Question

Explain the sources of variability in one-way between-subjects ANOVA (i.e., independent-measures ANOVA) and one-way within-subjects ANOVA (i.e., repeated-measures ANOVA)?

Answer 1

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Any process are under variations. To identify these variations is a key feature to solve many issues.

Generally speaking in ANOVA Total variations can be split or Express in terms of linear combinations of assignable cause of variation and Random cause of variation.

Particular here,

One Way ANOVA ( independent measures )

Total Variations = Variability due to between groups + Variability due to within groups

I.e, SST = SSB + SSW

where SST =Total Sum of Square

SSB = Sum of Squares due to between groups

SSW = Sum of Squares due to within groups

One Way ANOVA ( repeated measures )

Here Variability due to within groups can further split into Subject variability and Error Variability.

Total Variations = Variability due to Conditions (similar to between groups) + Variability due to Subjects + Variability due to Error

I.e ,

SST = SSC + SSS + SSE

In repeated measures we split the within groups Variability as SSS and SSE. This will reduce the error effect. I.e, In independent measure Error effect SSW which is higher than SSE of repeated measures. Thus F statisic of repeated measure is higher than that of independent measures , results as an increase in the power of the test to detect significant differences between means.