1. Chapter 10 – Quantitative Data Analysis

2. Chapter Objectives Understand differences in measurement scale ○ How to code measurements on the spread sheet Understand different analysis methods for different scales Understand how to read and interpret results Develop your own research with appropriate analysis method

3. Scales

4. Different Measurement Scales Type of ScalesKey CharacteristicsExamples Nominal Key characteristics of objects or individuals Categories or groups Sex Colour of eye or hair Occupation Department of employees Ordinal Importance attached or preference for certain variables Rank-orders Preference of hotel brands Preference of courses Interval Numbers with same intervals Distance between any two points on the scale Temperature Five-point (or seven-point or any number of points) scale (i.e., Likert Scale) Ratio Absolute value Size of the objects or individuals Sales turnover Number of customers Weight Time

5. Nominal Scale Nominal ○ Categories or groups ○ Gender, occupation, department of employees in an organization What was the type of restaurant that you have dined most recently?  Fast food restaurant  Casual dining restaurant  Upscale restaurant

6. Ordinal Scale Ordinal ○ Rank orders the categories ○ An individual’s preference of hotel brands (rank) ○ A hospitality student’s preference of courses (rank) Service Quality DimensionsRanking of Importance 1. Tangibles________ 2. Reliability________ 3. Responsiveness________ 4. Assurance________ 5. Empathy________

7. Interval Scale ○ Numbers with same intervals Distance from 1 to 2 is same as the distance from 2 to 3 ○ Measure the distance between any two points on the scale Likert Scale ○ A psychometric scale commonly used in research that employs questionnaires ○ The most widely used approach to scaling in survey research, such that the term is often used interchangeably rating scale ○ It is a statement which the respondent is asked to evaluate according to any kind of subjective or objective criteria The level of agreement or disagreement is measured

8. Example of Likert Scale Strongly Disagree Somewhat DisagreeNeutral Somewhat Agree Strongly Agree Tangibles of a restaurant  Reliabilities of service  Responsiveness of employees  Assurance of service  Empathy from employees  This question is asking how important you perceive service quality dimension of a restaurant. Please indicate the extent to which you agree or disagree with the following dimensions by checking the option you prefer Many research in social science utilize Likert scale for mean comparison, regression analysis, and so forth Most common form of Likert scale is 5-point or 7-point Likert scale Example of 5-point Likert scale

9. Ratio Scale ○ Has unique ‘zero’ origin ○ Multiplication & division 1a. What was the sales turnover for the start-up year?£______________ 1b. What is the sales turnover for 2006?£______________ 2a. How many people did you employ in the start-up year?_______________ 2c. How many people do/did you employ in 2006?_______________

10. Coding / Entering Data for Analysis Variable ○ An indicator of interest in a research ○ May take any of a specified set of values, perceptions, attitudes, and attributes What was the type of restaurant that you have dined most recently?  Fast food restaurant  Casual dining restaurant  Upscale restaurant Measurement

11. Entering Data What was the type of restaurant that you have dined most recently?  Fast food restaurant  Casual dining restaurant  Upscale restaurant

12. Entering Data Strongly Disagree Somewhat DisagreeNeutral Somewhat Agree Strongly Agree Tangibles of a restaurant  Reliabilities of service  Responsiveness of employees  Assurance of service  Empathy from employees 

13. Analysing Quantitative Data

14. Outline of Analysis Methods ScaleCentral TendencyDispersionMethods NominalModeVariance Chi Square (χ 2 ) OrdinalMode, MedianVariance Chi Square (χ 2 ) Interval * Mode, Median, Mean Standard Deviation t-test Correlation ANOVA Ratio Mode, Median, Mean Standard Deviation t-test Correlation ANOVA Regression Even though Interval scale is not designed for regression analysis, it is often considered continuous scale It is common to conduct regression analysis with interval scale

15. Descriptive Statistics #1 Mean ○ Sum of all values divided by their number ○ Standard Deviation ○ The amount of variation or dispersion from the average (mean) ○

16. Descriptive Statistics #2 Median ○ Middle piece of data ○ 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 6, 6, 6, 6, 6, 6, 6. ○ Median = 4 Mode ○ Most frequently observed value in the dataset ○ 4, 6, 1, 2, 6, 3, 4, 5, 2, 6, 6, 3, 3, 3, 6, 4, 6, 4, 2, 6 ○ Mode = 6

