RESEARCH HYPOTHESES TESTING THROUGH ANOVA & MANOVA TESTS

1. Σεμινάριο Ανάπτυξης Ανθρώπινου Δυναμικού RESEARCH HYPOTHESES TESTING THROUGH ANOVA & MANOVA TESTS Εισηγητής: Α. Βρεχόπουλος, M.B.A., Ph.D. Οικονομικό Πανεπιστήμιο Αθηνών Πρόγραμμα Διδακτορικών ΣπουδώνΤμήμα Διοικητικής Επιστήμης και ΤεχνολογίαςELTRUN - Εργαστήριο Ηλεκτρονικού Επιχειρείν

2. Introduction

3. Quantitative Ph.D. Research: Indicative Structure • Chapter 1: Introduction • Chapter 2: Literature Review • Chapter 3: Research Hypotheses and Methodology • Chapter 4: Analysis of Results • Chapter 5: Discussion • Chapter 6: Conclusions and Recommendations

4. My Ph.D. structure • Chapter 1: Introduction • Chapter 2: Background Research Material • Chapter 3: Research Methodology • Chapter 4: Initial Research • Chapter 5: Developing Alternative Virtual Store Layouts • Chapter 6: Analysis of the Laboratory Experiment Results • Chapter 7: Conclusions and Recommendations

5. Literature Review - Develop the Research Methodology Year 1 Literature Review Year 2-3 Target the Research Area Year 1 Run the Conclusive Research and Collect the Data Year 2-3 Literature Review & Exploratory Research Year 1-2 Analyze the Results, Test the Hypotheses and Discuss the Findings Year 3 Find and Document the Research Problem, Question and Objectives Year 2 Provide Conclusions, Implications and Future Research Directions Year 3 Formulate the Research Hypotheses Year 2 Year ? HOLIDAYS? An Indicative Ph.D. Process

6. Research Design Hypotheses Development Exploratory Design To provide insights and understanding of the nature of marketing phenomena Conclusive Design To test specific hypotheses and examine relationships Descriptive Research Description of something, usually market characteristics or functions Causal Research Obtain evidence regarding cause-and-effect (causal) relationships Research Design Classification What happens? Why happens? What happens?

7. Research Design Classification Research Design Exploratory Design Conclusive Design Qualitative Exploration Quantitative Exploration Descriptive Research Causal Research Cross-sectional design Longitudinal design Single cross-sectional Multiple cross-sectional

8. A Classification of Research Data Marketing Research Data Secondary Data Primary Data Qualitative Data Quantitative Data Exploration Description Cause and Effect

9. Qualitative Research Procedures Direct (non- disguised) Indirect (disguised) Group Interviews (i.e., focus groups) Depth Interviews (i.e., personal interviews) Observation Techniques Projective Techniques A Classification of Qualitative Research Procedures

10. Data Assemply The gathering of data of disparate sources (i.e. tape recording) Data Reduction (coding) The organizing and structuring of qualitative data Data Display Involves summarizing and presenting the structure that is seen in collected qualitative data Data Verification Involves seeking alternative explanations of the interpretations of qualitative data, through other data sources Stages of the Qualitative Data Analysis

11. Survey methods Personal Face-to-face Telephone Mail In-home In-office Street interviewing CAPI Computer-assisted personal interviewing Traditional telephone CAPI Computer-assisted telephone interviewing Traditional mail survey Electronic mail survey Mail Panel Major Methods employed in Descriptive Research Designs

12. Major Methods employed in Descriptive Research Designs Observation Methods Personal Observation Trace Analysis Electronic Observation Content Analysis Audit

13. Causal Research design: experimentation • Causality: when the occurrence of X increases the probability of the occurrence of Y. • Definitions and Concepts: • Independent variables: variables that are manipulated by the researcher and whose effects are measured and compared • Test units (subjects): individuals, organizations or other entities whose response to independent variables of treatments is being studied. • Dependent variables: variables that measure the effect of the independent variables on the test units (e.g., brand name). • Extraneous variables: variables, other than the independent variables, which influence the response of the test units. • Experiment: the process of manipulating one or more independent variables and measure the effects on one or more dependent variables, while controlling for the effect of the extraneous variables. • Experimental design: the set of experimental procedures specifying (a) the test units and sampling procedure, (b) the independent variables, (c) the dependent variables, and (d) how to control the extraneous variables.

