
SS
mean

Results_Q

Mean_a—Mean_b	t	df

P	one-tailed
P	two-tailed

For independent samples, these results pertain to the "usual" t-test,
which assumes that the two samples have equal variances.

F-Test for the Significance of the Difference
between the Variances of the Two Samples_Q

df₁	df₂	F	P

[Applicable only to independent samples.] P>.05 indicates no significant difference detected between the variances of the two samples.

t-Test Assuming Unequal Sample Variances
[Applicable only to independent samples.]_Q

Mean_a—Mean_b	t	df

P	one-tailed
P	two-tailed

For purposes of significance tests and calculation of confidence intervals, values of df associated with the unequal-variance condition are rounded to the nearest integer.

	Observed	Confidence Intervals
	Observed	0.95	0.99
Mean_a		±	±
Mean_b		±	±
Mean_a−Mean_b [Assuming equal sample variances.]		±	±
Mean_a−Mean_b [Assuming unequal sample variances.]		±	±

Print this Window

Home

Click this link only if you did not arrive here via the VassarStats main page.