1. If the normality assumption is met, but the equal varianceassumption is not met, what alternative analysis could be used inplace 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 anon-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 referredto as the sphericity assumption. What is the null hypothesis thatis being tested when the Mauchly Test of Sphericity is used?

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

(4. - 5.) Individuals diagnosed with depression volunteered toparticipate in a study investigating the effect of type oftreatment on depression. All participants were considered to bemoderately depressed at the beginning of the study. Participantswere randomly assigned to receive one of four treatments:anti-depressant (AD), in-person psychotherapy (PSY), web-basedtherapy (WB), or placebo drug (PL). After a designated treatmentperiod, depression level was measured using a standard depressionmeasure (lower scores indicate less depression).

4. Being diligent, the researcher conducted tests of theassumptions prior to conducting the main analysis. The results ofthese tests are below. Based on the results of these tests, does itseem reasonable that the researcher moved forward with the analysisusing 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 testedand the Shapiro-Wilk test fails to reject; the normality assumptionis met, but the homogeneity of variance assumption is not met. b.Yes, both of the tests presented failed to reject the nullhypothesis being tested, suggesting that both the normality andhomogeneity of variance assumptions are met. c. Yes, both of thetests presented reject the null hypothesis being tested suggestingthat both the normality and homogeneity of variance assumptions aremet. d. No, the Levene test rejects the null hypothesis beingtested and the Shapiro-Wilk test fails to reject; the normalityassumption is not met, but the homogeneity of variance assumptionis met.

5. The results from the analysis of data for this study ispresented below. Based on using a significance level of .05, was itappropriate for the researcher to conduct the post hoc tests thatare presented?

           Df Sum Sq Mean Sq Fvalue 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 15.8967470.1239   

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 13.0967470.4899   

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 notstatistically significant. b. No, it was not appropriate, theoverall test was statistically significant. c. Yes, it wasappropriate, the overall test was statistically significant. d. No,it was not appropriate, the overall test was not statisticallysignificant.