Question

1. If the normality assumption is met, but the equal variance assumption is not met, what alternative analysis could be used in place of the traditional F test for a one-way ANOVA design?

a. Kruskal-Wallis test. b. Welch test. c. Independent t-test. d. Friedman test

2. Which one of the following would be considered a non-parametric alternative to a one-way between subjects ANOVA?

  a. Kruskal-Wallis test. b. Welch test. c. Independent t-test. d. Friedman test

3. As you know, most statistical analyses come with assumptions. Use of repeated measures ANOVA has an assumption that is referred to as the sphericity assumption. What is the null hypothesis that is being tested when the Mauchly Test of Sphericity is used?

a. the variances for the differences are all equal. b. the population means are all equal c. the sample variances are all equal

(4. - 5.) Individuals diagnosed with depression volunteered to participate in a study investigating the effect of type of treatment on depression. All participants were considered to be moderately depressed at the beginning of the study. Participants were randomly assigned to receive one of four treatments: anti-depressant (AD), in-person psychotherapy (PSY), web-based therapy (WB), or placebo drug (PL). After a designated treatment period, depression level was measured using a standard depression measure (lower scores indicate less depression).

4. Being diligent, the researcher conducted tests of the assumptions prior to conducting the main analysis. The results of these tests are below. Based on the results of these tests, does it seem reasonable that the researcher moved forward with the analysis using a traditional F test for a one-way ANOVA?

Levene's Homogeneity Test

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data : depscore and treatment   

statistic : 1.11828

num df     : 3   

denum df   : 16   

p.value    : 0.3709916   

Result     : Variances are homogeneous.

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Shapiro-Wilk Normality Test

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data : depscore and treatment

Level Statistic p.value   Normality

1    AD 0.9899775 0.9796155 Not reject

2    PL 0.9733112 0.8960491 Not reject

3   PSY 0.9519245 0.7509285 Not reject

4    WB 0.9736478 0.8981076 Not reject

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a. No, the Levene test rejects the null hypothesis being tested and the Shapiro-Wilk test fails to reject; the normality assumption is met, but the homogeneity of variance assumption is not met. b. Yes, both of the tests presented failed to reject the null hypothesis being tested, suggesting that both the normality and homogeneity of variance assumptions are met. c. Yes, both of the tests presented reject the null hypothesis being tested suggesting that both the normality and homogeneity of variance assumptions are met. d. No, the Levene test rejects the null hypothesis being tested and the Shapiro-Wilk test fails to reject; the normality assumption is not met, but the homogeneity of variance assumption is met.

5. The results from the analysis of data for this study is presented below. Based on using a significance level of .05, was it appropriate for the researcher to conduct the post hoc tests that are presented?

            Df Sum Sq Mean Sq F value Pr(>F)

treatment    3 343.0   114.3   4.949 0.0128 *

Residuals   16 369.6    23.1                

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Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Posthoc multiple comparisons of means : Tukey HSD

    95% family-wise confidence level

$treatment

diff    l wr.ci upr.ci pval   

PL-AD   7.2 -1.496747 15.896747 0.1239   

PSY-AD 6.2 -2.496747 14.896747 0.2150   

WB-AD 11.6 2.903253 20.296747 0.0074 **

PSY-PL -1.0 -9.696747 7.696747 0.9872   

WB-PL   4.4 -4.296747 13.096747 0.4899   

WB-PSY 5.4 -3.296747 14.096747 0.3197   

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

a. Yes, it was appropriate, the overall test was not statistically significant. b. No, it was not appropriate, the overall test was statistically significant. c. Yes, it was appropriate, the overall test was statistically significant. d. No, it was not appropriate, the overall test was not statistically significant.

Answer 1

1.
If the equal variance assumption is not met, we use
b. Welch test

2.
A non-parametric alternative to a one-way between subjects ANOVA is,
a. Kruskal-Wallis test.

3.
The null hypothesis for Mauchly Test of Sphericity is,
a. the variances for the differences are all equal.

4.
p-value for Levene's Homogeneity Test (0.3709916) is greater than 0.05 so we fail to reject the null hypothesis
We also fail to reject null hypothesis for Shapiro-Wilk Normality Test.

b. Yes, both of the tests presented failed to reject the null hypothesis being tested, suggesting that both the normality and homogeneity of variance assumptions are met.

5.
P-value for F test (Anova test) is 0.0128 which is less than 0.05 significance levels.
Thus at least one of the groups have significant mean differences and post-hocs test should be conducted.

c. Yes, it was appropriate, the overall test was statistically significant.