Question

Overview: Introduce comparing mean differences between 3 or more groups on a single dependent variable Objectives: The student will comprehend how to conduct a) a One-Way Anova, b) multiple comparision follow up proceedures, c) effect size calculations Readings: Ch 11 Activities and Assessments: Ch Review and Practice Problems; RStudio Application Activities.

One-Way ANOVA RStudio Application Activities

Activity 1 One-Way ANOVA

What is the null hypothesis for this study?

What is the research hypothesis for this study?

What are the mean and standard deviation for all 60 scores? (Code I used to generate this was:

aggregate(Table_9_10_Data$TESTSCORE, list(Table_9_10_Data$CLASS), FUN=mean)

aggregate(Table_9_10_Data$TESTSCORE, list(Table_9_10_Data$CLASS), FUN=sd)

What are SSB, SSW, and SSt? (I couldn’t get the tapply function to work. Instead I used the following code:

ANOVA <- aov(TESTSCORE~CLASS, data = Table_9_10_Data)

summary(ANOVA)

The <- sign makes a title of the lable left of it. So in the above case "ANOVA" is the title we give to the function to the right of the <-. Then we summon this title when we use the "summary" function.

Why are the degrees of freedom 3 and 56?

What is the F-ratio value?

What is the significance value (i.e., p-value) for this F-ratio?

Why is the MSW (Residuals) so relatively small?

What is your conclusion regarding the null hypothesis?

If the written test is designed to measure human performance knowledge, does the pattern of the means make sense? (Hint: Think about the typical human performance curriculum)

Why weren’t the Sophomores labeled S?

Answer 1

A One-Way ANOVA is used to compare means of three or more groups, requiring assumptions like normality and equal variances. The null hypothesis states all means are equal, while the alternative suggests at least one is different. The F-ratio, along with the p-value, is used to determine the statistical significance of the group mean differences.

Step-by-step explanation:

Understanding One-Way ANOVA

A One-Way ANOVA (analysis of variance) is used to compare the means of three or more independent groups to see if at least one group mean is statistically different from the others. To perform a One-Way ANOVA, several assumptions must be met, including the normal distribution of the populations, equal variances among the groups, and independent random sampling. The null hypothesis for a One-Way ANOVA states that all group means are equal, while the alternative hypothesis suggests that at least one group mean is different.

The F-ratio is the test statistic for a One-Way ANOVA. It is calculated by comparing the variance between group means (MSbetween or SSB) to the variance within the groups (MSwithin or SSW). SSt stands for the total sum of squares, which combines both SSB and SSW. Degrees of freedom for the F-ratio are calculated based on the number of groups (which explains the 3 df for between groups, as there might be four groups in this particular study) and the total number of observations minus the number of groups (which explains the 56 df for within groups).

The significance value, or p-value, indicates whether the F-ratio is statistically significant. A small MSW (Residuals) suggests that the scores within each group are relatively close to their group mean, indicating low variability within groups. Based on the p-value and the F-ratio, conclusions about the null hypothesis are drawn. The pattern of the means should be reviewed in the context of the typical human performance curriculum to determine if it makes sense.