Question

There are four treatment groups in the experiment, with 13 lizards within each treatment

T1: Brown lizard, brown leaf

T2: Brown lizard, green leaf

T3: Green lizard, green leaf

T4: Green lizard, brown leaf

Of the categorical variables and their interactions, which is more biologically important(e.g, which explains more of the variation in the response variable)? Calculate the percent of variation explained by each variables

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Mean of Fitness

	Brown leaves	Green leaves
Brown lizard	8.088210	7.157375
Green lizard	9.053549	10.004778

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Use underneath table to acquire MS and F-statisitc

	degree of freedom	Sum of Squares
Lizard Color	1	50.880
Leaf Color	1	0.001
LizardColor:LeafColor(interaction)	1	12.398
Residuals	52	97.122

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For all F-statistics of LizardColor, LeafColor, and LizardColor:LeafColor(interaction), the critical value of F statisitc is 3.18(alpha = 0.05)

Answer 1

Sum of squares due to total=SST=50.880+0.001+12.398+97.122=160.401

Effect size for the categorical variables and their interactions:

percentage of variation for Lizard Color=(50.880/160.401)*100=31.72%

percentage of variation for Leaf Color=(0.001/160.401)*100=0.000006*100=0.0006%

percentage of variation for LizardColor:LeafColor(interaction)=(12.398/160.401)*100=0.0773*100=7.73%

Since percentage of variation for Lizard Color is maximum so Lizard Color  is more biologically important (since it explains more of the variation in the response variable).