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

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

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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