Marketing Research Data Analysis

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MarketingResearchCh11.pdf

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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

Value of Statistical Analysis

• Helps researchers understand responses

– Summary statistics - Used to identify important information present in large amounts of data

• Basic statistics

• Descriptive analysis

Measures of Central Tendency

Mean

• Arithmetic average of a sample

Median

• Middle value of a rank-ordered distribution

Mode

• Most common value in the set of responses to a question

Measures of Dispersion

Range

• Distance between the smallest and largest values in a set of responses

Standard deviation

• Average distance of the distribution values from the mean

Variance

• Average squared deviation about the mean of a distribution of values

How to Develop and Test Hypotheses

• Review research objectives and background information

• Develop null and alternative hypotheses

• Determine the sampling distribution, and select an appropriate sampling test

• Determine the level of statistical significance

• Determine if differences are statistically significant and meaningful

• Accept or reject the null hypothesis

Analyzing Relationships of Sample Data

• Sample statistics - Used to make inferences regarding a population's parameters

– Population parameters - Variable or quantified characteristics of the entire population

• Factors influencing the choice of an appropriate statistical technique

– Number of variables

– Scale of measurement

– Parametric versus nonparametric statistics

Univariate Statistical Tests

• Used to test hypotheses with propositions about sample characteristics against given standards

– Propositions are translated to null hypotheses

• Test one variable at a time

Bivariate Statistical Tests

• Test hypotheses that compare the characteristics of two variables

• Types

– Chi-square

– t-test

– Analysis of variance

Cross-Tabulation

• Used in examining relationships and reporting the findings for two variables

• Purpose - To determine if differences exist between subgroups of the total sample

• Frequency distribution of responses on two or more sets of variables

Chi-Square Analysis

• Assesses how closely the observed frequencies fit the pattern of the expected frequencies – Referred to as a goodness-of-fit test

• Where, – n - Number of cells

– i - Cell number

Comparing Means

• 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 from the sample population

Using the t-Test to Compare Two Means

• t-test: Utilizes t distribution

– Used when the sample size is smaller than 30, and the standard deviation is unknown

• Formula to calculate the value of t

– Where,

1 2

- Mean of sample 1

- Mean of sample 2

- Standard error of the difference between the two means

S X X

Analysis of Variance (ANOVA)

• ANOVA: Determines whether three or more means are statistically different from one another

– Null hypothesis

µ1 = µ2 = µ3

• F-test: Statistically evaluates the differences between the group means in ANOVA

Analysis of Variance (ANOVA) (continued)

• Follow-up test: Flags the means that are statistically different from each other

– Performed after an ANOVA determines that there are differences between means

• n-way ANOVA: Analyzes several independent variables at the same time

– Interaction effect: Multiple independent variables in an ANOVA acting together to affect dependent variable means

Figure 11.16 - n-Way ANOVA Means Result

Descriptive Statistics

Dependent Variable:X24 -- Likely to Recommend

x30 -- Distance Driven... X32-- Gender Mean Std. Deviation N

Less than 1 mile Male 4.39 .569 74

Female 3.67 .888 12

Total 4.29 .666 86

1 -- 5 miles Male 3.78 .850 45

Female 3.68 1.077 31

Total 3.74 .943 76

More than 5 miles Male 3.00 .463 57

Female 2.65 .812 34

Total 2.87 .636 91

Total Male 3.78 .861 176

Female 3.22 1.059 77

Total 3.61 .960 253

Figure 11.16 - n-Way ANOVA Means Result (continued)

Pairwise Comparisons

Dependent Variable:X24 -- Likely to Recommend

(I) x30 -- Distance

Driven to Restaurant

(J) x30 -- Distance

Driven to Restaurant

Mean Difference

(l-J)

Std. Error Sig.-a 95% Confidence

Interval for

Difference*

95% Confidence

Interval for

Difference*

(I) x30 -- Distance

Driven to Restaurant

(J) x30 -- Distance

Driven to Restaurant

Mean Difference

(l-J)

Std. Error Sig.-a Lower Bound Upper Bound

Less than l mile 1 -- 5 miles .302* .143 .035 .021 .582

More than 5 miles 1.206* .139 .000 .932 1.479

1 -- 5 miles Less than 1 mile -.302* .143 .035 -.582 -.021

More than 5 miles .904* .117 .000 .674 1.134

More than 5 miles Less than 1 mile -1.206* .139 .000 -1.479 -.932

1 -- 5 miles -.904* .117 .000 -1.134 -.674

Based on estimated marginal means

* The mean difference is significant at the .05 level.

a. Adjustment for multiple comparisons: Least Significant Difference (equivalent to no adjustments).

Perceptual Mapping

• Used to develop maps that illustrate the perceptions of respondents

– Map - Two-dimensional visual representation

• Applications in marketing research

– New-product development

– Image measurement

– Advertising

– Distribution

Exhibit 11.18 - Perceptual Map of Six Fast-Food Restaurants

Marketing Research in Action Examining Restaurant Image Positions

• What are other areas of improvement for Remington's?

• Run post-hoc ANOVA tests between the competitor groups

– What additional problems or challenges did this reveal?

• What new marketing strategies can be suggested?