14. Validity in Experimentation • Internal Validity: a measure of accuracy of an experiment. It measures whether the manipulation of the independent variables, or treatments, actually caused the effects on the dependent variable(s). • External Validity: a determination of whether the cause-and-effect relationships found in the experiment can be generalized.

15. Experimental Method • Between Groups: each subject is assigned to a different condition. • Advantages: elimination of learning effects. • Disadvantages: (a) greater number of subjects are required, (b) individual differences between users can bias the results  problem handling: careful selection of subjects ensuring that all are representative of the population. • Within groups: each subject performs under each different condition. • Advantages: (a) less costly than between-groups, (b) less chance of effects from variation between subjects. • Disadvantages: suffer from transfer of learning effects.

16. Factor Laboratory Field Environment Artificial Realistic Control High Low Internal Validity High Low External Validity Low High Time Short Long Number of units Small Large Ease of implementation High Low Cost Low High Laboratory vs. Field Experiments

17. Primary Scales of Measurement Nominal: A scale whose numbers serve only as labels of tags for identifying and classifying objects with a strict one-to-one correspondence between the numbers and theobjects. Ordinal: a ranking scale in which the numbers are assigned to objects to indicate the relative extent to which some characteristics are possessed. Thus, it is possible to determine whether an object has more or less of a characteristic than some other Object but not how much more or less (e.g. ranking of teams in a tournament). Interval: a scale in which the numbers are used to rank the objects such that numerically equal distances on the scale represent equal distances in the characteristic being measured. Ratio: ratio scale allows the researcher to identify or classify objects, rank order the objects, and compare intervals or differences.

18. Nominal Scale Ordinal Scale Interval Scale Ratio Scale No. Bank Preference Ratings Preference Ratings 1-7 11-17 1 Bank AEK 1 7 17 60% 11 Bank PAO 4 14 0% 23 Bank OSFP 5 15 0% 27 Bank PAOK 7 17 0% 37 Bank ARIS 5 15 0% 44 Bank HRAKLIS 3 5 15 30% 48 Bank OFH 6 16 0% 54 Bank PANIONIOS 6 16 0% 56 Bank IOANNINA 2 7 17 10% 80 Bank PANAXAIKI 2 12 0% Primary Scales of Measurement: An Example

19. Primary Scales of Measurement: An Example 7 11 3 Numbers assigned to runners Nominal 3rd 2nd 1st Rank order of winners Ordinal 8.2 9.1 9.6 Performance Rating on a 0 to 10 scale Interval 15.2 14.1 13.4 Time to finish, in seconds Ratio

20. Questionnaire Design Process • Specify the information needed • Specify the type of interviewing method • Determine the content of individual questions • Design the question to overcome the respondent’s inability and unwillingness to answer • Decide on the question wording • Arrange the question in proper order • Identify the form and layout • Reproduce the questionnaire • Eliminate problems by pre-testing

21. The Sampling Design Process Define the population Determine the Sampling Frame Select Sampling Techniques Determine the Sample Size Execute the Sampling Process Validate the Sample

22. Sampling Techniques Sampling Techniques Non-probabilitysampling techniques Probability sampling techniques Convenience Sampling Simple Random Sampling Judgemental Sampling Systematic Sampling Quota Sampling Stratified Sampling Snowball Sampling Cluster Sampling

23. Univariate vs. Multivariate Statistical Techniques • Univariate techniques are appropriate when each variable is analyzed in isolation. • Multivariate techniques are suitable for analyzing data when the variables are analyzed simultaneously. • Dependence techniques: are appropriate when one or more variables can be identified as dependent variables and the remaining as independent variables. • Interdependence techniques the variables are not classified as dependent or independent; rather the whole set of interdependent relationships is examined.

24. A Classification of Univariate Statistical Techniques Univariate Techniques Metric Data (i.e., interval or ratio) Non-metric data (i.e., nominal, ordinal) • One sample • t-test, z- test Two or more samples One sample Frequency, Chi-square, K-S, etc. Two or more samples Independent t-test z-test One-way ANOVA Related Paired t-test Independent Chi-square Mann-Whitney K-S, etc. Related Wilcoxon McNemar Chi-square, etc.

