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COURSE: JUST 3900 Tegrity Presentation Developed By: Ethan Cooper

COURSE: JUST 3900 Tegrity Presentation Developed By: Ethan Cooper. Final Exam Review. Chapter 10: Independent Measures t -test. Question 1: One sample from an independent-measures study has n = 5 with SS = 48. The other sample has n = 9 and SS = 32.

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COURSE: JUST 3900 Tegrity Presentation Developed By: Ethan Cooper

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  1. COURSE: JUST 3900 Tegrity Presentation Developed By: Ethan Cooper Final Exam Review

  2. Chapter 10: Independent Measures t-test • Question 1: One sample from an independent-measures study has n = 5 with SS = 48. The other sample has n= 9 and SS = 32. • Compute the pooled variance for the sample. • Compute the estimated standard error for the mean difference.

  3. Chapter 10: Independent Measures t-test • Question 1 Answer:

  4. Chapter 10: Independent Measures t-test • Question 2: What is the null hypothesis when using an independent measures t-test?

  5. Chapter 10: Independent Measures t-test • Question 2 Answer: • = 0

  6. Chapter 10: Independent Measures t-test • Question 3: An independent measures t-test results in a t-statistic of t = 3.53. Each sample consists of n = 8. Compute the effect size using r2?

  7. Chapter 10: Independent Measures t-test • Question 3 Answer: • This is a large effect.

  8. Chapter 10: Independent Measures t-test • Question 4: A researcher is conducting an independent measures t-test (two-tail) with two samples of n = 8. M1 = 3 and M2 = 6. The estimated standard error is s(M1 – M2) = 0.85. Is there a significant treatment effect? (α = 0.05)

  9. Chapter 10: Independent Measures t-test • Question 4 Answer: • Critical t = ±2.131 • -3.53 < -2.131, therefore we reject the null. There is a significant effect.

  10. Chapter 10: Independent Measures t-test • Question 5: The boundaries for a confidence interval are at t = ± 1.753. The sample sizes are n = 7 and n = 10. How confident are we that the unknown mean difference falls in this interval?

  11. Chapter 10: Independent Measures t-test • Question 5 Answer: • Find df. • df= 9 + 6 = 15 • Use the t distribution to find the alpha level where t = 1.753 and df = 15 intersect. • α = 0.10 • An alpha of 0.10 corresponds to 10% in the tails, leaving 90% in the body. • 100 – 10 = 90 • Therefore, we are 90% confident that our mean difference falls in this interval.

  12. Chapter 10: Independent Measures t-test • Question 6: A researcher wants to conduct an independent measures t-test, but first, he wants to make sure the homogeneity assumption is not violated. Each sample has n = 8 and the sum of squares for each are SS = 16 and SS = 24. Use an F-Max test to see if the assumption is violated (α = 0.05).

  13. Chapter 10: Independent Measures t-test • Question 6 Answer: • Find the variances. • Find the critical F-Max statistic • F-Maxcrit = 4.99 • Find F-Max • 1.50 < 4.99, therefore the assumption of homogeneity is not violated.

  14. Chapter 12: ANOVA • Question 1: Which of the following F-ratios is most likely to reject the null? • F = 1.25 • F = 1.00 • F = 2.75 • F = 4.50 • None of the Above

  15. Chapter 12: ANOVA • Question 1 Answer: • D) F = 4.50 • F values closer to 1.00 are less likely to fall in the critical region and thus, are less likely to reject the null.

  16. Chapter 12: ANOVA • Question 2: Which of the following are possible alternative hypotheses for ANOVA? • H1: μ1 ≠ μ2 = μ3 • H1: μ1 ≠ μ2 ≠ μ3 • H1: μ1 = μ2 ≠ μ3 • All of the above • None of the Above

  17. Chapter 12: ANOVA • Question 2 Answer: • D) All of the above • The alternative hypothesis for ANOVA states that there is a difference between our population means, but it does not identify which means are different.

  18. Chapter 12: ANOVA • Question 3: What is the advantage of using ANOVA over an independent measures t-test?

  19. Chapter 12: ANOVA • Question 3 Answer: • ANOVA can be used when comparing more than two populations without increasing the risk of Type I error.

  20. Chapter 12: ANOVA • Question 4: What accounts for between treatments variance?

  21. Chapter 12: ANOVA • Question 4 Answer: • Between treatments variance (MSbetween) is caused by both treatment effects and random, unsystematic error.

  22. Chapter 12: ANOVA • Question 5: Compute effect size (η2) for a data set with SSbetween = 70 and SSwithin = 46.

  23. Chapter 12: ANOVA • Question 5 Answer:

  24. Chapter 12: ANOVA • Question 6: A researcher is using Tukey’s HSD to find which treatments (k = 3 treatments) in his study had an effect. MSwithin = 3.83 and n = 5. The mean difference between treatments A and B is – 4. Is this a significant mean difference? (α = 0.05)

  25. Chapter 12: ANOVA • Question 6 Answer: • Find q. • q = 3.77 • Find HSD. • Compare HSD to . • 4 > 3.30, therefore treatment A is significantly different from treatment B.

