In: Statistics and Probability
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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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
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.