Use the Kruskal-Wallis test and perform these steps. a....

Use the Kruskal-Wallis test and perform these steps. a. State the hypotheses and identify the claim. b. Find the critical value. c. Compute the test value. d. Make the decision. e. Summarize the results. Use the traditional method of hypothesis testing unless otherwise specified. Speaking Confidence Fear of public speaking is a common problem for many individuals. A researcher wishes to see if educating individuals on the aspects of public speaking will help people be more confident when they speak in public. She designs three programs for individuals to complete. Group A studies the aspects of writing a good speech. Group $\mathrm{B}$ is given instruction on delivering a speech. Group $\mathrm{C}$ is given practice and evaluation sessions on presenting a speech. Then each group is given a questionnaire on selfconfidence. The scores are shown. At $\alpha=0.05$, is there a difference in the scores on the tests? $$ \begin{array}{ccc} \text { Group A } & \text { Group B } & \text { Group C } \\ \hline 22 & 18 & 16 \\ 25 & 24 & 17 \\ 27 & 25 & 19 \\ 26 & 27 & 23 \\ 33 & 29 & 18 \\ 35 & 31 & 31 \\ 30 & 17 & 15 \\ 36 & 15 & 36 \end{array} $$

Use the Kruskal-Wallis test and perform these steps.
a. State the hypotheses and identify the claim.
b. Find the critical value.
c. Compute the test value.
d. Make the decision.
e. Summarize the results.
Use the traditional method of hypothesis testing unless otherwise specified.
Speaking Confidence Fear of public speaking is a common problem for many individuals. A researcher wishes to see if educating individuals on the aspects of public speaking will help people be more confident when they speak in public. She designs three programs for individuals to complete. Group A studies the aspects of writing a good speech. Group $\mathrm{B}$ is given instruction on delivering a speech. Group $\mathrm{C}$ is given practice and evaluation sessions on presenting a speech. Then each group is given a questionnaire on selfconfidence. The scores are shown. At $\alpha=0.05$, is there a difference in the scores on the tests?
$$
\begin{array}{ccc}
\text { Group A } & \text { Group B } & \text { Group C } \\
\hline 22 & 18 & 16 \\
25 & 24 & 17 \\
27 & 25 & 19 \\
26 & 27 & 23 \\
33 & 29 & 18 \\
35 & 31 & 31 \\
30 & 17 & 15 \\
36 & 15 & 36
\end{array}
$$

Key Concepts

Decision Making

Decision making in hypothesis testing involves comparing the calculated H statistic to the critical value. If H exceeds the critical value, the null hypothesis is rejected; otherwise, it is not rejected. This step ensures that the evidence is strong enough to support a claim of significant differences among the groups.

Conclusion Interpretation

The final step involves summarizing the results in context. This means clearly reporting whether the analysis provided sufficient evidence to conclude that differences exist among the groups, and discussing what these differences might imply in the practical setting of the study.

Test Statistic Calculation

The test statistic, often denoted by H, is calculated by first ranking all observations across groups, then assessing the differences in rank sums among the groups. This computation reflects how much the groups' rankings diverge from what would be expected if they came from the same distribution.

Kruskal-Wallis Test

The Kruskal-Wallis test is a nonparametric method used to compare three or more independent groups to assess whether their population distributions differ. Instead of relying on the normality assumption, it uses ranked data, making it suitable for ordinal data or when the assumptions required for ANOVA are not met.

Hypothesis Formulation

In the context of the Kruskal-Wallis test, hypothesis formulation involves establishing a null hypothesis that all groups have the same distribution (or median) and an alternative hypothesis that at least one group’s distribution differs from the others. This sets the foundation for a controlled statistical decision-making process.

Critical Value Determination

The critical value is determined based on the chosen level of significance (alpha) and the degrees of freedom, calculated as the number of groups minus one. It is typically obtained from a chi-square distribution table and serves as the benchmark against which the test statistic is compared.

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