ANOVA mixed split plot -formula and example

What is ANOVA mixed split plot design

ANOVA mixed split plot designs are complex designs that employ both independent and repeated measures. The best way to explain this is to present the layout of these experimental designs.

TABLE SHOWING THE LAYOUT OF MIXED SPLIT-PLOT DESIGNS

Subjects	Drug 1	Drug 2
DEPRESSIVE 1 2 3 4 5 6	50 55 56 50 56 54	68 63 65 67 69 68
SCHIZOPHRENIC 7 8 9 10 11 12	99 100 110 90 105 115	122 125 130 135 140 131

Observe that there are two independent groups, depressive, and schizophrenic. Also observe that each subject of the depressive and schizophrenic groups is repeatedly tested, once with Drug 1, and later with Drug 2. This is a repeated measures arrangement So here we have a design in which independent and repeated measures are mixed. The name split plot comes from the fact that this design is extensively used in agricultural research.

ANOVA mixed split plot designs -formula

As in all ANOVA, the formula for these designs is: $$F={{MS_{between}} \over {MS_{within}}}$$ We read this as follows: Mean square between over mean square within. What is mean square, you ask. It is the mean of squares. What is squares, you ask. Squares is the statistical term for squared deviations (of squared differences) of each score X from the mean. What are the squared differences, you ask. Remember the formula for variance? $$s^2 ={\sum{({X}-{\bar{X})}}^2 \over {n}}$$ Look at the numerator $${\sum({X}-\bar{X})}^2$$ These are the squared differences summed. To complete our reasoning, we go back to where we started, the F formula, or F ratio, the formula for ANOVA. Why mean sums of squares? Simple because like all average, we divide by the number of scores. If you are observant, you will notice that the F formula is a modified t formula.

FORMAT OF ANOVA MIXED SPIT PLOT SUMMARY TABLE

SOURCE	SS	df	MS	F	p
Between Independent
B	*	*	*	*	*
Error	*	*	*
Total	*	*
Between repeated measures
A	*	*	*	*	*
AxB	*	*	*		*
Error	*	*	*
Total		*
TOTAL		*

HOW TO CALCULATE df OF ANOVA MIXED SPIT PLOT SUMMARY TABLE

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