Question

In: Statistics and Probability

There are four treatment groups in the experiment, with 13 lizards within each treatment T1: Brown...

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

Calculate the main effect of lizard color, as the difference in the relevant summary statistic for brown lizard minus green lizards, and interpret it's significance from your statistical test. Describe what the main effect is telling you about the biology of the system.

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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), this is a 2way ANOVA

Solutions

Expert Solution

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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