M303 Hypothesis Testing IV
Where we are
One-sample · paired · independent · ANOVA · chi-square
Choose the test, read the evidence, and state the marketing conclusion.
Learning Objectives
The test from the number, scale, and structure of the variables.
The null, alternative, and direction before running a test.
Statistical evidence without “accepting” the null or claiming causality.
The five tests to the historical Microsoft campaign case.
Previous class review
ANOVA tests whether every pair of population means differs.
FALSEA chi-square test compares observed counts with counts expected under independence.
TRUEA significant chi-square result by itself establishes that one categorical variable caused the other.
FALSEWith exactly two independent groups, ANOVA and the independent t-test address the same global mean-comparison question.
TRUEStart with the structure—not the software
One continuous variable compared with μ₀.
Two continuous measurements from each respondent.
Continuous outcome across two independent groups.
Continuous outcome across three or more groups.
Association between categorical variables.
Application 1: must fairness exceed 5?
A client will change price only if the population mean fairness rating exceeds 5.0 on a 7-point scale. The sample mean is 5.5.
What test and alternative hypothesis match the decision?
H₀: μ = 5
Hₐ: μ > 5
Application 2: does interest differ by age?
Interest is yes/no. “Yes” responses: 59 of 120 under age 18, 38 of 110 ages 18–25, and 21 of 70 over age 25.
Does intention to visit differ across age groups?
Test whether interest is independent of age group.
Application 3: is Brand Y rated higher?
Every participant rates Brand X, Brand Y, and Brand Z on the same 11-point scale, from very unfavorable to very favorable; the midpoint represents indifference. Brand Y is the focal brand.
How do we test whether Brand Y’s mean exceeds Brand X’s?
Pair each participant’s Brand Y and Brand X ratings.
Capstone case: evaluate the “I’m a PC” campaign
Who saw the campaign?
Who liked the campaign?
Is price more important than design or coolness?
Was the average response positive?
Question 1: what predicts campaign reach?
Does PC ownership affect whether consumers have seen the campaign?
χ²Does Mac ownership affect whether consumers have seen the campaign?
χ²Ownership and campaign reach are categorical variables. Report association, not causation.
Question 2: who evaluates the campaign differently?
Does mean campaign evaluation differ by PC ownership?
Independent tDoes mean campaign evaluation differ by Mac ownership?
Independent tDoes mean evaluation differ across combined PC/Mac ownership groups?
ANOVA FQuestion 3: is price the dominant attribute?
Is the mean importance of price higher than the mean importance of design?
Paired tIs the mean importance of price higher than the mean importance of coolness?
Paired tEach respondent rates the importance of all three attributes.
Question 4: was average evaluation positive?
First, summarize how participants rated the campaign across the available dimensions.
Then test whether the average evaluation exceeds the neutral benchmark.
Use descriptive statistics for the profile of ratings.
Use a right-tailed one-sample t-test for the average-positive claim.
A p-value is only the start of the interpretation
Reject or fail to reject H₀.
Which mean is higher, or which pattern differs?
How large is the difference or association?
What action does the evidence support?
Use careful conclusion language
The data are sufficiently inconsistent with H₀ at the chosen significance level.
Fail to reject H₀; do not claim that H₀ has been proven true.
It may reflect a small effect, noisy measurement, insufficient sample size, or a genuinely null relationship.
Practice: name the test before revealing it
Campaign reach by PC ownership
Chi-squareCampaign evaluation across two ownership groups
Independent tCampaign evaluation across combined PC/Mac ownership categories
ANOVA FPrice importance compared with design importance for the same respondents
Paired tAverage campaign evaluation compared with a neutral benchmark
One-sample tTo sum up
Sampling error creates uncertainty.
Hypothesis tests measure how surprising the data are under H₀.
State H₀ and Hₐ before testing.
Let the number, type, and structure of variables choose the test.
Use one-sample, paired, and independent t-tests for mean questions.
Use ANOVA for several group means.
Use chi-square for categorical association.
Translate p-values into cautious marketing conclusions.
Next class
- Describe the direction and strength of an association.
- Separate association from prediction.
- Interpret regression coefficients in a marketing context.