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 Dec 2020

stats.libretexts.org stats.libretexts.org

The following ANOVA table illustrates the relationship between the sums of squares for each component and the resulting Fstatistic for testing the three null and alternative hypotheses for a twoway ANOVA.
The following ANOVA table illustrates the relationship between the sums of squares for each component and the resulting Fstatistic for testing the three null and alternative hypotheses for a twoway ANOVA.

 Nov 2020

mycsun.app.box.com mycsun.app.box.com

Repeated Measures ANOVA example.
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statistics.laerd.com statistics.laerd.com

You will want to report this as follows:
Reporting ANOVA in APA style.

 Oct 2020

www.scribbr.com www.scribbr.com

Example: Reporting the results of ANOVA
Example: Reporting the results of ANOVA
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statistics.laerd.com statistics.laerd.com

Underlying Assumptions: Normality
Repeated measures anova normality and sphericity

 Apr 2020

online.stat.psu.edu online.stat.psu.edu

Graphically, interactions can be seen as nonparallel lines connecting means when we are working with the simple twofactor factorial with 2 levels of each main effect (adapted from Zar, H. Biostatistical Analysis, 5th Ed., 1999). Remember interactions are referring to the failure of a response variable to one factor to be the same at different levels of another factor. So when lines are parallel the response is the same. In the plots below you will see parallel lines as a consistent feature in all of the plots with no interaction. In plots depicting interactions, you notice that the lines cross (or would cross if the lines kept going).
Main and interaction effects  graphs


statistics.laerd.com statistics.laerd.com

Step #3b
Mix anova when no interaction effect is found.

Step #3a:
Mix Anova interpretation step 3a

 May 2019

stats.stackexchange.com stats.stackexchange.com

Multiple comparisons: It is not good practice to test for significant differences among pairs of group means unless the ANOVA suggests some such differences exist. Nevertheless, I admit it is tempting to take another look at the comparison of G1 with G3 (ignoring the existence of G2 and perhaps assuming normality), but then you should use a Welch t test to account for the differences in sample variances, and you should not make claims about the result unless the Pvalue is as low as .01 or .02. Looking at that difference more carefully might prompt a subsequent experiment.
Test for significance among pairs when the overall f test is not significant.

 Apr 2019

statistics.laerd.com statistics.laerd.com

statistics.laerd.com statistics.laerd.com

There are two tests that you can run that are applicable when the assumption of homogeneity of variances has been violated: (1) Welch or (2) Brown and Forsythe test. Alternatively, you could run a KruskalWallis H Test. For most situations it has been shown that the Welch test is best. Both the Welch and Brown and Forsythe tests are available in SPSS Statistics (see our Oneway ANOVA using SPSS Statistics guide).
ANOVA is robust against violation of the assumption of equal variances, but...

However, platykurtosis can have a profound effect when your group sizes are small. This leaves you with two options: (1) transform your data using various algorithms so that the shape of your distributions become normally distributed or (2) choose the nonparametric KruskalWallis H Test which does not require the assumption of normality.
ANOVA is robust against violation of normality, but...
