Hypothesis Testing
Hypothesis Testing
When an interesting, relevant, empirical finding emerges from data analysis based on a sample, a simple yet penetrating hypothesis test question should occur to every manager and researcher as a matter of course: Does the empirical finding represent only a sampling accident? For example, suppose a study was made of wine consumption. Data analysis revealed that a random sample of 100 California residents consumes more wine per family than a random sample of 100 New York residents. It could be that the observed difference was only caused by sampling error; in actuality, there maybe no difference between the two populations. If the difference found in the two samples could be caused by sampling fluctuations, then it makes little sense to spend additional time on the results or to base decisions on them. If, on the other hand, the results are not simply caused by sampling variations, then there is reason to consider the results further. The hypothesis test question is thus a screening question. Empirical results should pass that test before the researcher spends much effort considering them further. Although the screening question implied by a hypothesis test is primarily used only to discard or discount results, the concept and its accompanying machinery are still an important part of analysis.
A primary objective of this chapter will be to provide a real understanding of the logic of hypothesis testing. The hope is that the reader will become conditioned to asking whether the result was an accident. Just thinking c: the question at the appropriate time is half the battle. Further, an effort wil be made to help the reader think in terms of a model or set of assumptions (such as there is no difference between California and New York in per capita wine consumption) in very specific terms. Hypothesis testing provides an excellent opportunity to be rigorous and precise in thinking and in presenting results.
The calculations will be presented for several hypothesis tests, although they need not be memorized. They can be looked up when needed and, in any case, a computer usually provides them. However, a knowledge of the specific calculations of some representative tests can increase understanding substantially.
In the first section, the four steps of hypothesis testing are developed in the context of an example. This is followed by sections describing two of the most important hypothesis tests used in marketing research. The second section discusses the hypothesis test used in cross-tabulations. Here the chi-square statistic, which is useful in interpreting a cross-tabulation table, is developed. The third section presents the hypothesis test used when differences between means are involved. The difference between means was one of the association measures used in the last chapter. It alsc appears in most experiments, as the material in Chapter 10 illustrated.
When an interesting, relevant, empirical finding emerges from data analysis based on a sample, a simple yet penetrating hypothesis test question should occur to every manager and researcher as a matter of course: Does the empirical finding represent only a sampling accident? For example, suppose a study was made of wine consumption. Data analysis revealed that a random sample of 100 California residents consumes more wine per family than a random sample of 100 New York residents. It could be that the observed difference was only caused by sampling error; in actuality, there maybe no difference between the two populations. If the difference found in the two samples could be caused by sampling fluctuations, then it makes little sense to spend additional time on the results or to base decisions on them. If, on the other hand, the results are not simply caused by sampling variations, then there is reason to consider the results further. The hypothesis test question is thus a screening question. Empirical results should pass that test before the researcher spends much effort considering them further. Although the screening question implied by a hypothesis test is primarily used only to discard or discount results, the concept and its accompanying machinery are still an important part of analysis.
A primary objective of this chapter will be to provide a real understanding of the logic of hypothesis testing. The hope is that the reader will become conditioned to asking whether the result was an accident. Just thinking c: the question at the appropriate time is half the battle. Further, an effort wil be made to help the reader think in terms of a model or set of assumptions (such as there is no difference between California and New York in per capita wine consumption) in very specific terms. Hypothesis testing provides an excellent opportunity to be rigorous and precise in thinking and in presenting results.
The calculations will be presented for several hypothesis tests, although they need not be memorized. They can be looked up when needed and, in any case, a computer usually provides them. However, a knowledge of the specific calculations of some representative tests can increase understanding substantially.
In the first section, the four steps of hypothesis testing are developed in the context of an example. This is followed by sections describing two of the most important hypothesis tests used in marketing research. The second section discusses the hypothesis test used in cross-tabulations. Here the chi-square statistic, which is useful in interpreting a cross-tabulation table, is developed. The third section presents the hypothesis test used when differences between means are involved. The difference between means was one of the association measures used in the last chapter. It alsc appears in most experiments, as the material in Chapter 10 illustrated.
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