1. Chapter Fifteen Copyright © 2006 McGraw-Hill/Irwin Data Analysis: Testing for Significant Differences

2. McGraw-Hill/Irwin 2 1.Understand how to prepare graphical presentations of data. 2.Calculate the mean, median, and mode as measures of central tendency. 3.Explain the range and standard deviation of a frequency distribution as measures of dispersion. 4.Understand the difference between independent and related samples. Learning Objectives

3. McGraw-Hill/Irwin 3 5.Explain hypothesis testing and assess potential error in its use. 6.Understand univariate and bivariate statistical tests. 7.Apply and interpret the results of the ANOVA and n-way ANOVA statistical methods. Learning Objectives

4. McGraw-Hill/Irwin 4 Basic statistics and descriptive analysis –common to all marketing research projects –Central tendency and dispersion –t-distribution and associated confidence interval estimation –Hypothesis testing –Analysis of variance Value of Testing for Differences in Data

5. McGraw-Hill/Irwin 5 Graphics –help the grasp of the essence of the information developed in the research project Charts –an effective visual aid to enhance the communication process and add clarity and impact to research reports Guidelines for Graphics Understand how to prepare graphical presentations of data

6. McGraw-Hill/Irwin 6 Bar Chart –data in the form of bars that may be horizontally or vertically oriented To depict both absolute and relative magnitudes, differences and change Histogram –form of bar chart where each bar’s height is the relative or cumulative frequency of a value of a specific variable Understand how to prepare graphical presentations of data Guidelines for Graphics

7. McGraw-Hill/Irwin 7 Exhibit 15.2 Understand how to prepare graphical presentations of data

8. McGraw-Hill/Irwin 8 Understand how to prepare graphical presentations of data

9. McGraw-Hill/Irwin 9 Line Chart–connects a series of data points with a continuous line –To show trends over several periods of time–useful in explaining comparisons between variables –To illustrate multiple comparisons to the viewer–each line needs to have its own label and must different in form or color –Area Chart–the area below the line is filled in to dramatically display the information Understand how to prepare graphical presentations of data Guidelines for Graphics

10. McGraw-Hill/Irwin 10 Exhibit 15.4 Understand how to prepare graphical presentations of data

11. McGraw-Hill/Irwin 11 Pie Charts–for displaying relative proportions– –Each section of the pie chart is the relative proportion –Not useful to display comparative information between several variables –Seven sections—considered to be the pratical maximum Understand how to prepare graphical presentations of data Guidelines for Graphics

12. McGraw-Hill/Irwin 12 Exhibit 15.5 Understand how to prepare graphical presentations of data

13. McGraw-Hill/Irwin 13 Exhibit 15.6 Understand how to prepare graphical presentations of data

14. McGraw-Hill/Irwin 14 Exhibit 15.7 Understand how to prepare graphical presentations of data

15. McGraw-Hill/Irwin 15 Mean–arithmetic average of the sample, all values of a distribution of responses are summed and divided by the number of valid responses Mode–most common value is the set of responses to a question; the response most often given to a question. Median–middle value of a rank ordered distribution, exactly half of the responses are above and below the median value Calculate the mean, median, and mode as measures of central tendency Measures of Central Tendency

16. McGraw-Hill/Irwin 16 Three Measures of Central Tendency– strengths and weaknesses 1.Nominal Data–mode is the best measure 2.Median–ordinal data 3.Mean–interval or ratio data Calculate the mean, median, and mode as measures of central tendency Measures of Central Tendency

17. McGraw-Hill/Irwin 17 Calculate the mean, median, and mode as measures of central tendency Exhibit 15.8

18. McGraw-Hill/Irwin 18 Calculate the mean, median, and mode as measures of central tendency Exhibit 15.9

19. McGraw-Hill/Irwin 19 Measures of Central Tendency–cannot tell the whole story about a distribution of responses Measures of Dispersion–how close to the mean or other measure of central tendency the rest of the values in the distribution fall Range–the distance between the smallest and largest value in a set of responses Explain the range and standard deviation of a frequency distribution as measures of dispersion Measures of Dispersion

20. McGraw-Hill/Irwin 20 Standard Deviation–average distance of the dispersion values from the mean –Deviation–difference between a particular response and the distribution mean –Average squared deviation–used as a measure of dispersion for a distribution Variance–average squared deviations about the mean of a distribution of values Explain the range and standard deviation of a frequency distribution as measures of dispersion Measures of Dispersion

