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

Introduction

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

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

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

Research Design Classification What happens? Why happens? Research Design 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 Hypotheses Development What happens?

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

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

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

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

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

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

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.

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.

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.

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

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 the objects. 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.

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

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

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

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

Non-probability sampling techniques Convenience Sampling Simple Random Sampling Judgemental Sampling Systematic Sampling Quota Sampling Stratified Sampling Snowball Sampling Cluster Sampling

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.

Univariate Statistical Techniques A Classification of Univariate Statistical 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 Frequency, Chi-square, K-S, etc. Univariate Techniques Independent t-test z-test One-way ANOVA Related Paired t-test Chi-square Mann-Whitney K-S, etc. Wilcoxon McNemar Chi-square, etc.

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

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

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

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

ANOVA and MANOVA for Hypotheses Testing

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

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.

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.

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

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.

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.

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

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

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

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).

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

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

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

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).

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

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.

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.

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.

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

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

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

e. Two-Way Repeated Measures ANOVA In the two-way repeated measures design you have two independent variables, with or more levels, which are within-subject in nature. That is, each subject performs in all conditions. Assumptions Random selection Population Normality Homogeneity of variance Sphericity

e. Two-Way Repeated Measures ANOVA: Example (1/7) A graphic designer wished to determine which combination of colours and backgrounds produce the most aesthetically pleasing display. Five subjects were explosed to two different types of background (hatched and spotted) and lettering of four different colours (red, blue, green and yellow). Subjects were requested to rate the pleasingness of these displays on a 20 point scale (1=least pleasing to 20 = most pleasing). Tasks: (a) determine whether background influences the subject’s rating, (b) determine whether colour of lettering influences the subject’s rating and (c determine whether the influence of background on rating depends on letter colouring.

e. Two-Way Repeated Measures ANOVA: Example (2/7)

e. Two-Way Repeated Measures ANOVA: Example (3/7)

e. Two-Way Repeated Measures ANOVA: Example (4/7)

e. Two-Way Repeated Measures ANOVA: Example (5/7)

e. Two-Way Repeated Measures ANOVA: Example (6/7)

e. One-Way Repeated Measures ANOVA: Example (7/7) The main effect for background is significant (p<.05) and thus we can conclude that type of background does affect subject’s ratings. The main effect of colour is significant and therefore we can say that the colour of lettering does affect the subject’s ratings. The background by colour interaction effect was not significant and thus we can conclude that, although main effects for both background and colour independently were significant, the effect of one independent variable (background) does not depend on the effect of the other (colour) in influencing pleasingness ratings by subjects.

Example of Interaction Effects A cereal manufacturer wishes to examine the impact of e different color possibilities (red, blue, green) and three different shapes (stars, cubes and balls) on the overall consumer evaluation of a new cereal  3 x 3 factorial design (9 possible combinations). Three overall effects can be tested: The main effect of color: are there any differences between the mean ratings given to red (i.e. including all ratings of red stars, red cubes, and red balls), blue and green? The main effect of shape: are there any differences between the mean ratings given to stars (i.e. including all ratings of red stars, blue stars, and green stars), cubes and balls? The interaction effect of color and shape: Does the effect of color depend on what shape we are considering – Does the effect of shape depend on what color we are considering? Red (stars, cubes, balls) Blue (stars, cubes, balls) Green (stars, cubes, balls) Stars (red, blue, green) Cubes (red, blue, green) Balls (red, blue, green) Red Stars Red Cubes Red Balls Blue Stars Blue Cubes Blue Balls Green Stars Green Cubes Green Balls

f. Multivariate Analysis of Variance (MANOVA) The extension of univariate analysis of variance to the involvement of multiple dependent variables is termed multivariate analysis of variance. When there is evidence that these dependent variables are conceptually and theoretically related, MANOVA is the analysis of choice. MANOVA is used to assess group differences across multiple metric dependent variables simultaneously. That is, in MANOVA each treatment group is observed on two or more dependent variables. Assumptions Cell sizes Univariate and multivariate normality Linearity Homogeneity of regression Homogeneity of variance-covariance matrices Multicollinearity and singularity

f. Multivariate Analysis of Variance (MANOVA): Example (1/7) A social scientist wished to compare those respondents who had lodged an organ donor card with those who had not. 388 new drivers completed a questionnaire that measured their attitudes towards organ donation, their feelings about organ donation and their previous exposure to the issue. It was hypothesized that individuals who agreed to be donors would have more positive attitudes towards organ donation, more positive feelings towards organ donation and greater previous exposure to the issue. Therefore, the independent variable was whether a donor card had been signed, and the dependent variables were attitudes towards organ donation, feelings towards organ donation and previous exposure to organ donation. Conceptually and theoretically these dependent variables were believed to be related and thus MANOVA was the analysis of choice.

f. Multivariate Analysis of Variance (MANOVA): Example (2/7)

f. Multivariate Analysis of Variance (MANOVA): Example (3/7)

f. Multivariate Analysis of Variance (MANOVA): Example (4/7)

f. Multivariate Analysis of Variance (MANOVA): Example (5/7)

f. Multivariate Analysis of Variance (MANOVA): Example (6/7)

f. Multivariate Analysis of Variance (MANOVA): Example (7/7) A person’s decision to act as a donor is significantly influenced by their feelings towards organ donation. The “feelings” dependent variable contribute to the significant multivariate effect. No significant main effects were found for the other dependent measures (attitudes, exposure). MANOVA is an intricate analysis and is more straightforward when there is only one independent variable and only a few dependent variables. As the number of independent (i.e., interaction effects) and dependent variables increase, the analysis becomes more complex.

Key Issues in the Ph.D. Process Contribution (“What we know now that we didn’t know before?): Theory Provision of direct managerial implications (DMST Ph.D.!!!) Future research directions/perspectives Avoid assumptions  document!!! Confirmatory? Multidisciplinary approach!!! Exploit research opportunities exist at the last chapter of previous PhDs/Papers!!! Disseminate and test your work!!! Stress? NO  interest!!! Generic Guidelines to get a Ph.D.: “relax”, “work hard”, “manage your time”, “have hobbies”, “cooperate”, “listen to your supervisor”, “be patient”, “build your business and academic profile”, “networking”, “plan”, “be professional”, “disseminate knowledge”, “follow best-practice”, “be flexible”, “classify research streams and researchers”, “gather material (textbooks, papers, etc.)”, “teaching-presentations”, etc. Exploit Projects!!!  One project can support thousands of Ph.Ds!!! Publish!!! and Review Papers!!!

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