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Testing for Differences Between Two Groups or Among More than Two Groups

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## Testing for Differences Between Two Groups or Among More than Two Groups

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**Testing for Differences Between Two Groups or Among More**than Two Groups**Why Differences are Important**• Market segmentation holds that within a market, there are different types of consumers who have different requirements, and these differences can be the bases of marketing strategies.**Why Differences are Important**• Some differences are obvious – differences between teens’ and baby boomers’ music preferences. • Other differences are not so obvious and marketers who “discover” these subtle differences may take advantage of huge gains in the marketplace.**Why Differences are ImportantMarket Segmentation**• Differences must be statistically significant • Statistical significance of differences: the differences in the sample(s) may be assumed to exist in the population(s) from which the random samples are drawn**Why Differences are ImportantMarket Segmentation**• Differences must be meaningful • Meaningful difference: one that the marketing manager can potentially use as a basis for marketing decisions**Why Differences are ImportantMarket Segmentation**• Differences should be stable • Stable difference: one that will be in place for the foreseeable future • Differences must be actionable • Actionable difference: the marketer can focus various marketing strategies and tactics, such as advertising, on the market segments to accentuate the differences between segments**Small Sample Sizes:The Use of a t Test or a z Test**• Most of the equations in this chapter will lead to the computation of a z value. • There are certain circumstances in which the z test is not appropriate. • The t-test should be used when the sample size is 30 or less. • The t-test is defined as the statistical inference test to be used with small sample sizes (n is less than or equal to 30).**Determining Statistical Significance: The P value**• Statistical tests generate some critical value usually identified by some letter; i.e., z, t or F. • Associated with the value will be a p value which stands for probability of supporting the null hypothesis (no difference or no association). • If the probability of supporting the null hypothesis is low, say 0.05 or less, we have significance!**Determining Statistical Significance: The P value**• P values are often identified in SPSS with abbreviations such as “Sig.” or “Prob.” • P values range from 0 to 1.0. • See MRI 17.1 on page 491.**Some Example P Values and Their Meaning**• First, we MUST determine the amount of sampling error we are willing to accept and still say the results are significant. Convention is 5% (0.05), and this is known as the “alpha error.”**Some Example P Values and Their Meaning**• P=0.05… • P=0.01… • P=0.10… • P=0.051… • P=0.99… significant significant not significant not significant not significant**Testing Differences: Percentages or Means?**• There are statistical tests for when a researcher wants to compare the means or percentages of two different groups or samples. • Percentages are calculated for questions with nominal or ordinal level of measurement. • Means are calculated for questions with interval or ratio (metric level of measurement.)**Testing the Difference Between Two Percentages**• Null hypothesis: no difference between the means being compared • Alternative hypothesis: a true difference between the compared means**Testing the Difference Between Two Percentages**• Finding if the difference between two percentages is significant? • Finding arithmetic differences between %s. • Translate the difference into number of standard errors from hypothesized value of 0. • Make an assessment of the probability of support for the null hypothesis. See formula…**Testing the Difference Between Two Percentages (p. 492)**• Formula for significance of the difference between two percentages:**How do you know when the results are significant?**• If the null hypothesis is true we would expect there to be 0 differences between the two percentages. • Yet we know that, in any given study, differences may be expected due to sampling error. • IF the null hypothesis were true, we would expect 95% of the z scores computed from 100 samples to fall between + and -1.96 standard errors.**How do you know when the results are significant?**• IF the computed z value is greater than + or -1.96, it is not likely that the null hypothesis of no difference is true. Rather, it is likely that there is a real statistical difference between the two percentages.