1. Data Analysis: Analyzing Individual Variables and Basics of Hypothesis Testing Chapter 20

2. Data Analysis: Two Key Considerations Is the variable to be analyzed by itself or in relationship to other variables? What level of measurement was used? If you can answer these two questions, data analysis is easy... SLIDE 20-1

3. Frequency Analysis Finance? Number Percent Percent Percent Yes30303030 No707070100 100100100 Valid Cumulative Did Family Finance Car Purchase? SLIDE 20-2

4. Histogram and Frequency Polygon of Income: Car Ownership Study Income Absolute Frequency of Occurrence 28 24 20 16 12 8 4 0 15,000 25,000 35,000 45,000 55,00075,00095,000 65,00085,000105,000 8 25 15 18 88 7 3 1 3 SLIDE 20-3

5. Cumulative Distribution of Income: Car Ownership Study 85000 15000 25000 3500055000 4500065000 7500095000 105000 Relative Frequency 0.2 0.1 Income 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 SLIDE 20-4

6. Raw Data for Better Smiles Dental Office Please rate the quality of service provided by Better Smiles Dental Office on the following scales: veryvery poorpoor neutralgoodgood Dental technicians(2)(6)(36)(32)(24) Receptionist(10)(16)(18)(36)(20) Dentist(17)(17)(35)(21)(10) Number of respondents selecting each response category shown in red SLIDE 20-5

7. Two-Box Results, with Descriptive Statistics two-boxmean(s.d.) Dental technicians56%3.70(0.97) Receptionist56%3.40(1.25) Dentist31%2.90(1.21) (n=100) SLIDE 20-6

8. Confidence Interval Formula for Proportion p +/- z(sampling error for proportion) p +/- z p(1-p) n √ wherep = relevant proportion obtained from sample z = size corresponding to desired degree of confidence n = sample size SLIDE 20-7

9. CAUTION in Interpreting Confidence Intervals The confidence interval only takes sampling error into account. It DOES NOT account for other common types of error (e.g., response error, nonresponse error). The goal is to reduce TOTAL error, not just one type of error. SLIDE 20-8

10. Confidence Interval Formula for Means x +/- z(sampling error for mean) x +/- z s n √ wherex = mean obtained from sample z = z-score corresponding to desired degree of confidence s = sample standard deviation n = sample size SLIDE 20-9 ^ ^

11. Typical hypothesis Testing Procedure Specify Null and Alternative Hypotheses after Analyzing the Research Problem Choose an Appropriate Statistical Test Considering the Research Design and after Determining the Sampling Distribution That Applies Given the Chosen Test Statistic Specify the Significance Level (Alpha) for the Problem Being Investigated Collect the Data and Compute the Value of the Test Statistic Appropriate for the Sampling Distribution Determine the Probability of the Test Statistic under the Null Hypothesis Using the Sampling Distribution Specified in Step 2 Compare the Obtained Probability with the Specified Significance Level and Then Reject or Do Not Reject the Null Hypothesis on the Basis of the Comparison SLIDE 20-10

12. Common Misinterpretations of What “Statistically Significant” Means Viewing p-values as if they represent the probability that the results occurred because of sampling error (e.g., p=.05 implies that there is only a.05 probability that the results were caused by chance). Assuming that statistical significance is the same thing as managerial significance. Viewing the  or p levels as if they are somehow related to the probability that the research hypothesis is true (e.g., a p-value such as p>.001 is “highly significant” and therefore more valid than p<.05). SLIDE 20-11

13. Decision Errors in the Courtroom True Situation: Defendant Verdict Innocent Guilty Innocent Guilty Error Probability:  Correct Decision Probability: 1-  Error Probability:  Correct Decision Probability: 1-  SLIDE 20-12

14. Types of Errors in Hypothesis Testing True Situation: Null Hypothesis Research conclusions True False Reject H o Error: Type I Significance Level Probability:  Correct Decision Confidence Level Probability: 1-  Error: Type II Probability:  Correct Decision Power of Test Probability: 1-  Do not reject H o SLIDE 20-13

15. Probability of Z = 1.50 with One-Tailed Test SLIDE 20-14 Shaded Area = 0.9332 z = 1.500

16. Illustration of β Error and Power for Several Assumed True Population Proportions for the Hypothesis π < 0.2 SLIDE 20-15 Area=.05 PANEL A: CRITICAL P FOR NULL HYPOTHESIS PANEL B: REGION OF NON-REJECTION WHEN  =.22 AND THUS NULL HYPOTHESIS IS FALSE; PATTERNED AREA =  ERROR =.6480 PANEL C: REGION OF NON-REJECTION WHEN  =.21 AND THUS NULL HYPOTHESIS IS FALSE; PATTERNED AREA =  ERROR =.8413 PANEL D: REGION OF NON-REJECTION WHEN  =.25 AND THUS NULL HYPOTHESIS IS FALSE; PATTERNED AREA =  ERROR =.0856 *  =.21  =.22  =.20  =.25 z=.2263-.25 = -1.368.0173 z=.2263-.21 = 1.000.0163 z=.2263-.22 =.380.0166 p p p p