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Statistics: Principles and Methods, 7th Edition by Gouri K. Bhattacharyya, Richard A. Johnson

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15

Nonparametric Inference

1 The Wilcoxon Rank-Sum Test for Comparing Two Treatments

2 Matched Pairs Comparisons

3 Measure of Correlation Based on Ranks

4 Concluding Remarks

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Wines can be ranked without reference to a quantitative scale of measurement. Individuals use non-quantitative characteristics to help select their favorite wines.

Selecting the Best Vintage

Using their professional judgment, wine critics do give a numeral rating as a guide to overall qualitative placement and wine quality. However, ratings among critics differ on the same bottle of wine and even the meaning of 90 points on one scale is different from that of 90 points on another critic's scale. Ratings can never substitute for your own palate or your own wine tasting rankings.

The term nonparametric pertains to inference procedures that apply to any population distribution, not just a normal distribution. Nonparametric procedures typically utilize simple aspects of the sample data such as order relationships. Stretching or compressing the scale of measurement does not change them. Consequently, the null distribution of a nonparametric test statistic can be determined without regard to the underlying distribution.

What type of observations are especially suited to a nonparametric analysis? Characteristics like degree of apathy, taste preference, and surface gloss cannot be evaluated on an objective numerical ...

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