Research for Marketing Decisions

Dr. Thomas Lee Trimester 1, 2018

Important announcement

• AT3 is due Monday 16 April (study week) by 11.30pm

• Submit through relevant TII links on Moodle site

• AT3 is worth 40%

– Research proposal = 60%

• See case study and marking criteria on Moodle site

– Data analysis report = 40%

• See brief and marking criteria on Moodle site

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On the agenda today: • Week 8 Content

– Data Analysis: Basic Concepts • Frequency distribution (or simple tabulation) • Hypothesis testing • Cross-tabulation (via chi-square test)

• Week 9 content – Data analysis: Hypothesis testing

• Test of differences – One-sample – Independent-samples – Paired-samples

• SPSS Practice Questions

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Data Analysis: Data Preparation and Basic Concepts

WEEK 9 READINGS: CHAPTERS 11 AND 12

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Classification of hypothesis testing procedures

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Hypothesis Testing

Test of Association Test of Difference

Recap: Types of data and statistical techniques

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Nominal and ordinal scales

Non-metric data (categorical)

Non-parametric tests – Frequencies

– Cross-tabulations – Chi-square (hypothesis testing)

Interval and ratio scales

Metric data (numerical)

Parametric tests – t-tests – ANOVA

– Regression

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Recap: Hypothesis testing process

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Recap: Probability values in hypothesis testing

• p-value is the largest level of significance (typically 0.05 or 5%) at which we would not reject H0 (i.e., making Type I error)

• In general, the smaller the p-value, the greater the confidence in sample findings

– E.g., p-value of 0.78 vs. 0.02

• If the computed probability estimate or p-value is smaller than the significance level (usually 5% or 0.05), reject H0. If the probability estimate or p-value is larger than the significance level, do not reject H0.

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Hypothesis testing related to differences

• In tests of associations, the null hypothesis is that there is no association between the variables (H0: . . is not related to . . ). Tests of association could be done using non-parametric (e.g., chi-square) or parametric (e.g., correlation, regression) tests.

• In tests of differences, the null hypothesis is that there is no difference (H0: . . is not different from . . .). Tests of differences could relate to means or proportions.

• Parametric tests assume that the variables of interest are measured on at least an interval scale (e.g., 7-point Likert).

• These tests can be further classified based on whether one or two samples are involved and whether the samples are independent or paired (i.e., one-sample vs. independent-samples vs. paired-samples t-tests).

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Hypothesis testing related to differences

• The samples are independent if they are drawn randomly from different populations.

• For the purpose of analysis, data pertaining to different groups of respondents (e.g., males and females), are generally treated as independent samples, when examining differences between the two.

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Hypothesis testing related to differences

• The samples are paired when the data for the two samples relate to the same group of respondents (e.g., before and after service encounter).

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Conducting t-tests

1. Problem definition/RQ 2. Formulate null and alternative hypos 3. Select an appropriate test (e.g., one-sample,

independent-samples or paired-samples) 4. Choose level of significance 5. Determine probability estimate 6. Compare with level of significance 7. Reject or do not reject H0 8. Draw marketing research conclusion

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One-sample t-test

• Testing population mean against a known or given standard

• Scenario: – Based on a previous survey, the mean preference among

teenagers for Tommy Hilfiger was 5.

– It is possible that preference for Tommy Hilfiger could have increased or decreased since the last survey.

• In this case, the hypotheses take the following form:

– H0: µ = 5.0 (known or given standard) – H1: µ  5.0

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One-sample t-test

• The p-value is 0.177, which is greater than 0.05. Hence, H0 cannot be rejected.

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Two independent samples

• Examining mean differences between two different populations. For example: – Male vs. female users – Preference between teenagers and adults for TH

• In this case, the hypotheses take the following form:

• Null: Two population means are equal (no difference) • Alternative: Two population means are unequal (different)

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)()(: 210

femalemaleH  

)()(: 211

femalemaleH  

Two independent samples

• If both populations are found to have the same variance, a pooled variance estimate is computed from the two sample variances.

• If the two populations have unequal variances, the t statistic should be computed accordingly.

• An F test of sample variance may be performed if it is not known whether the two populations have equal or unequal variance. In this case, the hypotheses are:

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Equality of variances example

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ID Group Score Mean SD

1 1 10

10.8 0.979796

2 1 12

3 1 10

4 1 12

5 1 10

6 2 8

10.8 2.712932

7 2 14

8 2 10

9 2 14

10 2 8

T-tests for independent samples

• If the probability of F (the p value) is > .05, then t based on the equal variance estimate can be used (top row)

• If the probability of F (the p value) is < .05, then t based on the unequal variance estimate can be used (bottom row)

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Two independent samples: Conclusion

• Thus, the conclusion is that the teenagers (mean = 5.50) and adults (mean = 4.00) differ significantly in their preferences for the Tommy Hilfiger brand (p < .01).