  26. Chapter 12: ANOVA • Question 7: Which of the following is not an assumption required for the independent-measures ANOVA? • The observations within each sample must be independent. • The samples must all be the same size. • The populations from which the samples are selected must be normal. • The populations from which the samples are selected must have equal variances (homogeneity of variance). • All of the above are required assumptions.

  27. Chapter 12: ANOVA • Question 7 Answer: • B) The samples must all be the same size. • ANOVA requires the same assumption as independent measures t tests: • The observations must be independent. • The populations variances must all be the same. • The populations must be normally distributed.

  28. Chapter 12: ANOVA • Question 8: F = n = 16 for each sample k = 3 treatments

  29. Chapter 12: ANOVA • Question 8 Answer: n = 16 for each sample k = 3 treatments F = 10/4 = 2.50

  30. Chapter 17: Chi-Square • Question 1: In what situations would we use nonparametric tests as substitutes for parametric tests?

  31. Chapter 17: Chi-Square • Question 1 Answer: • The data do not meet the assumptions needed for a standard parametric test. • The data consist of nominal or ordinal measurements, so that it is impossible to compute standard descriptive statistics such as the mean and standard deviation.

  32. Chapter 17: Chi-Square • Question 2: To investigate the phenomenon of “home-team advantage,” a researcher recorded the outcomes from 64 college football games on one weekend in October. Of the 64 games, 42 were won by home teams. Does this result provided enough evidence that home teams win significantly more than would be expected by chance? Assume winning and losing are equally likely events if there is no home-team advantage. Use α = 0.05

  33. Chapter 17: Chi-Square • Question 2 Answer: • Step 1: State the hypothesis • H0: There is no home-team advantage. • H1: There is a home-team advantage. f0

  34. Chapter 17: Chi-Square • Question 2 Answer: • Step 2: Locate the critical region • Find df. • df = C – 1 = 2 – 1 = 1 • Use df and alpha level (α = 0.05) to find the critical Χ2 value for the test. • Χ2crit = 3.84

  35. Chapter 17: Chi-Square • Question 2 Answer: • Step 3: Calculate the Chi-Square Statistic • Identify proportions required to compute expected frequencies (fe). • The null specifies the proportion for each cell. With a sample of 64 games, the expected frequencies for each category (wins/losses) are equal in proportion (50%). • Calculate the expected frequencies with proportions from H0. • fe = pn = (0.50) * (64) = 32 games in each category • Calculate the Chi-Square Statistic f0 fe

  36. Chapter 17: Chi-Square • Question 2 Answer: • Step 3: Calculate the Chi-Square Statistic

  37. Chapter 17: Chi-Square • Question 2 Answer: • Step 4: Make a Decision • If X2 ≤ 3.84, fail to reject H0 • If X2> 3.84, reject H0 • 6.25 > 3.84, thus, we reject H0, which means home-team advantage does effect the outcome of college football games.

  38. Chapter 17: Chi-Square • Question 3: A researcher obtains a sample of 200 high school students. The students are given a description of a psychological research study and asked whether they would volunteer to participate. The researcher also obtains an IQ score for each student and classifies the students into high, medium, and low IQ groups. Do the following data indicate a significant relationship between IQ and volunteering? (α = 0.05)

  39. Chapter 17: Chi-Square 150 50 50 50 100

  40. Chapter 17: Chi-Square • Question 3 Answer: • Step 1: State the hypothesis • H0: There is no relationship between volunteering and IQ. • H1: There is a relationship between volunteering and IQ.

  41. Chapter 17: Chi-Square • Question 3 Answer: • Step 2: Locate the critical region. • Find df. • df = (R -1)*(C – 1) = (2 – 1)*(3 – 1) = (1)*(2) = 2 • Use df (2) and alpha level (0.05) to find the critical X2 value. • X2crit = 5.99

  42. Chapter 17: Chi-Square • Question 3 Answer: • Step 3: Calculate the Chi-Square Statistic for Independence • Compute expected frequencies where 150 50 50 100 50

  43. Chapter 17: Chi-Square • Question 3 Answer: • Step 3: Calculate the Chi-Square Statistic for Independence • 4.75

  44. Chapter 17: Chi-Square • Question 3 Answer: • Step 4: Make a Decision • If X2 ≤ 5.99, fail to reject H0 • If X2 > 5.99, reject H0 • 4.75 > 5.99, thus, we fail to reject H0, which means there is not a significant relationship between volunteering and IQ.

  45. Chapter 17: Chi-Square • Question 4: A researcher completes a chi-square test for independence and obtains X2 = 6.2 for a sample of n = 40 participants. • If the frequency data formed a 2 X 2 matrix, what is the phi-coefficient for the test? • If the frequency data formed a 3 X 3 matrix, what is Cramer’s V for the test?

  46. Chapter 17: Chi-Square • Question 4 Answer:

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