Archive:Advanced ANOVA/Assumptions: Difference between revisions
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This page outlines the assumptions for various '''ANOVA''' models, including [[t-test|''t''-tests]]. | |||
This page outlines | |||
==All models== | ==All models== | ||
# [[Dependent variable]]s must be: | # [[Dependent variable]]s must be: | ||
#* Measured at interval or ratio | #* Measured at interval or ratio [[level of measurement]]. | ||
#* [[Normal distribution|Normally distributed]] in all groups of the [[independent variable]]. | #* [[Normal distribution|Normally distributed]] in all groups (of the [[independent variable]]s). | ||
#** ANOVA is quite robust to violations of this assumption if sample sizes are large and approximately equal (> 15 cases per group) | #** ANOVA is quite robust to violations of this assumption if sample sizes are large and approximately equal (> 15 cases per group) | ||
==[[{{BASEPAGENAME}}/Testing differences|''t''-tests]], [[{{BASEPAGENAME}}/One-way ANOVA|one-way ANOVA]] and [[{{BASEPAGENAME}}/Factorial ANOVA|factorial ANOVA]]== | ==[[{{BASEPAGENAME}}/Testing differences|''t''-tests]], [[{{BASEPAGENAME}}/One-way ANOVA|one-way ANOVA]] and [[{{BASEPAGENAME}}/Factorial ANOVA|factorial ANOVA]]== | ||
In addition, for between-group designs, it is assumed that: | |||
# The data in each cell is '''[[normality|normally distributed]]'''. | # The data in each cell is '''[[normality|normally distributed]]'''. | ||
# '''Homogeneity of variance''': | #* e.g., for a 2 by 2 factorial ANOVA with age and gender as the IVs, check the distributions of the DV for, say, younger females, older females, younger males, and older males. | ||
# The data in each cell has '''[[Homogeneity of variance|homogenous variance]]''': | |||
#* The [[variance]] for each cell should be similar - a rule of thumb is that one ''SD'' should not be more than double another cell ''SD''. | #* The [[variance]] for each cell should be similar - a rule of thumb is that one ''SD'' should not be more than double another cell ''SD''. | ||
#* If violated, | #* If violated, | ||
#** the ''p | #** the ''p''-values for significance tests are inaccurate. | ||
#** [[SPSS]] has | #** [[SPSS]] has tests to adjust for hetereogeneity of variance. | ||
# '''Cells are independent''' - Cases represent random samples from the target populations and the scores of the test variable should be independent of each other (i.e., the scores in one cell are not dependent on the scores in another cell). | # '''Cells are independent''' - Cases represent random samples from the target populations and the scores of the test variable should be independent of each other (i.e., the scores in one cell are not dependent on the scores in another cell). | ||
#* Inaccurate ''p-''values are produced if the independence assumption is violated. | #* Inaccurate ''p-''values are produced if the independence assumption is violated.<noinclude> | ||
<noinclude> | |||
[[Category:{{BASEPAGENAME}}]] | [[Category:{{BASEPAGENAME}}]] | ||
</noinclude> | </noinclude>{{ntnes}} | ||
Latest revision as of 05:49, 27 May 2009
This page outlines the assumptions for various ANOVA models, including t-tests.
All models
- Dependent variables must be:
- Measured at interval or ratio level of measurement.
- Normally distributed in all groups (of the independent variables).
- ANOVA is quite robust to violations of this assumption if sample sizes are large and approximately equal (> 15 cases per group)
In addition, for between-group designs, it is assumed that:
- The data in each cell is normally distributed.
- e.g., for a 2 by 2 factorial ANOVA with age and gender as the IVs, check the distributions of the DV for, say, younger females, older females, younger males, and older males.
- The data in each cell has homogenous variance:
- Cells are independent - Cases represent random samples from the target populations and the scores of the test variable should be independent of each other (i.e., the scores in one cell are not dependent on the scores in another cell).
- Inaccurate p-values are produced if the independence assumption is violated.