Module 8. Assignment:

Question A:

Results:

After the ANOVA test was performed in R, we got these results: 

Source: Group;

Df: 2

Sum Sq: 82.11

Mean Sq: 41.06

F-value: 21.36

Pr(>F): 4.08e-05

Source: Residuals;

Df: 15

Sum Sq: 28.83

Mean Sq: 1.92

Interpretation:

We used a one-way ANOVA to test if stress levels affect the reaction scores after taking the drug. Therefore, our null hypothesis (H_O) is if the mean reaction score is the same for all three stress groups. Next, our alternative hypothesis (H_1) is if at least one group is different.

After running the test, we gathered a p-value of 4.08e-05, which is significantly smaller than the significant level of 0.05. Therefore, we have no choice but to reject the null hypothesis. Meaning, that there is a notable difference between the stress groups and that stress levels play a large role on the reaction scores after taking the drug. Those under high stress tend to have higher scores, indicating that the drug's effect may vary depending on the subject's stress level. 

Question B:







B1:

From the linear model results, we see that:

Estimate:

Intercept: 10.125

groupctr.8w: 2.225

groupnone: 1.583

grouppassive: 1.250

Std Error:

Intercept: 0.619

groupctr.8w: 0.918

groupnone: 0.876

grouppassive: 0.876

T-Value:

Intercept: 16.355

groupctr.8w: 2.423

groupnone: 1.809

grouppassive: 1.428

P-Value:

Intercept: 1.19e-12

groupctr.8w: 0.0255

groupnone: 0.0864

grouppassive: 0.1696

Interpretation:

From the data that we gathered after performing the test, we can safely say that the eight-week control group convey a significant difference compared to the active group as its p-value is less than 0.05. To add, it is the only group that is statistically different due to the other two groups having a p-value above 0.05.

B2:

After running the ANOVA test, we get these results:

Group:

Df: 3

Sum Sq: 14.78

Mean Sq: 4.926

F-Value: 2.142

Pr(>F): 0.129

Residuals:

Df: 19

Sum Sq: 43.69

Mean Sq: 2.299

Interpretation:

Our null hypothesis (H_0) is if all the means of the groups are equal.

Our alternative hypothesis (H_1) is if at least one group mean is different.

From the results, we see that the p-value is 0.129, which is greater than the significance level of 0.05. Therefore, we fail to reject the null hypothesis.

In addition, we can confirm that there is no significant difference among the four Zelazo groups, as it suggest that the conditions of the treatment do not create large differences in this dataset. 

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