25. A Classification of Multivariate Statistical Techniques Multivariate Techniques Dependence Techniques Interdependence Techniques • One Dependent Variable • Cross Tabulation • ANOVA • ANCOVA • Multiple Regression • Discriminant Analysis • Conjoint Analysis • More than one Dependent Variables • Multivariate analysis of • variance and covariance • Canonical correlation • Multiple discriminant • analysis Variable inter-dependence - Factor Analysis • Inter-object similarity • Cluster Analysis • Multidimensional • Scaling

26. Internet Based Research Approaches • Online Experiments • Online Focus Groups • Online Observation • Online In-Depth Interviews • Online Survey Research • E-mail Surveys • Web Surveys • Online Panels • Combination of offline with online data

27. Online Research Advantages • Fast and inexpensive • Reach a diverse, large group of Net users worldwide or a small niche of specialized users • Computer entry reduces errors • Honest responses to sensitive questions

28. Online Research Disadvantages • Self-selection bias • Respondent authenticity uncertain • Dishonest responses • Duplicate submissions

29. ANOVA and MANOVA for Hypotheses Testing

30. Relationship between t-test, analysis of variance, analysis of covariance and regression Metric Dependent Variables One or more independent variables One independent variable Categorical: factorial Categorical and interval Interval • binary Regression ANOVA Analysis of Covariance • t test One factor More than one factor One-way ANOVA N-way ANOVA

31. Definitions and Useful Information • Analysis of Variance is statistical technique used to determine whether samples came from populations with equal means. • Univariate analysis of variance (ANOVA) employs one dependent measure • Multiavariate analysis of variance (MANOVA) compares populations on two or more dependent variables • Factor: Categorical independent variables. The independent variables must all be categorical (non-metric) to use ANOVA. A particular combination of factor levels is called treatment. • In one-way ANOVA the interest lies in testing the null hypothesis that the category means are equal in the population: Ho: μ1=μ2=μ3...=μn • Non-parametric techniques: when you have serious violations of the distribution assumptions of parametric tests, then non-parametric techniques can be used. These tests tend to be less powerful that their parametric counterparts. Alternatively, some non-parametric tests are appropriate for data measured on scales which are not interval or ratio. Kruskal-Wallis is the corresponding to ANOVA non-parametric test.

32. Definitions and Useful Information • The null hypothesis is that all means are equal • Scale: • Dependent variables: metric (interval or ratio) • Independent variables: categorical (non-metric) • One way ANOVA involves only one categorical variable (i.e. signle factor) where the treatment is the same as a factor level. If two or more factors are involved, the analysis is termed n-way ANOVA. • Factorial design: a design with more than one factor (treatment). In factorial designs we examine the effects of several factors simultaneously by forming groups based on all possible combinations of the levels of the various treatment variables. • Interaction effects: In n-way ANOVA when assessing the relationship between two variables, an interaction occurs if the effect of X1 depends on the level of X2 and vice versa.

33. Analysis of Variance: Categories • One-Way between Groups ANOVA with Post-Hoc Comparisons • One-way between Groups ANOVA with Planned Comparisons • Two-Way between Groups ANOVA • One-Way Repeated Measures ANOVA • Two-Way Repeated Measures ANOVA • Multivariate Analysis of Variance (MANOVA) Coakes and Steed, 1999

34. a. One-Way between Groups ANOVA with Post-Hoc Comparisons • When the researcher wants to compare the means of more than two groups a One-Way Analysis of variable is appropriate. The null hypothesis is rejected if any pair of means is unequal. However, in order to locate where the significant lies, this requires post-hoc analysis (e.g. Tukey’s honestly significant difference post-hoc test). • Assumptions • Random Selection – the sample should be independently and randomly selected from the population of interest • Population normality – populations from which the samples have been drwan should be normal. • Kolmogorov-Smirnov statistic (Shapiro-Wilks statistic for samples less than 50 observations) – if the significance level is greater than .05 then normality is assumed • Homogeneity of variance – the scores in each group should have homogeneous variances. • If Levene’s test for homogeneity of variances is not significant (p>.05) the researcher can be confident that the population variances for each group are approximately equal.

