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Basic Data Analysis for Quantitative Research

Basic Data Analysis for Quantitative Research . 11. McGraw-Hill/Irwin. Learning Objectives. Explain measures of central tendency and dispersion Describe how to test hypotheses using univariate and bivariate statistics Apply and interpret analysis of variance

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Basic Data Analysis for Quantitative Research

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  1. Basic Data Analysis for Quantitative Research 11 McGraw-Hill/Irwin

  2. Learning Objectives • Explain measures of central tendency and dispersion • Describe how to test hypotheses using univariate and bivariate statistics • Apply and interpret analysis of variance • Utilize perceptual mapping to present research findings

  3. Statistical Analysis • Every set of data collected needs some summary information developed that describes the numbers it contains • Central tendency and dispersion, • Relationships of the sample data, and • Hypothesis testing

  4. Mode Response Most Often Given to a Question Median Middle Value of a Rank Ordered Distribution Measures of Central Tendency Mean Arithmetic Average

  5. Measures of Central Tendency • Each measure of central tendency describes a distribution in its own manner: • for nominal data, the mode is the best measure. • for ordinal data, the median is generally the best. • for interval or ratio data, the mean is generally used.

  6. Measures of Dispersions • Describes how close to the mean or other measure • of central tendency, the rest of the values fall Range Distance between the smallest and largest value in a set Standard Deviation Measure of the average dispersion of the values about the mean

  7. Exhibit 11.3 Output for Measures of Dispersion

  8. 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 Hypothesis Testing

  9. Univariate Tests of Significance • Tests of one variable at a time • z-test • t-test • Appropriate for interval or ratio data

  10. Exhibit 11.7 Univariate Hypothesis Test Using X16

  11. Bivariate Statistical Tests • Compare characteristics of two groups or two variables • Cross-tabulation with Chi-Square • t-test to compare two means • Analysis of variance (ANOVA) to compare three or more means

  12. Exhibit 11.8 Cross-Tabulation

  13. Chi-Square Analysis • Chi-square analysis enables the researcher to test for statistical significance between the frequency distributions of two or more nominally scaled variables in a cross-tabulation table to determine if there is any association between the variables

  14. Exhibit 11.9 SPSS Chi-Square Crosstabulation Example

  15. Comparing means • Requires interval or ratio data • The t-test is the difference between the means divided by the variability of random means • The t-value is a ratio of the difference between the two sample means and the std error • The t-test tries to determine if the difference between the two sample means occurred by chance

  16. Exhibit 11.10 Comparing Two Means with Independent Samples t-Test

  17. Exhibit 11.11 Paired Samples t-Test

  18. Analysis of Variance • Analysis of Variance (ANOVA) is a statistical technique that determines if three or more means are statistically different from each other • The dependent variable must be measurable; either interval or ratio scaled • The independent variable must be categorical • “One-way ANOVA” means that there is only one independent variable

  19. F-Test • The F-test is the test used to statistically evaluate the differences between the group means in ANOVA

  20. Total Variance in a Set of Responses Can Be Separated Into Between Group and Within Group Variance. Larger the Difference in the Variance Between Groups, the Larger the F-Ratio. The Higher (Larger) the F-Ratio, the More Likely It is That the Null Hypothesis Will be Rejected. Determining Statistical Significance using F-Test

  21. Follow-up Tests • Anova does not tell us where the significant differences lie – just that a difference exists • Tukey • Duncan • Scheffe

  22. n-way ANOVA • Appropriate for multiple independent variables and for experimental designs with multiple variables involved in groups • Example: men and women are shown humorous and non-humorous ads and then attitudes toward brand are measured. IV = gender and ad type

  23. Exhibit 11.12 Example ANOVA

  24. Exhibit 11.14 Post-hoc ANOVA Test

  25. Perceptual Mapping • Perceptual mapping is a process that is used develop maps showing the perceptions of respondents • The maps visually represent respondent perceptions in two dimensions

  26. Exhibit 11.19 Perceptual Map of Fast-Food Restaurants

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