《商务统计学概论》（英文版） CHAPTER 14 Nonparametric methods

CHAPTER 14 Nonparametric methods to accompany Introduction to business statistics fourth edition, by ronald m. Weiers Presentation by priscilla Chaffe -Stengel Donald n. stengel o 2002 The Wadsworth Group

CHAPTER 14: Nonparametric Methods to accompany Introduction to Business Statistics fourth edition, by Ronald M. Weiers Presentation by Priscilla Chaffe-Stengel Donald N. Stengel © 2002 The Wadsworth Group

l Chapter 14- Learning objectives Differentiate between nonparametric and parametric hypothesis tests Determine when a nonparametric test should be used instead of its parametric counterpart ppropriately apply each of the nonparametric methods introduced C 2002 The Wadsworth Group

Chapter 14 - Learning Objectives • Differentiate between nonparametric and parametric hypothesis tests. • Determine when a nonparametric test should be used instead of its parametric counterpart. • Appropriately apply each of the nonparametric methods introduced. © 2002 The Wadsworth Group

l Chapter 14 Key terms Nonparametric tests Wilcoxon signed friedman test rank test. randomized block One sample design Paired samples · Sign test, paired Wilcoxon rank sum samples test, two independent Runs test for samples randomness ° Kruskal- Wallis test,· Lilliefors test for three or more normality independent samples C 2002 The Wadsworth Group

Chapter 14 Key Terms Nonparametric tests • Wilcoxon signed rank test: – One sample – Paired samples • Wilcoxon rank sum test, two independent samples • Kruskal-Wallis Test, three or more independent samples • Friedman test, randomized block design • Sign Test, paired samples • Runs test for randomness • Lilliefors test for normality © 2002 The Wadsworth Group

l Nonparametric Tests Advantages: Disadvantages: Fewer assumptions Sample data usea less about the population efficientl > Shape Power of nonparametric >>Variance analysis lower Valid for small samples Places greater reliance Defined over a range of on statistical tables if computer statistical variables nominal and ordinal scales included package or spreadsheet not being used Calculations simple C 2002 The Wadsworth Group

Nonparametric Tests • Advantages: – Fewer assumptions about the population »Shape »Variance – Valid for small samples – Defined over a range of variables, nominal and ordinal scales included – Calculations simple • Disadvantages: – Sample data used less efficiently – Power of nonparametric analysis lower – Places greater reliance on statistical tables if computer statistical package or spreadsheet not being used © 2002 The Wadsworth Group

l Wilcoxon Signed rank Test One sample Requirements: Variable -Continuous data Scale- Interval or ratio scale of measurement The Research Question(H1): Test the value of a single population median, m,>,<mo Critical value/Decision rule: w, Wilcoxon signed rank test C 2002 The Wadsworth Group

Wilcoxon Signed Rank Test, One Sample • Requirements: – Variable - Continuous data – Scale - Interval or ratio scale of measurement • The Research Question (H1 ): Test the value of a single population median, m {, >, <} m0 • Critical Value/Decision Rule: W, Wilcoxon signed rank test © 2002 The Wadsworth Group

I An example Problem 14.8: According to the director of a county tourist bureau, there is a median of 10 hours of sunshine per day during the summer months. For a random sample of 20 days during the past three summers, the number of hours of sunshine has been recorded below. use the 0.05 level in evaluating the director s claim 89810977 97798119 107811812 C 2002 The Wadsworth Group

An Example • Problem 14.8: According to the director of a county tourist bureau, there is a median of 10 hours of sunshine per day during the summer months. For a random sample of 20 days during the past three summers, the number of hours of sunshine has been recorded below. Use the 0.05 level in evaluating the director’s claim. 8 9 8 10 9 7 7 9 7 7 9 8 11 9 10 7 8 11 8 12 © 2002 The Wadsworth Group

团 An example, continued hrs d d, hrs d d There are 8-22 7 with rank 1 8 1,23,45,6,7 8-22 11+11 average rank= 4 1000 6 with rank 2 9-11 1000 8,9,10,11,12,13 7-33 7-33 average rank= 10.5 7-33 5 with rank 3 14,15,16,1718 7-33 8-22 average rank =16 7-33 2+22 C 2002 The Wadsworth Group

An Example, continued hrs. di|di| hrs. di|di| 8 –2 2 9 –1 1 9 –1 1 8 –2 2 8 –2 2 11 +1 1 10 0 0 9 –1 1 9 –1 1 10 0 0 7 –3 3 7 –3 3 7 –3 3 8 –2 2 9 –1 1 11 +1 1 7 –3 3 8 –2 2 7 –3 3 12 +2 2 There are: 7 with rank 1 1, 2, 3, 4, 5, 6, 7 average rank = 4 6 with rank 2 8, 9, 10, 11, 12, 13 average rank = 10.5 5 with rank 3 14, 15, 16, 17, 18 average rank = 16 © 2002 The Wadsworth Group

团 An example, continued rsdd rank r+ r hrs. d d Rank R+ r 8-2210.5-10.5 4 9-114 4 8-2210.5 10.5 8-2210.5-10.5 11+114 4 1000 114 4 9-114 1000 7-3316 16 7-3316 16 7-3316 16 8-2210.5 10.5 9-114 4 11+114 4 7-3316 16 8-2210.5 10.5 7-3316 16 2+2210.510.5 So,ΣR+=185,∑R-=1525 C 2002 The Wadsworth Group

An Example, continued hrs. di|di| Rank R+ R– hrs. di|di| Rank R+ R– 8 –2 2 10.5 - 10.5 9 –1 1 4 - 4 9 –1 1 4 - 4 8 –2 2 10.5 - 10.5 8 –2 2 10.5 - 10.5 11 +1 1 4 4 - 10 0 0 - - - 9 –1 1 4 - 4 9 –1 1 4 - 4 10 0 0 - - - 7 –3 3 16 - 16 7 –3 3 16 - 16 7 –3 3 16 - 16 8 –2 2 10.5 - 10.5 9 –1 1 4 - 4 11 +1 1 4 4 - 7 –3 3 16 - 16 8 –2 2 10.5 - 10.5 7 –3 3 16 - 16 12 +2 2 10.5 10.5 - So, SR+ = 18.5, SR– = 152.5 © 2002 The Wadsworth Group

l An Example, continued °L.H0:m=10 hours h1m≠10 hours IL Rejection Region: a=0.05, n=18 data values not equal to the hypothesized median of 10 If 2r+130, reject Ho II. Test statistics. ∑R+=18.5 ∑R-=152.5 C 2002 The Wadsworth Group

An Example, continued • I. H0 : m = 10 hours H1 : m  10 hours • II. Rejection Region: a = 0.05, n = 18 data values not equal to the hypothesized median of 10 If SR+ 130, reject H0 . • III. Test Statistics: SR+ = 18.5 SR– = 152.5 © 2002 The Wadsworth Group

I An example, concluded IV. Conclusion since the test statistic of ER+=18.5 falls below the critical value of W=41 we reject Ho with at least 95% confidence V Implications: There is enough evidence to dispute the directors claim that this county has a median of 10 days of sunshine per day during the summer months C 2002 The Wadsworth Group

An Example, concluded • IV. Conclusion: Since the test statistic of SR+ = 18.5 falls below the critical value of W = 41, we reject H0 with at least 95% confidence. • V. Implications: There is enough evidence to dispute the director’s claim that this county has a median of 10 days of sunshine per day during the summer months. © 2002 The Wadsworth Group