MKTG3001 Chap.9 Testing Group Differences and Correlation
Testing Group Differences and Correlation
This chapter moves from describing survey data to testing it.
You learn to frame a null hypothesis (no difference between groups) against an alternative hypothesis (a difference exists), and to reject the null only when p < 0.05. Every hypothesis needs two named variables: the independent variable sorts respondents into groups, and the dependent variable is the Likert-type rating averaged within each group.
Two groups call for an independent-samples t-test; three or more call for a one-way ANOVA, and the count comes from the groups present in the data rather than from how many answer boxes the questionnaire printed.
The chapter closes with Pearson correlation, which links two Likert-type variables through a coefficient r between −1.00 and +1.00: its sign gives direction, its magnitude gives strength, and a value from 0.61 to 0.80 is classed as strong.
What this chapter covers
- 01
Null and alternative hypotheses for group differences
- 02
Independent and dependent variables in a hypothesis
- 03
Independent-samples t-test for exactly two groups
- 04
One-way ANOVA for three or more groups
- 05
Choosing a test by the groups in the data
- 06
Pearson correlation direction and strength
Worked example · free
Reading correlation direction and the strong range for bike-share ratings
- 1Pearson correlation fits because each pair consists of two Likert-type variables, and every coefficient lies on a scale running from −1.00 to +1.00.
- 2For app ease and renewal, r = 0.72 is positive, so members who find the app easier also tend to report a higher chance of renewing; 0.72 falls inside the 0.61 to 0.80 band, which makes the association strong.
- 2For waiting and satisfaction, r = −0.35 is negative, so more frequent waiting accompanies lower satisfaction; its magnitude sits much closer to zero than 0.72 does, so this link is clearly weaker. Neither coefficient shows that one variable predicts the other.
Key terms
- Null hypothesis
- A testable statement, written H₀, proposing that no difference exists between the groups being compared.
- Independent variable
- A categorical variable that separates respondents into the groups whose means are compared.
- Independent-samples t-test
- A test that checks whether the mean of a variable differs significantly between exactly two independent groups.
- One-way ANOVA
- A test that checks whether the mean of a variable differs significantly across three or more independent groups.
- Pearson correlation
- A coefficient, r, ranging from −1.00 to +1.00, that summarises the direction and strength of the linear relationship between two variables.
Testing Group Differences and Correlation FAQ
How do I decide between a t-test and ANOVA for survey data?
Count the groups your coded data actually contains for the grouping question. Two groups point to an independent-samples t-test; three or more point to one-way ANOVA. A question with five printed options that you later merge into two categories therefore needs a t-test, so always check the recoding before naming the method.
What does fail to reject the null hypothesis mean?
It means the p-value was not below 0.05, so the sample did not provide enough evidence of a difference between groups. It is not proof that the groups are identical. In an essay, say there is no statistically significant difference and avoid claiming the groups are the same.
Is a correlation of 0.7 strong in marketing research?
Under the bands taught in this course, a coefficient between 0.61 and 0.80 counts as strong, so 0.7 qualifies. Strength depends on the size of the number, not its sign, so a coefficient of −0.7 describes an equally strong relationship running in the negative direction.
Can I use Pearson correlation with a multiple-choice question?
Only when both variables are Likert-type ratings. A single-response question that lists categories such as brands or store formats has no meaningful numeric order, so a coefficient computed on its codes would be meaningless. For a categorical grouping question paired with a rating, compare group means with a t-test or ANOVA instead.
Why can't I just compare the two group averages?
Sample means almost always differ a little by chance. A gap of 0.4 on a five-point scale might be real or might be noise from who happened to answer. The statistical test converts that gap into a p-value, and only a value below 0.05 lets you report the difference as significant.
Exam move
Revise this chapter as a sequence of decisions rather than a list of definitions. Take any rating question you can invent, pair it with a grouping question, and practise saying aloud which variable is independent, which is dependent, and how many groups the data hold. Then write H₀ and H₁ for that pair from memory.
For correlation, drill the two-part reading: sign for direction, magnitude for strength, and memorise the strong band of 0.61 to 0.80 exactly. Because the exam is closed book and handwritten, rehearse 200 to 250 word answers to appropriateness questions in the style of the reflective questions: a verdict, a justification naming the variable types and group count, and a plain-language conclusion.
Time yourself so each answer fits a realistic share of a two-hour paper.
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