CHAPTER 16What The Experts SayLearning ObjectivesGet This! My Name Is Important to MeGet This! My Name Is Important to Me – cont’dNow Ask YourselfParametric TestsTests of DifferenceZ-test: Difference Between Meanst-Test: Difference Between MeansDifference Between Two Proportions and Independent SamplesSlide 12Slide 13Analysis of VarianceSlide 15Variance Between GroupsSlide 17Variance Within GroupsF-TestTests of AssociationsScatter DiagramsRegression AnalysisRegression Equation and Regression LineSlide 24Least-Squares MethodSlide 26Standard Deviation of RegressionSlide 28Correlation AnalysisTotal Deviation, Coefficient of Determination, and Correlation CoefficientSlide 31Coefficient of Determination (r2)Correlation CoefficientDecision Time!Net ImpactChapter 16 End of PresentationMarketing Research, 2nd EditionAlan T. ShaoCopyright © 2002 by South-Western42510011 0010 1010 1101 0001 0100 1011PPT-1CHAPTER 16BIVARIATE STATISTICS:PARAMETRIC TESTSMarketing Research, 2nd EditionAlan T. ShaoCopyright © 2002 by South-Western42510011 0010 1010 1101 0001 0100 1011PPT-2What The Experts SayWhat’s the point in doing surveys if you can’t analyze the data? Converting and reducing data into meaningful results is a marketing researcher’s key responsibility.--SPSS Web Page, “Analysis,” http://www.spss.com/spssmr/solutions/analysis.htm, February 19, 2001.Marketing Research, 2nd EditionAlan T. ShaoCopyright © 2002 by South-Western42510011 0010 1010 1101 0001 0100 1011PPT-3Learning Objectives•Discuss the importance of parametric statistics•Describe the difference between tests of differences and tests of associations•Explain how to use z- and t-tests to compare two groups•Describe and calculate the F-test•Discuss the meaning and use of analysis of variance•Describe correlation and regression analyses•Calculate and interpret correlation and regression statistics•Compute one-way analysis of variance manually and by computerMarketing Research, 2nd EditionAlan T. ShaoCopyright © 2002 by South-Western42510011 0010 1010 1101 0001 0100 1011PPT-4Get This! My Name Is Important to Me•In the book, How to Win Friends and Influence People, Dale Carnegie wrote, “Remember that a person’s name is to that person the sweetest and most important sound in any language.”•A professor classified students into three groups: names (those he could remember), no-names (those he could not remember), and neutral-names (those whose names he never made reference to during the conversations).•At the end of a meeting with each student, the professor would state “Oh, I have to ask you something else. My wife is selling cookies for the church. If you want any, they’re only 25 cents.” This offer was made to examine if remembrance of a student’s name made a difference regarding whether or not he or she would comply with a request (that is, purchase the cookies).Marketing Research, 2nd EditionAlan T. ShaoCopyright © 2002 by South-Western42510011 0010 1010 1101 0001 0100 1011PPT-5•The results were analyzed using several different statistical techniques, one being analysis of variance.•He found:–Not being able to remember a student’s name produced compliance results (that is, purchasing the cookies) no different from those of a condition in which the issue of a student’s name was never raised.–The higher purchasing rate for those students whose names were remembered indicates that name remembrance facilitates compliance.Get This! My Name Is Important to Me – cont’dMarketing Research, 2nd EditionAlan T. ShaoCopyright © 2002 by South-Western42510011 0010 1010 1101 0001 0100 1011PPT-6Now Ask Yourself•Based on your knowledge of statistics, do you have faith in the findings since various statistical tools were used to analyze the data? Was it really necessary for the researchers to run statistical tests to generate their findings?•What was meant by, “The professor decided to use this method [analysis of variance] since it tests whether there are statistically significant differences among the means of each of the student groups”?•Were the results surprising to you? If so, what did you expect? If not, why not?Marketing Research, 2nd EditionAlan T. ShaoCopyright © 2002 by South-Western42510011 0010 1010 1101 0001 0100 1011PPT-7Parametric Tests•The sample data should be randomly drawn from a normally distributed population.•The sample data drawn must be independent of each other.•When examining central tendency for which two or more samples are drawn, the population should have equal variances.The hypothesis tests assume that variables under investigation are measured using either interval or ratio scales. Furthermore, it is necessary to make some additional assumptions.Marketing Research, 2nd EditionAlan T. ShaoCopyright © 2002 by South-Western42510011 0010 1010 1101 0001 0100 1011PPT-8Tests of Difference•the first population and its samples are identified by subscript 1•the second population and its samples are identified by subscript 2• 1 represents the mean of the sample drawn from population 1• 2 represents the mean of the sample drawn from population 2Can be used whenever a researcher is interested in comparing some characteristic of one group with a characteristic of another and determining whether or not a significant difference exists between the two groups.Marketing Research, 2nd EditionAlan T. ShaoCopyright © 2002 by South-Western42510011 0010 1010 1101 0001 0100 1011PPT-9 where [Formula 16-1] where = the difference between sample means = the difference between population means and = sample means for the two variables = standard error of the difference between the meansZ-test: Difference Between MeansUsed to determine whether two population means differ from each other. This can be determined by using either the z-test or t-test, depending on the sample size and whether or not the population standard deviation is known for either group.If the sample size is at least 30 and the population standard deviations are known, the z-test should be used.)(212121)()(xxXXz222112)(21nnxx)(21XX )(211X2X21xx Marketing Research, 2nd EditionAlan T. ShaoCopyright © 2002 by South-Western42510011 0010 1010 1101 0001 0100 1011PPT-10t-Test: Difference Between MeansWhen the sample size is less than 30 and the population standard