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How to report

Variable Group mean

Equality of variances

Mean difference Sig.

Teens Adults

Preference for TH 5.5000 4.0000 Equal

NS 1.5000 .006**

Attitude …

Purchase intention …

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Notes: NS not significant; *p < .05; **p < .01; ***p < .001.

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Paired samples

• Examining two sets of observations in relation to the same respondents. For example:

– Do shoppers consider brand name to be more important than price?

– Same respondents rating:

• Two competing brands

• The relative importance of two product attributes

• The difference in these cases is examined by a paired- samples t-test

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Paired samples t-test

• To determine absence or existence of difference, the paired difference variable, denoted by D, is formed and its mean and variance calculated.

• The relevant hypotheses are:

H0: D = 0 (paired variables have equal means)

H1: D  0 (paired variables have unequal means)

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t-tests for paired samples

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Paired samples t-test

• A paired-samples t-test could be used to determine if teenagers differed in their preference for TH before and after seeing the new ad.

• We can see that the mean difference between the before and after variables is -2.4.

• The probability estimate or p-value is less than 0.01. As the p- value is less than 0.05, the null hypothesis should be rejected.

• Therefore, we can conclude that teenagers differed significantly in their preference for TH before (mean = 5.50) and after (mean = 7.90) seeing the new ad (p <.001).

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How to report

Variable Mean Mean difference Sig.

Preference before ad exposure 5.50 -2.40 .000***

Preference after ad exposure 7.90

Attitude towards …

Attitude towards …

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Notes: NS not significant; *p < .05; **p < .01; ***p < .001.

Types of t-test

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Type Example Hypotheses Test variables

One-sample To determine whether preference for National Park has increased or decreased since the last survey with a known score of 5.0.

H0 :  = 5.0 HA :  ≠ 5.0

One metric variable (preference for National Park)

Independent- samples To determine whether

teenagers have a difference preference than adults before entering the National Park.

H0 : 1 = 2 HA : 1 ≠ 2

One non-metric variable (categorical; e.g., age group) and one metric variable (e.g., preference)

Paired-samples To determine if there is a difference in preference before and after visiting the National Park amongst teenagers.

H0 : D = 0 HA : D ≠ 0

Two metric variables (e.g., preference before and preference after)

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Quick test

• For each of the following questions, indicate the null and alternative hypotheses, and the appropriate test to be undertaken:

– Do female and male respondents differ in their attitudes towards Ad1?

– Do respondents within the sample have a positive attitude towards Ad1?

– Do respondents within the sample differ in their attitudes towards Ad1 and Ad2?

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SPSS Exercise – Test of differences

• t-tests – One-sample – Independent-samples – Paired-samples

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One-sample t-test demo

• Suppose the management of Wollongong National Park is interested in knowing whether the mean preference amongst teenagers (Sample 1) before entering the Park has increased or decreased since the last survey which yielded a score of 5. Answer the following questions: – What are the null and alternative hypotheses? – Has the preference of teenagers changed since the last survey?

• Open the “National Park” dataset • Follow your tutor’s instructions • Refer to the “one-sample t-test” guide on Moodle

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Independent-samples t-test demo

• Suppose the management of Wollongong National Park is interested in knowing whether teenagers (Sample 1) differ from adults (Sample 2) in their preferences before entering the park. Answer the following questions: – What are the null and alternative hypotheses? – Do teenagers and adults differ in their preferences for the National

Park before entering the Park? • Open the “National Park” dataset • Follow your tutor’s instructions • Refer to the “independent-samples t-test” guide on Moodle

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Paired-samples t-test demo

• Suppose the management of Wollongong National Park is interested in knowing whether there is a difference amongst teenagers (Sample 1) in their preference before and after visiting the Park. Answer the following questions: – What are the null and alternative hypotheses? – Are the preferences of teenagers before and after visiting the

Park significantly different? • Open the “National Park” dataset • Follow your tutor’s instructions • Refer to the “paired-samples t-test” guide on Moodle

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Practice

• Open the “Internet Data” dataset. • Answer the following questions

– Test the hypothesis that the mean familiarity with the Internet exceeds 4.0.

– Is the Internet usage different for males compared to females? Formulate the null and alternative hypotheses, and conduct the test.

– Do the respondents differ in their attitude towards the Internet and attitude towards technology? Formulate the null and alternative hypotheses, and conduct the test.

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