|
Number of means |
Comparisons |
Type of Comparisons |
Statistical test |
Tails |
|
|
|
|
|
|
|
2 |
Hypothetical population mean with population standard deviation versus Sample mean |
Any difference |
Z score with Normal distribution |
2-tailed |
|
2 |
Hypothetical population mean with population standard deviation versus Sample mean |
Direction (greater than, less than, longer than, shorter than, etc.) |
Z score with Normal distribution |
1-tailed |
|
2 |
Hypothetical population mean without population standard deviation versus Sample mean |
Any difference |
One sample Student's t test |
2-tailed |
|
2 |
Hypothetical population mean without population standard deviation versus Sample mean |
Direction (greater than, less than, longer than, shorter than, etc.) |
One sample Student's t test |
1-tailed |
|
2 |
Two sample means, no relationships between samples |
Any difference |
Two Independent Samples Student's t test |
2-tailed |
|
2 |
Two sample means, no relationships between samples |
Direction (greater than, less than, longer than, shorter than, etc.) |
Two Independent Samples Student's t test |
1-tailed |
|
N/A |
Two samples, relationships exists (same subject exposed to 2 treatments or matched pairs) |
Any difference |
Two Dependent Samples Student's t test |
2-tailed |
|
N/A |
Two samples, relationships exists (same subject exposed to 2 treatments or matched pairs) |
Direction (greater than, less than, longer than, shorter than, etc.) |
Two Dependent Samples Student's t test |
1-tailed |
|
|
|
|
|
|
|
3 or more |
3 or more means being compared |
Any difference |
ANOVA |
F test is 1-tailed |
|
3 or more |
3 or more means being compared after a significant ANOVA |
Any difference between all possible pairwise comparisons of means |
Tukey's HSD
SNK |
2-tailed |
|
3 or more |
3 or more means being compared after a significant ANOVA |
Any differences between each experimental group mean and the control group mean |
Dunnett's test |
2-tailed |
|
3 or more |
3 or more means being compared after a significant ANOVA |
Directed differences (greater than, less than, longer than, shorter than, etc.) between each experimental group mean and the control group mean |
Dunnett's test |
1-tailed |
|
3 or more |
3 or more means being compared after a significant ANOVA |
Means are merged into groups and compared against other means or other merged groups of means (1 versus 2 and 3; 2 and 3 versus 1, 4 and 5, etc.) |
Scheffe test |
Not specified |