21. McGraw-Hill/Irwin 21 Explain the range and standard deviation of a frequency distribution as measures of dispersion Exhibit 15.10

22. McGraw-Hill/Irwin 22 Hypothesis–empirically testable though yet unproven statement developed in order to explain phenomena –Preconceived notion of the relationships that the captured data should present–a hypothesis. Explain hypothesis testing and assess potential error in its use Hypothesis Testing

23. McGraw-Hill/Irwin 23 Independent Samples–two or more groups of responses that are tested as though they may come from different populations Related Samples–two or more groups of responses that originated from the sample population Paired sample–questions are independent–the respondents are the same –Paired samples t-test--used for differences in related samples Understand the difference between independent and related samples Hypothesis Testing

24. McGraw-Hill/Irwin 24 First Step–to develop the hypotheses that is to be tested –Developed prior to the collection of data –Developed as part of a research plan –Make comparisons between two groups of respondents to determine if there are important differences between the groups –Important considerations in hypothesis testing are: Magnitude of the difference between the means Size of the sample used to calculate the means Explain hypothesis testing and assess potential error in its use Hypothesis Testing

25. McGraw-Hill/Irwin 25 Null Hypothesis (Ho)–a statement that asserts the status quo –Alternative Hypothesis (H1) a statement that is the opposite of the null hypothesis, that the difference exists in reality not simply due to random error Represents the condition desired –Null hypothesis is accepted–there is no change to the status quo –Null hypothesis is rejected–the alternative hypothesis is accepted and the conclusion is that there has been a change in opinions or actions –Null hypothesis refers to a population parameter–not a sample statistic Explain hypothesis testing and assess potential error in its use Hypothesis Testing

26. McGraw-Hill/Irwin 26 Statistical Significance –Inference Regarding a Population –Type I Error–made by rejecting the null hypothesis when it is true; the probability of alpha (α) Level of Significance--.10,.05, or.01 Explain hypothesis testing and assess potential error in its use Hypothesis Testing

27. McGraw-Hill/Irwin 27 Type II Error–failing to reject the null hypothesis when the alternative hypothesis is true; the probability of beta (β). –Unlike alpha (α), which is specified by the researcher, beta (β) depends on the actual population parameter. –Type I and Type II errors–sample size can help control these errors Can select an alpha (α) and the sample size in order to increase the power of the test and beta (β) Explain hypothesis testing and assess potential error in its use Hypothesis Testing

28. McGraw-Hill/Irwin 28 Purpose of Inferential Statistics –Sample –Sample Statistics –Population Parameter The actual population parameters are unknown since the cost to perform a census of the population is prohibitive Frequency Distribution Analyzing Relationships of Sample Data

29. McGraw-Hill/Irwin 29 Univariate Tests of Significance –involve hypothesis testing using one variable at a time z-test –sample size >30 and the standard deviation is unknown t-test– –sample size <30 and the standard deviation is unknown, assumption of a normal distribution is not valid Analyzing Relationships of Sample Data Understand univariate and bivariate statistical tests

30. McGraw-Hill/Irwin 30 Explain the range and standard deviation of a frequency distribution as measures of dispersion Exhibit 15.11

31. McGraw-Hill/Irwin 31 Bivariate Hypotheses–where more than one group is involved Null hypotheses–that there is no difference between the group means µ1 = µ2 or µ1 - µ2 = 0 Analyzing Relationships of Sample Data Understand univariate and bivariate statistical tests

32. McGraw-Hill/Irwin 32 Using the t-Test to Compare Two Means –Univariate t-test and the Bivariate t-test–require interval or ratio data t-test –useful when the sample size is < 30 and the population standard deviation is unknown Bivariate test—assumption is that the samples are drawn from populations with normal distributions and that the variances of the populations are equal Analyzing Relationships of Sample Data Understand univariate and bivariate statistical tests

33. McGraw-Hill/Irwin 33 t-test for differences between group means–as the difference between the means divided by the variability of random means –t-value–ratio of the difference between two sample means and the standard error –t-test–provides a rational way of determining if the difference between the two sample means occurred by chance. Analyzing Relationships of Sample Data Understand univariate and bivariate statistical tests

34. McGraw-Hill/Irwin 34 The formula for calculating the t value is _ _ Z = x 1 – x 2 S x 1 – x 2 Analyzing Relationships of Sample Data Understand univariate and bivariate statistical tests

