topic Re: standard deviations in one way analysis of variance with blocks in Discussions

standard deviations in one way analysis of variance with blocks

MFVIT — Thu, 08 Jun 2023 21:03:01 GMT

Hello,

I used the fit y by x platform of JMP to analyze the effect of two products on a response. I also have a blocking variable. The block means report is the following:

Means and Std Deviations

Level Number Mean Std Dev Std Err Mean Lower 95% Upper 95%
A 52 3.75 0.563468 0.078139 3.631591 3.945332
B 52 3.97 0.563468 0.078139 3.7854372 4.0991782

Why are standard deviations the same (the actual standard deviations estimated from each sample are different)? What is the formula behind

Many thanks.

Re: standard deviations in one way analysis of variance with blocks

Mark_Bailey — Fri, 19 Feb 2021 15:01:09 GMT

A primary assumption of the ANOVA model is that the errors are constant across all groups. So the 'sum of squared errors' are 'pooled' across all groups. The estimates are not the simple standard deviation of each group as you would get from Distribution with By( group ) role.

The same assumption is made by the two-sample t-test, unless a correction is made.

Re: standard deviations in one way analysis of variance with blocks

MFVIT — Tue, 23 Feb 2021 08:38:17 GMT

Thank you for your response.

I understand your point. When the Means and standard deviations command is selected in the JMP Fit Y by X platform, the results depend on the use of the blocks. If blocks are not used the group standard deviations are calculated while if a block effect is added the standard deviations are calculated as you said.