- True or False?: In rejecting an ANOVA null hypothesis, you are saying there is a significant difference between all groups.
- List methods to compare the "locations" of
multiple
- Why are
*post hoc*comparisons unwarranted when an ANOVA is insignificant? - How many
*post hoc*comparisons are possible when testing 3 group means? 4 groups? 5 groups? - Why does the LSD
*t*test have*N*-*k*degrees of freedom (and not*n*_{1}+*n*_{2}- 2)? - List three conditions for valid statistical inference.
- List the distributional and sampling assumptions for ANOVA.
- Which are more important, validity assumptions or distributional assumptions? Why?
- Identify two ways to assess the equal variance assumption.
- State the null and alternative hypotheses tested by Levene's procedure.
- These are two conditions required by ANOVA but not by the Kruskal-Wallis test.
- State the null and alternative hypotheses tested by the Kruskal-Wallis procedure.
- List three ways to compare locations when groups variances differ.
**Vocabulary words**:*Post hoc*comparison; Family of test; Family-wise error rate; LSD (the procedure, not the drug); Bonferroni; Standard error of the mean difference, Validity assumptions, Distributional assumptions, Homoscedasticity, Heteroscedasticity, Levene's test, Non-parametric test, Kruskal-Wallis test

**13.1 ** * Weight gain and junk food*. Last week's analysis of
the data set

Source SS df MS F

Between 46.30 2 23.15 29.69

Within 9.37 12 .78

(A)Conduct post hoc comparison using the least square difference method. It is OK to assume homoscedasticity. [For each comparison,se_{mean dif}= (0.780 * (1/5 + 1/5)) = 0.5586]

(B)Incorporate Bonferroni's adjustment into each of the post hoc comparisons.

(C)Download the data set deermice.sav (right-click > Save as) and replicate the analyses in SPSS (Analyze > Comparison of Means > One-way ANOVA > PostHoc).

(D)ANOVA addresses random error only. We are also concerned about bias. List the three types of systematic errors (biases) that may effect statistical analyses.

(E)In addition to the validity assumptions, ANOVA has distributional and sampling assumptions. Name these.

(F)Test the groups for unequal variance using Levene's output from SPSS. (Click the Options button and check thehomogeneity of variancebox.) Show all hypothesis testing steps.

(G)Conduct a Kruskal-Wallis test with SPSS by clickingAnalyze > Non-Parametric Tests >. The test variable iskIndependent SamplesWTGAINand the group variable is GROUP. You must define the range of the independent variable with the Define button (minimum is 1, maximum is 3). Under the null hypothesis, the Kruskal-Wallis statistic has a chi-squared distribution withk- 1 degrees of freedom. Interpret your results.

**13.2 ****Fever reduction**.**
** Analysis of this data in the prior unit revealed a significant difference in fever
reduction between aspirin (_{1}
= 1.50 ^{o}F), aspirin
and acetaminophen (_{2}
= 0.36 ^{o}F), and acetaminophen
alone (_{3} = 0.08
^{o}F). Each group had 5 observations.
The ANOVA *F*_{stat} was 6.52 with 2 and 12 df (*P* = 0.012).
The mean square within (*s*^{2}_{w }) was 0.4338.
Conduct post hoc comparisons of the results using Bonferroni's method. Show all
work and *interpret* your results.

**13.3 ** * The problem of multiple comparisons. * When two or more events are

(A)What is the probability of making 3 correct independent decisions in a row? What is the probability of getting at least 1 of the three wrong? [Note: Pr(at least one wrong) = 1 - Pr(all correct).]

(B)What is the probability of making 10 correct independent decisions in a row? What is the probability of getting at least 1 wrong out of the 10?

(C)What is the probability of making 20 correct independent decisions in a row. What is the probability of making at least one incorrect decisions out of the 20?

**13.****4 *** Bronchial reactivity*. An
exercise in the prior chapter looked at bronchial reactivity in asthmatics
following exposure to noxious gases. The analysis revealed
significant differences in airway reactivity. Summary statistics and the ANOVA
results are shown below. Now conduct post hoc comparisons using the LSD method (bronch-react.sav).
In each instance, state the null hypothesis, test statistic, df, and

**13.5 *** Sense of coherence. *
Summary statistics and an ANOVA table for the "sense of coherence"
data (soc.sav) introduced in the prior chapter are shown below. Conduct post-hoc
comparisons using a Bonferroni adjustment. Summarize the results.

**13.6 ****Smoking and birth weight**.** **This
data set (smoking-moms.sav) was
introduced in the prior chapter. Descriptive statistics and the ANOVA table for
the problem are reported below. Conduct post hoc comparisons of all the groups
with the LSD method. (There are 6 possible post-hoc comparisons.) State the null
hypothesis in each instance, report the *t *statistics, their *df*,
and *P *value. Interpret each test.

**13.7 *** Maternal adaptation * (Howell, 1995,
pp. 302 - 304; mat-role.sav).

**13.8 - 13.20 **Reserved for future use.

**13.21 ****Testosterone levels in roosters (visual
inspection of boxplots)**. * *A
zoologist wanted to determine if testosterone in three strains of mature roosters
differed (Hampton, 1994, p. 147). Data are:

Strain A:439568134897229329

Strain B:103115 098126115120

Strain C:107 099102105 089110Here are side-by-side boxplots of the data:

Based on this evidence, would you perform ANOVA? Explain your reasoning.

**13.22 *** Testosterone levels in roosters (K-W procedure). *Download
rooster.sav (right-click > Save as).
Conduct a Kruskal-Wallis procedure on the data with the help of SPSS. List the
hypotheses (null and
alternative), test statistic, and its df, and your conclusion.

**13.23 *** Smoking and birth weight (assess homoscedasticity). *Return to the data
discussed in Exercise 13.6 (smoking-moms.sav). A colleague suggests you have violated the
equal variance assumption. Rebut this criticism by interpreting the
relevant information n the descriptive statistics table that appears as part of
Exercise 13.6.

**13.24**. ** Smoking and birth weight (Levene's). **Support
the equal variance claim you made in Exercise 13.23 with Levene's procedure. List
the null and alternative
hypothesis, the test statistic and its dfs, and your conclusion. (Use SPSS
for computations smoking-moms.sav.)

**13.25. **** Smoking and birth weight (K-W). ** To appease your critic, you conduct a
non-parametric test (even though it is not required). Conduct a K-W procedure,
and compare its results to those achieved by one-way ANOVA.

Key to Odd Numbered Exercises Key Even Numbered Exercises (may not be posted)