### Null hypothesis

1.Briefly explain what rejecting the following null hypothesis would tell us:

H0:µ1=µ2=µ3=…=µJ(1 point)

2. Write the correct alternative hypothesis associated with this null hypothesis. (1 point)

3.Suppose a friend of yours has found a statistically significant omnibus ANOVA F test indicating there are mean differences on happiness among the 4 different age groups in his study. Consequently, he conducts independent samples t-tests to determine which specific age groups differed.

3.Suppose a friend of yours has found a statistically significant omnibus ANOVA F test indicating there are mean differences on happiness among the 4 different age groups in his study. Consequently, he conducts independent samples t-tests to determine which specific age groups differed.

a)What is the probability of making at least one type 1 error if your friend runs independent samples t-tests on all possible pairs of means, assuming he uses an alpha=.05 per t-test? (Show your work) (1 point)

b) What would be a better alternative to conducting independent samples t-tests in this situation and why? (2 points)

4.A researcher conducts two studies both comparing statistics anxiety scores for three groups of graduate students: statistics majors, psychology majors, and sociology majors. Descriptive statistics from the two studies are presented below. Possible scores on the statistics anxiety scale range from 20 to 100 points. Both studies were based on a total of 45 participants, with 15 participants in each of the 3 groups.

Study 1:

Statistics Psychology Sociology

Study 2:

Statistics Psychology Sociology

Statistics Psychology Sociology

a) If oneway ANOVAs were conducted on the two studies, what aspects of the ANOVA would remain the same and what aspects would differ between the two ANOVAs and why? (3 points)

b) For Study 1 compute the sums of squares between. (Show your work) (1 point)

c) For Study 1 compute the sums of squares within. (Show your work) (1 point)

d) For study 1 compute the effect size based on ?2 for this study and indicate if this represents a small, medium,or large effect size. (1 point)

5. Use the descriptive statistics and partial ANOVA summary table provided below to answer the questions below regarding whether or not first year teachers’perceptions of their student teaching experiences differ according to their teaching area, i.e., secondary, elementary, or special education.

5. Use the descriptive statistics and partial ANOVA summary table provided below to answer the questions below regarding whether or not first year teachers’perceptions of their student teaching experiences differ according to their teaching area, i.e., secondary, elementary, or special education.

Descriptives

studtch perceptions of student teaching experiences

N Mean Std. Deviation

N Mean Std. Deviation

1.00 secondary 179 5.4637 1.78584

2.00 elementary 159 5.7788 1.54895

3.00 special ed 27 5.3642 1.82576

Total 365 5.5936 1.69301

2.00 elementary 159 5.7788 1.54895

3.00 special ed 27 5.3642 1.82576

Total 365 5.5936 1.69301

Test of Homogeneity of Variances

studtch perceptions of student teaching experiences

Levene Statistic Sig.

1.744 .176

Levene Statistic Sig.

1.744 .176

ANOVA

studtch perceptions of student teaching experiences

Sum of Squares df Mean Square F

Between Groups (1)_____ (3)_____ 4.949 (7)_____

Within Groups 1033.433 (4)_____ (6)_____

Total (2)_____ (5)_____

Sum of Squares df Mean Square F

Between Groups (1)_____ (3)_____ 4.949 (7)_____

Within Groups 1033.433 (4)_____ (6)_____

Total (2)_____ (5)_____

a) State the null and alternative hypotheses tested by this ANOVA. (1 point)

b) Find the critical value at alpha = .05. (1 point)

c) Complete the 7 missing pieces of information in the ANOVA summary table (Show your work). (3 1/2 points)

d) State your statistical decision. (1 point)

e) Draw your conclusion. (1 point)

f) If one of the questions of interest was whether or not special education teachers had less positive student teaching experiences than either elementary or secondary education teachers, indicate the contrast coefficients you would use to answer this question.

g) Use the ANOVA score model to determine the effect of being an elementary educationrespondent. (This is a computed number so show your work) (1 point)

h) For an elementary education respondent with an observed score of 3, what is the “error” component in their score? (This is a computed number. Show your work) (1 point)

i) Briefly explain what the “error” identified in h) might represent. (1 point)

6. In another analysis from the same study of first year teachers,perceived teaching skills were compared across the three teaching areas.

Using the results of the Tukey test below, which groups did and did not differ and in which direction? i.e., who seemed to feel their teaching skills were relatively stronger? Weaker? (1 point)

Tukey’s Studentized Range (HSD) Test for tchskill

NOTE: This test controls the Type I experimentwise error rate.

Alpha 0.05

Error Degrees of Freedom 574

Error Mean Square 1.28185

Critical Value of Studentized Range 3.32313

Error Degrees of Freedom 574

Error Mean Square 1.28185

Critical Value of Studentized Range 3.32313

Comparisons significant at the 0.05 level are indicated by ***.

Difference

teaching Between Simultaneous 95%

Comparison Means Confidence Limits

teaching Between Simultaneous 95%

Comparison Means Confidence Limits

elementary – secondary 0.39011 0.15818 0.62204 ***

elementary – special ed 0.48073 0.03946 0.92200 ***

secondary – elementary -0.39011 -0.62204 -0.15818 ***

secondary – special ed 0.09062 -0.34328 0.52453

specialed – elementary -0.48073 -0.92200 -0.03946 ***

specialed – secondary -0.09062 -0.52453 0.34328

elementary – special ed 0.48073 0.03946 0.92200 ***

secondary – elementary -0.39011 -0.62204 -0.15818 ***

secondary – special ed 0.09062 -0.34328 0.52453

specialed – elementary -0.48073 -0.92200 -0.03946 ***

specialed – secondary -0.09062 -0.52453 0.34328

7. On a different ANOVA, assume you have examined Levene’s test and found it to be statistically significant. In addition, you note that the sample sizes of several groups are quite different, and that the largest group has the smallest variance of all groups in the analysis. You wish to conduct the ANOVA using an alpha of .05.

a) What assumption appears to be violated in this situation? (1 point)

b) In this situation, what is the nominal value of alpha for the ANOVA? (1 point)

c) In this situation, would the actual value of alpha for the ANOVA tend to be larger or smaller than the nominal alpha you gave in b)? Explain your answer. (1 point)