17. SPSS Example (Descriptive Statistics) Analyze  Descriptive Statistics  Descriptives... Enter Variables  Options

18. SPSS Example (Descriptive Statistics) Descriptive Statistics NMinMaxMeanStd. DeviationVariance Price Reduction296153.540.7800.608 New Product Development298153.700.8080.653 Advertising297153.280.9150.837 Relationship Marketing297153.060.8050.648 Valid N (listwise)292 Price Reduction ○ Min = 1, Max = 5 ○ Mean = 3.54 ○ Standard Deviation = 0.780 ○ Variance = 0.608

19. SPSS Example (Frequencies) Analyse  Descriptive Statistics  Frequencies Statistics or Charts

20. SPSS Example (Frequency) Frequency ○ 41.5% (n=124) of employees work at Housekeeping department ○ 24.4% (n=73) of employees work at Food & Beverage department

21. SPSS Example #2 Bar Chart Example

22. Exploring Relationships between Variables b. Relationships

23. 1. Cross-Tabulation ( χ 2 test) Cross-tabulation ○ The representation of two variables in a matrix where all answers in one variable (e.g., gender) are presented in rows, and all answers in other (e.g., customer opinion) are presented in columns ○ χ 2 test is possible

24. SPSS Example (Cross-Tabulation) Analyze  Descriptive Statistics  Crosstabs… Statistics  Select Chi-square Hypothesis ○ H 0 : Employment status (part-time vs. full-time) does not differ according to the hotel brand scale

25. SPSS Example (Cross-Tabulation) Results ○ Pearson Chi-Square = 9.719 (p <.05) Null Hypothesis can be rejected Employment status (part-time vs. full-time) differs according to the hotel brand scale

26. 2. Correlation Pearson Correlation ○ The degree to which a change in a variable is related to a change in one or more other variable(s) ○ Identify the strength of relationship ○ Cannot tell the causal relationship One-tailed vs. Two-tailed ○ Specific direction is hypothesized  One-tailed ○ Non-directional hypotheses  Two-tailed

27. SPSS Example (Correlation) Analyze  Correlate  Bivariate… Option  Pearson Correlation Coefficient Hypothesis ○ H 1 : Service performance is negatively related to service performance but positively correlated to time spent training

28. SPSS Example (Correlation) Results ○ r Performance and Anxiety = -0.424 (p <.05) ; r Performance and Time = 0.379 (p <.05) Null Hypothesis can be rejected Performance is negatively correlated to service anxiety but positively correlated to time spent training

29. Exploring Relationships between Variables b. Mean Comparison

30. Independent Sample t-test ○ Compares the mean values of two different groups (μ 1 = μ 2 ) ○ If the mean values of two different groups are different (i.e., μ 1 – μ 2 = 0), t-value will be significant (p <.05) Dependent Variable ○ Measured by at least interval scale Independent Variable ○ Measured by categorical variable (e.g., male/female, part- time/full-time, etc.)

31. SPSS Example (Independent Sample t-test) Analyze  Compare Means  Independent Samples T Test… Hypothesis ○ H 0 : There is no significant difference between the check-in service speed of male and female employees You need to define groups In this case, male=1 and female=2

32. SPSS Example (Independent Sample t-test) Results ○ Equal variance assumption check If F-value is not significant (p >.05), read ‘Equal variances assumed’ row If F-value is significant (p <.05), read “Equal variance not assumed’ row ○ t-value = –2.981 (p <.05) Null Hypothesis can be rejected Speed of check-in service differs according to the gender of employees

33. Paired Sample t-test ○ Compares mean values of one group but measured at different times Independent Sample t-test vs. Paired Sample t-test ○ Independent sample t-test Group: 2 different groups Mean value: one for each group ○ Paired sample t-test Group: 1 group Mean value: two mean values measured at different times

34. SPSS Example (Paired Sample t-test) Analyze  Compare Means  Paired-Samples T Test… Hypothesis ○ H 0 : Potential customers’ attitudes toward a restaurant do not differ after they are exposed to a new advertisement You need to define two variables (Before or After advertisement)

35. SPSS Example (Paired Sample t-test) Results ○ t-value = –12.084 (p <.05) Null Hypothesis can be rejected Potential customers’ attitudes toward a restaurant differs after they are exposed to a new advertisement