35. McGraw-Hill/Irwin 35 Explain the range and standard deviation of a frequency distribution as measures of dispersion Exhibit 15.12

36. McGraw-Hill/Irwin 36 Explain the range and standard deviation of a frequency distribution as measures of dispersion Exhibit 15.14

37. McGraw-Hill/Irwin 37 Analysis of Variance (ANOVA)–statistical technique that determines if three or more means are statistically different from each other Multivariate Analysis of Variance (MANOVA)–multiple dependent variables can be analyzed together Analyzing Relationships of Sample Data Apply and interpret the results of the ANOVA and n-way ANOVA statistical methods

38. McGraw-Hill/Irwin 38 Requirements for the ANOVA –The dependent variable be either interval or ratio scaled –The independent variable be categorical Null hypothesis for ANOVA–states that there is no difference between the groups–the null hypothesis would be µ1 = µ2 = µ3 ANOVA technique–focuses on the behavior of the variance with a set of data ANOVA–if the calculated variance between the groups is compared to the variance within the groups, a rational determination can be made as to whether the means are significantly different Analyzing Relationships of Sample Data Apply and interpret the results of the ANOVA and n-way ANOVA statistical methods

39. McGraw-Hill/Irwin 39 Determining Statistical Significance in ANOVA –F-test–used to statistically evaluate the differences between the group means in ANOVA –Total variance–separated into between- group and within-group variance Analyzing Relationships of Sample Data Apply and interpret the results of the ANOVA and n-way ANOVA statistical methods

40. McGraw-Hill/Irwin 40 F distribution–ratio of these two components of total variance and can be calculated as follows –F ratio = Variance between groups Variance within groups The larger the F ratio –The larger the difference in the variance between groups –Implies significant differences between the groups –the more likely that the null hypothesis will be rejected Analyzing Relationships of Sample Data Apply and interpret the results of the ANOVA and n-way ANOVA statistical methods

41. McGraw-Hill/Irwin 41 ANOVA–cannot identify which pairs of means are significantly different from each other –Follow-up Tests—test that flag the means that are statistically different from each other Sheffé Tukey, Duncan and Dunn Analyzing Relationships of Sample Data Apply and interpret the results of the ANOVA and n-way ANOVA statistical methods

42. McGraw-Hill/Irwin 42 n-Way ANOVA –In a one-way ANOVA–only one independent variable –For several independent variables–a n-way ANOVA would be used –Use of experimental designs–provides different groups in a sample with different information to see how their responses change Analyzing Relationships of Sample Data Apply and interpret the results of the ANOVA and n-way ANOVA statistical methods

43. McGraw-Hill/Irwin 43 Explain the range and standard deviation of a frequency distribution as measures of dispersion Exhibit 15.15

44. McGraw-Hill/Irwin 44 Explain the range and standard deviation of a frequency distribution as measures of dispersion Exhibit 15.16

45. McGraw-Hill/Irwin 45 MANOVA–designed to examine multiple dependent variables across single or multiple independent variables –Statistical calculations for MANOVA– similar to n-way ANOVA and are in the statistical software packages such as SPSS and SAS Analyzing Relationships of Sample Data Apply and interpret the results of the ANOVA and n-way ANOVA statistical methods

46. McGraw-Hill/Irwin 46 Perceptual Mapping–process that is used to develop maps showing the perceptions of respondents. The maps are visual representations of respondents’ perceptions of a company, product, service, brand, or any other object in two dimensions –Has a vertical and a horizontal axis that are labeled with descriptive adjectives –Development of the perceptual map–rankings, mean ratings, and multivariate techniques Perceptual Mapping Utilize perceptual mapping to simplify presentation of research findings

47. McGraw-Hill/Irwin 47 Explain the range and standard deviation of a frequency distribution as measures of dispersion Exhibit 15.17

48. McGraw-Hill/Irwin 48 Explain the range and standard deviation of a frequency distribution as measures of dispersion Exhibit 15.18

49. McGraw-Hill/Irwin 49 Applications in Marketing Research 1.New-product development 2.Image measurements 3.Advertising 4.Distribution Perceptual Mapping Utilize perceptual mapping to simplify presentation of research findings

50. McGraw-Hill/Irwin 50 Value of Testing for Differences in Data Guidelines for Graphics Measures of Central Tendency Measures of Dispersion Hypothesis Testing Analyzing Relationships of Sample Data Perceptual Mapping Summary