35. a. One-Way between Groups ANOVA with Post-Hoc Comparisons: Example (1/3) • An economist wished to compare household expenditure on electricity and gas in four major cities in Australia. She obtained random samples of 25 two-person households from each city and asked them to keep records on their energy expenditure over a six month period.

36. a. One-Way between Groups ANOVA with Post-Hoc Comparisons: Example (2/3)

37. a. One-Way between Groups ANOVA with Post-Hoc Comparisons: Example (3/3)

38. b. One-Way between Groups ANOVA with Planned Comparisons • Planned or “a priori” comparisons are used when the researcher has specific expectations or predictions about some of the results. These comparisons are often of theoretical importance and are planned from the onset of the study. • Assumptions • Random selection • Population normality • Homogeneity of variance

39. b. One-Way between Groups ANOVA with Planned Comparisons: Example (1/3) • A dietary consultant has asked you to test the efficacy of 3 weight reduction programs. Carbohydrates were restricted in program A, protein was restricted in program B and fats were restricted in program C. Ten overweight volunteers were randomly assigned to each of the programs and their weight loss after eight weeks was recorded in kilograms. Positive scores signify a weight drop. The dietitian predicted that the diet type would influence the weight loss and that the loss would be greater for those restricting fats (program C).

40. b. One-Way between Groups ANOVA with Planned Comparisons: Example (2/3)

41. b. One-Way between Groups ANOVA with Planned Comparisons: Example (3/3)

42. c. Two-Way between Groups ANOVA • The two-way ANOVA operates in the same manner as the one-way ANOVA except that you are examining an additional independent variable. Each independent variable may possess two or more levels. In a two factor between-groups design, each subject has been randomly assigned to only one of the different levels of each independent variable. Each of the different cells represents the unique combinations of the levels of the two factors. • Assumptions • Random selection • Population normality • Homogeneity of variance

43. c. Two-Way between Groups ANOVA: An Example (1/3) • A toy distributor wished to determine which stores were the most successful in selling their stock. He wished to compare the sales in different types of stores in different locations. That is, he wished to compare sales in (a) discount toy stores, (b) department stores and (c) variety stores and stores in either the (i) central city district or in (ii) suburban shopping centers. Thus, the first independent variable was store type with three levels, the second independent variable was location with two levels and the dependent variable was the amount of toy sales in $1000 per week. Therefore, we have a 3 x 2 factorial design with six data cells (3 x 2 = 6). Four stores were randomly chosen for each of the six cells (n=4); sales for the total 24 stores were recorded (N=24). He wishes to ask three questions: (a) does type of store influence the sales of toys? (b) does location of store influence the sales of toys?, (c) does the influence of type of store on toy sales depend on the location of the store? (interaction effects).

44. c. Two-Way between Groups ANOVA: An Example (1/2)

45. c. Two-Way between Groups ANOVA: An Example (2/2) • When you have obtained a significant interaction it is necessary to conduct an analysis of simple effects. That is, you need to look at the effect of one factor at only one level of the other factor. For example, you could analyze the effect of the type of store on toy sales just in the city center of just for suburban shopping centers.

46. d. One-Way Repeated Measures ANOVA • Having the same subjects perform under every condition (within-groups). • Assumptions • Random selection • Population Normality • Homogeneity of variance • Sphericity – the variance of the population difference scores for any two conditions should be the same as the variance of the population difference scores for any other two conditions.

47. d. One-Way Repeated Measures ANOVA: Example (1/4) • You wish to determine whether practice enhances ability to solve GMAT problems. Eight participants were asked to solve as many GMAT problems as possible in ten minutes. They were then allowed to practice for an hour before being asked to complete another ten minute timed task. Participants were then given another practice session and another timed task. The number of GMAT problems correctly solved was recorded.

48. d. One-Way Repeated Measures ANOVA: Example (2/4)

49. d. One-Way Repeated Measures ANOVA: Example (3/4)

50. d. One-Way Repeated Measures ANOVA: Example (4/4)