Module #8 Assignment

#1 

> # Data for each group

> 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)
> 
> # Combine data into a data frame
> reaction_time <- c(high_stress, moderate_stress, low_stress)
> stress_level <- factor(rep(c("High_Stress", "Moderate_Stress", "Low_Stress"), each=6))
> 
> # Create a data frame
> data <- data.frame(Stress_Level = stress_level, Reaction_Time = reaction_time)
> 
> # Perform ANOVA
> anova_model <- aov(Reaction_Time ~ Stress_Level, data=data)
> 
> # Summary of ANOVA
> summary(anova_model)
             Df Sum Sq Mean Sq F value   Pr(>F)
Stress_Level  2  82.11   41.06   21.36 4.08e-05
Residuals    15  28.83    1.92                 
                
Stress_Level ***
Residuals       
---
Signif. codes:  
0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
> 
> # Detailed ANOVA table
> anova_table <- summary(anova_model)

The degrees of freedom for the stress levels are 2 (since there are 3 groups – High, Moderate, Low, so 3 - 1 = 2).
The residual degrees of freedom are 15 (since there are 18 observations and 18 - 3 = 15).
Sum of Squares (Sum Sq):
The sum of squares for stress levels is 82.11, which measures the variability between the different stress level groups.
The residual sum of squares is 28.83, which measures the group variability.
The mean square for stress levels is 41.06, calculated as Sum Sq / Df.
The mean square for the residuals is 1.92.
The F value is 21.36, which indicates the variance ratio between the groups to the variance within the groups.
The p-value is 0.000041, which is much smaller than 0.05. This indicates a statistically significant difference between the reaction times of the different stress levels.

#2

> # Data from Zelazo study
> active <- c(9.00, 9.50, 9.75, 10.00, 13.00, 9.50)
> passive <- c(11.00, 10.00, 10.00, 11.75, 10.50, 15.00)
> none <- c(11.50, 12.00, 9.00, 11.50, 13.25, 13.00)
> ctr_8w <- c(13.25, 11.50, 12.00, 13.50, 11.50)
> 
> # Combine the data into a data frame
> score <- c(active, passive, none, ctr_8w)
> group <- factor(rep(c("active", "passive", "none", "ctr_8w"), times = c(6, 6, 6, 5)))
> 
> # Create a data frame
> zelazo_df <- data.frame(Group = group, Score = score)
> 
> # Perform one-way ANOVA
> zelazo_aov <- aov(Score ~ Group, data = zelazo_df)
> 
> # Summary of the ANOVA
> summary(zelazo_aov)
            Df Sum Sq Mean Sq F value Pr(>F)
Group        3  14.78   4.926   2.142  0.129
Residuals   19  43.69   2.299               
> 
> # t-test between 'active' and 'passive'
> t.test(subset(zelazo_df, Group == "active")$Score, 
+        subset(zelazo_df, Group == "passive")$Score)

	Welch Two Sample t-test

data:  subset(zelazo_df, Group == "active")$Score and subset(zelazo_df, Group == "passive")$Score
t = -1.2839, df = 9.3497, p-value = 0.2301
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
 -3.4399668  0.9399668
sample estimates:
mean of x mean of y 
   10.125    11.375 

> # t-test between 'none' and 'ctr_8w'
> t.test(subset(zelazo_df, Group == "none")$Score, 
+        subset(zelazo_df, Group == "ctr_8w")$Score)

	Welch Two Sample t-test

data:  subset(zelazo_df, Group == "none")$Score and subset(zelazo_df, Group == "ctr_8w")$Score
t = -0.84986, df = 8.5046, p-value = 0.4187
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
 -2.364947  1.081614
sample estimates:
mean of x mean of y 
 11.70833  12.35000