Chapter 11 Basic Data Analysis for Quantitative Research

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 (ANOVA) • Utilize perceptual mapping to present research findings 11 -2

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 – Hypothesis testing 11 -3

Measures of Central Tendency Mean • The arithmetic average of the sample • All values of a distribution of responses are summed and divided by the number of valid responses Median • The middle value of a rank-ordered distribution • Exactly half of the responses are above and half are below the median value Mode • The most common value in the set of responses to a question • The response most often given to a question 11 -4

Exhibit 11. 2 - Dialog Boxes for Calculating the Mean, Median, and Mode 11 -5

Measures of Dispersion Range • The distance between the smallest and largest values in a set of responses Standard deviation • The average distance of the distribution values from the mean Variance • The average squared deviation about the mean of a distribution of values 11 -6

Exhibit 11. 3 - Measures of Dispersion 11 -7

Preparation of Charts • Charts and other visual communication approaches should be used whenever practical – Help information users to quickly grasp the essence of the results developed in data analysis – Can be an effective visual aid to enhance the communication process • Add clarity and impact to research reports and presentations 11 -8

How to Develop Hypotheses • Researchers have preliminary ideas regarding data relationships based on research objectives – Hypotheses - Ideas derived by researchers from previous research, theory and/or the current business situation • Developed prior to data collection – As a part of the research plan 11 -9

How to Develop Hypotheses • Null hypothesis - Based on the notion that any change from the past is due entirely to random error • Alternative hypothesis - States the opposite of the null hypothesis 11 -10

Sample Statistics and Population Parameters • Sample statistics are useful in making inferences regarding the population’s parameter – Population parameter - A variable or some sort of measured characteristic of the entire population 11 -11

Choosing the Appropriate Statistical Technique • Considerations that influence the choice of a particular technique: – Number of variables – Scale of measurement – Parametric versus nonparametric statistics 11 -12

Exhibit 11. 6 - Type of Scale and Appropriate Statistic 11 -13

Univariate Statistical Tests • Used to test hypotheses when the researcher wishes to test a proposition about a sample characteristic against a known or given standard 11 -14

Exhibit 11. 7 - Univariate Hypothesis Test Using X 16 –Reasonable Prices 11 -15

Bivariate Statistical Tests • Test hypotheses that compare the characteristics of two groups or two variables • Three types of bivariate hypothesis tests – Chi-square – t-test – Analysis of variance 11 -16

Cross-Tabulation • Useful for examining relationships and reporting the findings for two variables • Purpose is to determine if differences exist between subgroups of the total sample • A frequency distribution of responses on two or more sets of variables 11 -17

Exhibit 11. 8 - Example of a Cross. Tabulation: Gender by Ad Recall 11 -18

Chi-Square Analysis • Assesses how closely the observed frequencies fit the pattern of the expected frequencies – Referred to as a “goodness-of-fit” test 11 -19

Comparing Means: Independent Versus Related Samples • 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 11 -20

Using the t -Test to Compare Two Means • t-test: A hypothesis test that utilizes the t distribution – Used when the sample size is smaller than 30 and the standard deviation is unknown • Where, 11 -21

Exhibit 11. 11 - Paired Samples t-Test 11 -22

Analysis of Variance (ANOVA) • A statistical technique that determines whether three or more means are statistically different from one another • Null hypothesis for ANOVA always states that there is no difference between the dependent variable group 11 -23

Analysis of Variance (ANOVA) • F-test: The test used to statistically evaluate the differences between the group means in ANOVA 11 -24

Exhibit 11. 12 - Example of One-Way ANOVA 11 -25

Analysis of Variance (ANOVA) • Follow-up tests: A test that flags the means that are statistically different from each other – Performed after an ANOVA determines there are differences between means 11 -26

Exhibit 11. 13 - Results for Post-hoc ANOVA Tests 11 -27

n-Way ANOVA • A type of ANOVA that can analyze several independent variables at the same time • Multiple independent variables in an ANOVA can act together to affect dependent variable group means 11 -28

Exhibit 11. 14 - n-Way ANOVA Results —Santa Fe Grill 11 -29

Exhibit 11. 15 - n -Way ANOVA Means Result 11 -30

Perceptual Mapping • Used to develop maps showing the perceptions of respondents – Maps are visual representations of respondents’ perceptions of a company, product, service, brand, or any other object in two dimensions • Approaches used to develop perceptual maps – Rankings – Medians – Mean ratings 11 -31

Perceptual Mapping Applications in Marketing Research • • New-product development Image measurement Advertising Distribution 11 -32

Exhibit 11. 17 - Perceptual Map of Six Fast-Food Restaurants 11 -33

Marketing Research In Action: Examining Restaurant Image Positions—Remington’s Steak House • Run post-hoc ANOVA tests between the competitor groups – What additional problems or challenges did this reveal? • What new marketing strategies can be suggested? 11 -34