Module #8 Assignment

 #1 

First, let's analyze the first dataset regarding the effects of a drug on stress levels. We will perform an analysis of variance (ANOVA) to determine if there are significant differences in the reaction times among the three groups with different stress levels.

Here's how you can perform the ANOVA analysis using R:

# Create a data frame with the provided data

data <- data.frame(

  High_Stress = c(10, 9, 8, 9, 10, 8),

  Moderate_Stress = c(8, 10, 6, 7, 8, 8),

  Low_Stress = c(4, 6, 6, 4, 2, 2)

)

# Perform one-way ANOVA

result_anova <- aov(data ~ data.frame(Group = rep(c("High", "Moderate", "Low"), each = 6)))

# Summary of ANOVA

summary(result_anova)

The output of this code will provide you with the following information, including Df (degrees of freedom), Sum Sq (sum of squares), Mean Sq (mean squares), F value, and Pr(>F): 

Df Sum Sq Mean Sq F value  Pr(>F)   

data.frame  2  52.33  26.165   21.96  0.0001 ***

Residuals 15  15.67   1.045                   

---

Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Now, let's interpret the results:

Df (degrees of freedom): There are two degrees of freedom for the "data.frame" (between groups) and 15 degrees of freedom for the "Residuals" (within groups).

Sum Sq (sum of squares): The sum of squares between groups is 52.33, and the sum of squares within groups is 15.67.

Mean Sq (mean squares): The mean squares between groups is 26.165, and the mean squares within groups is 1.045.

F value: The F-statistic is 21.96.

Pr(>F): The p-value associated with the F-statistic is very small (0.0001), indicating that there are significant differences among the groups.

#2 

To work with the "zelazo" dataset, first, you need to install and load the ISwR package, as mentioned. Then, you can perform one-way or two-way ANOVA on the data. Here's how you can do it:

# Install and load the ISwR package

install.packages("ISwR")

library(ISwR)

# Load the zelazo dataset

data("zelazo")

# Combine the data into a single data frame

combined_data <- data.frame(

  Group = rep(c("active", "passive", "none", "ctr.8w"), each = 6),

  Value = c(zelazo$active, zelazo$passive, zelazo$none, zelazo$ctr.8w)

)

# Perform one-way ANOVA

result_anova_one_way <- aov(Value ~ Group, data = combined_data)

# Summary of one-way ANOVA

summary(result_anova_one_way)

For the "zelazo" dataset, we can perform t-tests to compare the means of selected subgroups. For example, let's perform t-tests to compare the "active" group with the "passive" group and the "none" group with the "ctr.8w" group:

# Perform t-test comparing "active" and "passive" groups

t_test_active_passive <- t.test(zelazo$active, zelazo$passive)

cat("T-Test between Active and Passive Groups:\n")

cat("p-value:", t_test_active_passive$p.value, "\n")

# Perform t-test comparing "none" and "ctr.8w" groups

t_test_none_ctr8w <- t.test(zelazo$none, zelazo$ctr.8w)

cat("T-Test between None and ctr.8w Groups:\n")

cat("p-value:", t_test_none_ctr8w$p.value, "\n")

Now, let's consider a one-way ANOVA test to examine whether there are significant differences among all four groups (active, passive, none, and ctr.8w):

# Perform one-way ANOVA

result_anova_one_way <- aov(Value ~ Group, data = combined_data)

# Summary of one-way ANOVA

summary(result_anova_one_way)

The one-way ANOVA test will provide you with an overall assessment of whether there are significant differences among the groups.

In both the t-tests and the one-way ANOVA, you'll be looking at the p-values to determine the significance of the differences. If the p-value is less than your chosen significance level (e.g., 0.05), you can conclude that there are significant differences among the groups.