36. One-Way ANOVA ○ Mean comparison of more than two groups (or factor) Independent Sample t-test vs. One-Way ANOVA ○ Independent sample t-test Mean comparison between two groups ○ One-way ANOVA Mean comparison among more than two groups

37. SPSS Example (One-Way ANOVA) Analyze  Compare Means  One-Way ANOVA… Hypothesis ○ H 0 : Restaurant customers’ overall satisfaction does not differ according to the type of restaurant ‘Post Hoc…’ to identify specific difference

38. SPSS Example (One-Way ANOVA) Results #1 (ANOVA) ○ F-value = 16.499 (p <.05) Null Hypothesis can be rejected Restaurant customers’ overall satisfaction differs according to the type of restaurant Results #2 (Post-Hoc test) ○ Fast Food < Limited Service < Upscale Restaurant

39. Two-Way ANOVA ○ Compares the mean differences between groups that can be split on two independent variables (factors) ○ Commonly used to identify interaction effects Education Level HighLowMean Gender Maleμ Male High μ Male Low μ Male Femaleμ Female High μ Female Low μ Female Meanμ High μ Low μ Total Main Effect High vs. Low Male vs. Female Interaction Effect Male Low vs. Female High Female High vs. Male Low

40. Exploring Relationships between Variables c. Causal Relationship

41. SPSS Example (Two-Way ANOVA) Analyze  General Linear Model  Univariate… Hypothesis ○ H 1 : The overall performance of employee would differ according to the gender of an employee ○ H 2 : The overall performance of employee would differ according to the education level of an employee ○ H 3 : There will be an interaction effect of gender and education level on overall performance of employee

42. SPSS Example (Two-Way ANOVA) Step #1: Descriptive Statistics ○ Results #1 (Descriptive Statistics) Step #2: Table Construction ○ Construct table for descriptive statistics

43. SPSS Example (Two-Way ANOVA) Step #3: Between-Subjects Effects ○ H 1 : F-value = 0.673 (p >.05) The overall performance of employee does not differ according to the gender of an employee ○ H 2 : F-value = 12.442 (p <.05) The overall performance of employee differs according to the education level of an employee ○ H 3 : F-value = 2.421 (p <.50) There is an interaction effect of gender and education level on overall performance of employee

44. SPSS Example (Two-Way ANOVA) Step #4: Graphical Illustration of Interaction Effect ○ Choose ‘Plots…’ Female undergraduate > Male undergraduate Female High School < Male High School

45. Multiple Regression ○ Examine the simultaneous effects of several independent variables on a dependent variable Correlation vs. Regression ○ Correlation No causal relationship ○ Regression Causal relationship A  B (A causes B)

46. Multiple Regression Y = β 0 + β 1 X 1 + β 2 X 2 + β 3 X 3 + ε ○ Y: Dependent variable ○ X 1, X 2, and X 3 : Independent variables ○ β 0 : Intercept ○ β 1, β 2, and β 3 : Regression coefficients ○ ε: Error term Regression is an approach for modeling the relationship between a dependent variable and one or more independent variables ○ The case of one independent variable is called simple linear regression ○ The case of more than one independent variables is called multiple linear regression Correlation vs. Regression ○ Regression can explain causal relationship but correlation cannot

47. Multiple Regression (Concepts to know) R 2 ○ The proportion of the original variance in dependent variable that is explained by the regression equation Multicollinearity ○ A problem referring to correlated independent variables Causes unexpected signs Small t-value ○ Can be detected by VIF and Tolerance

48. SPSS Example (Multiple Regression Analysis) Analyze  Regression  Linear… Statistics  Collinearity diagnostics Hypotheses ○ H 1 : Perceived quality of atmospherics will increase the overall satisfaction of restaurant customer ○ H 2 : Perceived quality of food will increase the overall satisfaction of restaurant customer ○ H 3 : Perceived quality of service will increase the overall satisfaction of restaurant customer

49. SPSS Example (Multiple Regression Analysis) Results #1 (Model Summary) ○ R 2 =.311 31.1% of total variance in Y has been explained by regression equation Results #2 (Post-Hoc test) ○ F-value = 43.535 (p <.05) At least one coefficient is not equal to zero

