This Part of Your Final Examination Is Take-Home, and As Such, You May Use Your Text And/Or

This part of your final examination is take-home, and as such, you may use your text, class notes, and/or handouts from the course website to assist you in answering the following questions. Read each of the questions carefully being sure to answer all parts fully to receive the maximum points possible.

You are to work independently on this exam.If you have questions, you are to discuss those with the instructor. By signing and dating this exam, you are indicating that you have adhered to the academic integrity of working independently on this exam.

Sign and Date

Dependent-Samples t Test

Using the SPSS© output from the Paired-Samples (Dependent) t Test, answer the following questions (where  = .05). In responding – be sure to use specifics – which includes reporting the specific values and indicators used to make your determinations.

Dr. Stats would like to see if there is a difference between the Pretest and the Posttest for her entire class. She does not have a prediction as to whether the performance will be higher or lower for the two sets of scores – she simply wants to determine if the class performed significantly different on the two test occasions.

1.(2 points) State (using symbols and words) the null hypothesis and the alternative hypothesis for the Dependent-Samples t Test.

H0:

Ha:

2.(1 point) Using the Table of Critical Values of Student’s t Distribution – what would the t critical value (tcrit) be for this Pretest / Posttest Dependent-Samples t-Test with  = .05.

3.(5 points)Using an alpha () level of .05, interpret the results from the Pretest / Posttest Dependent-Samples t Test:

3.a.Did you reject the null hypothesis in favor of the alternative hypothesis?

YESorNO(circle your answer selection)

3.b.Justify your answer, that is, how did you come to your decision? Make reference to any one of the three methods of determination. Be sure to include all applicable values for the methods that you choose.

3.c.If applicable, use one of the following formulas and determine/calculate the Effect Size for this scenario (show your work). If not applicable, briefly explain why.

or

3.d.Briefly discuss your findings (i.e., what do the results indicate or mean). Be sure to make reference to the group means and effect size (if applicable). Be sure to show all applicable values and symbols including the statistical strand for the results.

Independent-Samples t Test

Using the SPSS© output from an Independent Samples t Test, answer the following questions (where  = .05). In responding – be sure to use specifics – which includes reporting the specific values and indicators used to make your determination.

Dr. Kureous, a teacher at George Junior High, wants to determine if there is a significant difference between aMorning Class and anAfternoon Class on a Standardized Performance Test. He randomly selects 100 students from a school and then randomly assigns them to either the morning or afternoon class time for the study. He does not have a prediction as to whether one group will be better than the other – he simply wants to see if they differ significantly on their performance.

4.(1 point) For this study, the null hypothesis and the alternative hypothesis regarding the group means would be:

a.H0: 1 = 2Ha: 12

b.Ha: 1 = 2H0: 12

c.H0: M1 = M2Ha: M1M2

d.Ha: H0:

5.(1½ points) Has the assumption of independence been met for this data?

YESorNO(circle your answer selection)

Justify/explain your answer – that is, how did you come to your conclusion?

6.(2½ points) Has the assumption of normality been met for this data? Use an alpha () level of .001 looking at the Shapiro-Wilks test to justify your answer.

YESorNO(circle your answer selection)

Justify/explain your answer – that is, how did you come to your conclusion? (Hint: look at the SPSS printout). Be sure to show all applicable values and symbols.

7.(1 point) For this study, regarding the assumption of homogeneity of variance being met or not met and the justification of that conclusion:

a.Yes, assumption met – because p (.410)  (.05)

b.Yes, assumption met – because p (.002) <  (.05)

c.No, assumption not met – because p (.410)  (.05)

d.No, assumption not met – because p (.003) <  (.05)

8.(1½ points) After computing the test statistic (t-test) – complete the following tables for the Independent-Samples t-Test (Do not round – use the values from SPSS):

Mean

9.(3 points) Using an alpha () level of .05, interpret the results from the Independent-Samples t Test regarding the group means:

9.a.Did you reject the null hypothesis (regarding the group means) in favor of the alternative hypothesis based on the significance (p) level?

YESorNO(circle your answer selection)

9.b.Justify your answer, that is, how did you come to your decision?DO NOT make reference to the t critical value or the confidence intervals. Be sure to include all applicable values and symbols for this method.

9.c.If applicable, use the following formula and determine the Effect Size for this scenario (be sure to show your work). If not applicable, briefly explain why.

10.(2 points) What would you conclude about this study? In other words, who performed higher (how is this known) and was this significant or not at the .05 alpha level.Be sure to make reference to the group means (reporting the values) and effect size (if applicable). Also include the statistical strand for this study.

One-way Analysis of Variance

Using the SPSS© output from the One-way ANOVA Test, answer the following questions (where  = .05). In responding – be sure to use specifics – which includes reporting the specific values and indicators used to make your determinations.

A researcher is interested in determining if the format of instruction affects a student’s test score. She randomly assigns 25 students to a classroom using discussion as the format, 25 students to a classroom using lecture as the format, and 25 students to a control (no class) group. Students have been pre-screened and shown to be statistically equivalent in aptitude. At the end of the semester, students are given a standardized test to determine if any differences exist between the three groups’ performance.

11.(1½ points) What would the null hypothesis be for this study? Show/write the appropriate symbols and expression in words.

H0:

12.(1½ points) What would the alternative hypothesis be for this study? Show/write the appropriate symbols and expression in words.

Ha:

13.Prior to examining whether the group means differ; you need to test the underlying assumptions of the one-way analysis of variance.

13.a.(1½ points) Has the assumption of independence been met for this data? Indicate how you made your determination.

13.b.(2 points) Has the assumption of normality been met for this data, using an alpha level of .001? Indicate how you made your determination. Be sure to include all applicable values and symbols.

13.c.(1 point) Prior to examining whether the group means differ; you also need to test the assumption of homogeneity of variance. For this study, regarding the assumption of homogeneity of variance being met or not met and the justification of that conclusion:

a.Yes, assumption met – because p (.000) <  (.05)

b.Yes, assumption met – because p (.703) >  (.05)

c.No, assumption not met – because p (.000) <  (.05)

d.No, assumption not met – because p (.703) >  (.05)

14.(2 points) The next question that needs to be answered is whether all of the groups are the same in their average test performance based on their test scores using an alpha level of .05. If applicable (or indicate why not), use the Welch statistic. What is your conclusion (at this point) from this analysis? Indicate how you came to your conclusion. Be sure to include all applicable values and symbols.

15.(2 points) Using the following formula – calculate the measure of association (omega squared, 2) – and then briefly interpret (or illustrate) its meaning. Show your work.

16.(1 point) Write the statistical strand for this one-way ANOVA analysis.

17.(2 points) Assuming that you found a significant F, which pairs of groups differ? Indicate which post hoc procedure you used and why. Indicate your findings from the post hoc analysis. That is, how did you determine the pair to be significant or not (this must go beyond the * as an indication)? Be sure to discuss all unique pairwise comparisons.

18.(2 points) For each of the significant pairwise comparisons (be sure to indicate the pair), calculate and report the effect size using the following formula.

19.(3 points) Complete the three tables on the next page that present your statistical results from these analyses. Use the values reported in the SPSS output – you do not need to round.

Table 1

Means and Standard Deviations of Test Performance

Table 2

Analysis of Variance for Test Performance by Instructional Method

Table 3

Post Hoc Results for Test Performance by Instructional Method

Mean

*Significant at  = .05