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

Is the fitness of green lizards on green leaves higher than expected, based on the individual effects of lizards color and leaf color? Calculate the interactions as the difference between(the overall mean fitness plus the observed lizard fitness in the Green Lizards and Green Leaves treatments), minus (that expected based on the average fitness of Green Lizards plus the average fitness of lizards grown in Green Leaves). Interpret the significance from the results of your statistical test above

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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), and this is 2way ANOVA

Answer 1

	degree of freedom	Sum of Squares	MS	F	p-value
Lizard Color	1	50.88	50.88	27.24161	3.18263E-06
Leaf Color	1	0.001	0.001	0.000535	0.981628035
LizardColor:LeafColor(interaction)	1	12.398	12.398	6.638002	0.012861477
Residuals	52	97.122	1.86773077
Total	55	160.401

The hypothesis being tested is:

H0: There is no main effect of Lizard Color

Ha: There is a main effect of Lizard Color

The p-value is 0.0000.

Since the p-value (0.0000) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that there is a main effect of Lizard Color.

The hypothesis being tested is:

H0: There is no main effect of Leaf Color

Ha: There is a main effect of Leaf Color

The p-value is 0.9816.

Since the p-value (0.9816) is greater than the significance level (0.05), we fail to reject the null hypothesis.

Therefore, we cannot conclude that there is a main effect of Leaf Color.

The hypothesis being tested is:

H0: There is no interaction effect

Ha: There is an interaction effect

The p-value is 0.01286.

Since the p-value (0.01286) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that there is an interaction effect.

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