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Standard error of the parameter estimate in n-way ANOVA

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Standard error of the parameter estimate in n-way ANOVA

Scenario:

Experimental Design: RCBD with 3 blocks.

Response Variable: Biomass Wt.

Independent Variables: Treatments (2 levels), Time (1...8), Samples (4 samples per treatment per collection time).

SAS Procedure: Repeated measures in PROC MIXED.


1. Why are the model estimated standard errors of the means (estimates) equal at respective time (e.g. at time 1, ... at time 8)? For example,

Effect            Treat        Time       Estimate     Standard Error   DF  tValue  Pr>t

Treat*Time       1               1            266.14               79.7816

Treat*Time       2               1            198.33               79.7816

       .                 .                .

       .                 .                .

       .                 .                .

Treat*Time        1              8             986.49              88.2263

Treat*Time        2              8             703.17              88.2263

2. Why are the arithmetic mean (excel generated) and estimate of the mean very comparable, while model estimated standard errors and arithmetic standard errors (for lack of an appropriate word) not comparable?

                      Treat        Time   Arithmetic Mean    Standard Error

                         1               1            266.14               43.00

                         2               1            198.33               39.00

                         .                 .                 .                          .

                         .                 .                 .                          .

                         .                 .                 .                          .

                         1               8             986.49              94.00

                         2               8             703.17              79.00

3. Which standard error values should be used when publishing results?

Thank you.

                  

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