Chapter 11; Basic Data Analysis for Quantitative Research

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

Measures of Central Tendency

• Mean

• Median

• Mode

Mean

The numerical 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

Measures of Dispersion

• Range

• Standard deviation

• Variance

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.

Considerations of choosing a technique

1. Number of variables

2. Scale of measurement

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.

Means Comparison Statistical Tests

• Test hypotheses that compare the characteristics of two or more groups or variables.

  • T-test: compares 2 means

  • Analysis of Variance (ANOVA): compares 3 or more means

T-test

A hypothesis test that utilizes the t distribution.

• Especially useful when the sample size is smaller than 30 and the standard deviation is unknown.

Analysis of Variance (ANOVA)

A statistical technique that determines whether 3 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.

F-Test

The test used to statistically evaluate the differences between the group means in ANOVA

Follow-up tests (post hoc)

A test that flags the means that are statistically different from each other.

• Performed after an ANOVA determines there are differences between means.

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 2 dimensions.

Approaches used to develop perceptual maps

• Rankings

• Medians

• Mean ratings

Perceptual Mapping Applications in Marketing Research

• New product development

• Image measurement

• Advertising

• Distribution