Module #8 Assignment

 

Module 8 Assignment


Use the following to conduct an analysis of variance (ANOVA) in R to examine how the medicine affects stress levels:


data <- data.frame(

  StressLevel = factor(rep(c("High Stress", "Moderate Stress", "Low Stress"), each = 6)),

  StressRating = c(10, 9, 8, 9, 10, 8, 8, 10, 6, 7, 8, 8, 4, 6, 6, 4, 2, 2)

)


model <- aov(StressRating ~ StressLevel, data = data)


summary(model)


By grouping individuals into one of three stress levels and using the "aov" function to do an analysis of variance (ANOVA) with the stress rating as the dependent variable and the stress level as the independent variable, the aforementioned code will construct a data frame with the given data. The summary(model) output will include the following relevant information:

Df: Degrees of freedom, which represents the number of groups (levels of the independent variable) and the error degrees of freedom.

Sum Sq: The sum of squares, which measures the total variance in the data.

Mean Sq: The mean square, which is the sum of squares divided by degrees of freedom, and provides an estimate of variance.

F value: The test statistic for the ANOVA, which indicates whether there are significant differences between the groups.

Pr(>F): The p-value associated with the F value. A low p-value indicates statistical significance, suggesting that there are significant differences between groups.


If the p-value (Pr(>F)) is less than the selected significance level (e.g., 0.05), there are significant variations in how each group responds to stress. If this were the case, you would reject the null hypothesis that the drug's impact on stress reactions is the same regardless of the level of stress. How much the group means diverge from one another is indicated by the F value. More substantial differences are indicated by a higher F value. You can compute the mean square values using the degrees of freedom for the groups (Df) and the error term.

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