50. SPSS Example (Multiple Regression Analysis) Result #3: Coefficients and Multicollinearity Diagnostics ○ H 1 : t-value = 6.620 (p <.05) One unit increase in atmospheric quality significantly increases 0.329 unit in overall satisfaction H 1 : Supported ○ H 2 : t-value = 6.081 (p <.05) One unit increase in food quality significantly increases 0.277 unit in overall satisfaction H 2 : Supported ○ H 3 : t-value = 1.108 (p >.05) Increase in service quality does not significantly increase overall satisfaction H 1 : Not Supported No multicollinearity detected VIF < 10 Tolerance >.10

51. Exploring Relationships between Variables d. Advanced Methodologies

52. Factor Analysis ○ Define the underlying structure among the variables ○ Reduce the number of variables that will be used Reduces multiple and similar measurement items to one dimension (variable) Correlation Table Factor 1 (Physical Environment) Factor 2 (Service Quality)

53. SPSS Example (Factor Analysis) Analyze  Dimension Reduction  Factor… ○ Extraction  Principal component ○ Rotation  Varimax 14 measurement items related to the quality of coffee shops ○ Examining whether these measurement items can be reduced to few dimensions

54. SPSS Example (Factor Analysis) Result #1: Communalities ○ The variance accounted for by the factors Result #2: Total Variance Explained ○ 4 Factors were identified and 67.03% of total variance was explained

55. Result #2: Total Variance Explained ○ 4 Factors were identified (# of factors with Eigen value > 1) ○ 67.03% of total variance was explained by four factors

56. SPSS Example (Factor Analysis) Result #3: Factor Loadings ○ Loadings lower than 0.4 was not displayed Name each factor based on the measurement items included ○ Factor 1: Value ○ Factor 2: Advertisement ○ Factor 3: Accessibility ○ Factor 4: Coffee Quality

57. Utilization of Factors Utilization of Extracted Factors ○ Extracted factors in the previous example can be used for multiple regression analysis Things to consider 1. Utilization of factor scores Standardized score – Mean = 0, Standard Deviation = 1 2. Utilization of mean value Calculate mean value for measurement items included in each factor – Mean ≠ 0, Standard Deviation ≠ 1

58. SPSS Example (Factor Score + Multiple Regression Analysis) Hypotheses ○ H 1 : Perceived value will increase the overall satisfaction of coffee shop customer ○ H 2 : Perceived quality of advertisement will increase the overall satisfaction of coffee shop customer ○ H 3 : Perceived quality of accessibility will increase the overall satisfaction of coffee shop customer ○ H 4 : Perceived quality of coffee will increase the overall satisfaction of coffee shop customer Analyze  Dimension Reduction  Factor…  Score ○ Save as variables Analyze  Regression  Linear… (Move factor scores as independent variables)

59. SPSS Example (Factor Score + Multiple Regression Analysis) ○ R 2 = 0.314 ○ F-value = 32.337 ○ VIF, Tolerance = 1 (No multicollinearity) Varimax rotation minimizes correlation between dimensions Hypotheses Testing ○ H 1 : Perceived value significantly increase the overall satisfaction (Supported) ○ H 2 : Perceived quality of advertisement does not have significant influence on the overall satisfaction (Not supported) ○ H 3 : Perceived quality of accessibility does not have significant influence on the overall satisfaction (Not supported) ○ H 4 : Perceived quality of coffee significantly increase the overall satisfaction (Supported) Results

60. SPSS Example (Mean Value + Multiple Regression Analysis) How to calculate mean value in SPSS? Transform  Compute Variable… ○ Select ‘Statistical’ and ‘Mean’

61. Type variable name you want to create Numeric Expression ○ MEAN (m7, m5, m6, m8) ○ Generate mean value for each factor SPSS Example (Mean Value + Multiple Regression Analysis)

62. SPSS Example (Factor Score vs. Mean Value) Comparison of Results ○ Mean Value ○ Factor Score

63. SPSS Example (Factor Score vs. Mean Value) Similarity ○ Standardized β ○ Sign of coefficients ○ Significance level Differences ○ Unstandardized coefficients ○ t-value ○ Collinearity diagnostics Varimax Rotation: No collinearity at all Mean Value: Collinearity may exist Utilization of factor score or mean score depends on researcher’s decision