**2.5%**2.5% 95% +1.96 -1.96 Supported Not Supported Not Supported Tests of Differences between the Percents of 2 Groups p1 = p2 p1 > p2 p1 < p2**An Example: Testing the Difference Between Two Percentages**(p. 495) • Last year a Harris Poll showed 40% of surveyed companies were coming to college campuses to hire seniors (n=400 companies surveyed). • This year, the Harris Poll reported the percentage is 65% (n=100 companies surveyed). • Is this a significant difference?**An Example: Testing the Difference Between Two Percentages**(p. 495) • Applying the formula: P1=65 and P2=40 • Z=4.51 • Since the z value is greater than + or -1.96, the difference between the two percentages is significant!**Using SPSS to Test the Difference Between Two Percentages**• SPSS does not perform tests of significance of the difference between the percentages of two groups, but you can use SPSS to generate the relevant information and perform a hand calculation. • ANALYZE, FREQUENCIES will produce the percentages you need.**Testing the Difference Between Two Means**• The procedure for testing the significance of difference between two means from two different samples is identical to the procedure for testing two percentages. • Equations differ due to the use of a metric (interval or ratio) scale. • Note: Only use this test with large samples (30+).**An Example**• Sports Soft Drinks: the difference between males (9) and females (7.5) is significant; z =6.43.**Using SPSS to Test Differences Between Two Group Means**• The t-test is used to compare differences between two means (remember: “t for two”). • But the types of t-test depends upon whether the two groups upon which the means are calculated are independent (separate groups) or paired (the same group).**Using SPSS to Test Differences Between Two Group Means**• If the two groups are different, i.e., males vs. females, you would use INDEPENDENT SAMPLES t-test. • If the two groups are from the same sample, you would use PAIRED SAMPLES t-test.**An Example**• Is there a difference between subscribers vs. non-subscribers to City Magazine on “likely patronage”? • Since “likely patronage” is an interval scale, we can calculate a mean score. • There are two independent groups: subscribers vs. non-subscribers.**An Example**• To determine if subscribers’ mean score on “likely” is different from non-subscribers’ mean on “likely,” we should use SPSS: • ANALYZE, COMAPRE MEANS, INDEPENDENT SAMPLES T-TEST (See p. 500.)**An Example**• Is there a difference between the mean for “prefer simple décor” vs. the mean for “prefer elegant décor”? • Both “prefer simple décor” and “prefer elegant décor” are intervally scaled so it is proper to calculate a mean for each question.**An Example**• Second, since the same members of the sample answered both questions, the two groups generating the means to these questions are not independent, they are paired. • Under these conditions, it is appropriate to use SPSS: • ANALYZE, COMPARE MEANS, PAIRED SAMPLES T-TEST (See p. 503.)**Online Surveys and Databases:A “Significance” Challenge**to Marketing Researchers • Sample size has a great deal to do with statistical significance. • Sample size n appears in statistical formulas dealing with differences, confidence intervals, hypothesis tests, etc. • Online surveys allow data collection from large sample sizes, so most tests may be found to be significant • The difference should be meaningful as well.**Testing for Significant Differences Among More than Two**Groups • ANOVA • Analysis of variance (ANOVA): used when comparing the means of three or more groups • ANOVA will “flag” when at least one pair of means has a statistically significant difference, but it does not tell which pair.**Testing for Significant Differences Among More than Two**Groups • When the F values “Sig.” is less than or equal to 0.05, ANOVA is telling you that “at least one pair of means is significantly different.” • To determine which pair(s) are different, you must rerun the test and select a POST HOC test (Duncan).**Sammenligning af gennemsnittet for flere end to populationer**i Studievalgsundersøgelsen**Testing for Significant Differences Among More than Two**Groups • Output shows Sig. is 0.000 meaning that with significance level 5% at least one pair of means is different. • Now rerun the ANOVA but select Duncan under the POST HOC button.**stx afviger signifikant fra htx**• stx, hhx og hf afviger ikke signifikant fra hinanden • hhx, hf og htx afviger heller ikke signifikant fra hinanden • Bemærk, intransitiviteten!**In Summary: Test of Differences Among More than Two Groups**• The basic logic • ANOVA (Analysis of Variance). • Test all pairs of averages simultaneously**In Summary: Test of Differences Among More than Two Groups**• If no pair is different at the 95% level of confidence, stop the analysis and say all pairs are “Equal.” • If at least one pair is different at the 95% level of confidence, make a table to show what pairs are “Equal” or “Unequal” by running post hoc test.