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PARAMETRIC VERSUS NONPARAMETRIC STATISTICS

PARAMETRIC VERSUS NONPARAMETRIC STATISTICS. Heibatollah Baghi, and Mastee Badii. Parametric Assumptions. Parametric Statistics involve hypothesis about population parameters (e.g., µ, ρ ).

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PARAMETRIC VERSUS NONPARAMETRIC STATISTICS

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  1. PARAMETRIC VERSUS NONPARAMETRIC STATISTICS Heibatollah Baghi, and Mastee Badii

  2. Parametric Assumptions • Parametric Statistics involve hypothesis about population parameters (e.g., µ, ρ). • They require assumptions about the population distribution. For example, the assumptions for t test for independent samples are: • Each of the two populations of observations is normally distributed • The populations of observations are equally variable : that is σ2 = σ2. (Assumption of homogeneity of variance )

  3. Nonparametric Alternative • The parametric assumptions cannot be justified: normal distribution, equal variances, etc. • The data as gathered are measured on nominal or ordinal data • Sample size is small.

  4. Spearman Rank Correlation • The Spearman rank correlation is used when: • Distribution assumptions required by Pearson r are in question • Small sample size

  5. Example • X: The student’s popularity measure • Y: The student’s average academic achievement • Research questions : Is popularity related to achievement ?

  6. Test of Association Using Spearman Rank Correlation Because of doubts regarding the distributional assumptions coupled with small sample size, select the Spearman Rank Correlation to answer this question

  7. Calculation of Spearman Rank Correlation Spearman rank correlation

  8. Continued Calculation of Spearman Rank Correlation Difference between ranks

  9. Continued Calculation of Spearman Rank Correlation Number of cases

  10. Continued Calculation of Spearman Rank Correlation X: The student’s popularity measure Y: The student’s average academic achievement

  11. Continued Calculation of Spearman Rank Correlation

  12. Continued Calculation of Spearman Rank Correlation

  13. Continued Calculation of Spearman Rank Correlation

  14. Continued Calculation of Spearman Rank Correlation

  15. Continued Calculation of Spearman Rank Correlation

  16. Continued Calculation of Spearman Rank Correlation

  17. Test of Significance • Calculated rRank= -0.26 • Critical value for alpha 0.05 for Spearman Rank Correlation with 8 subjects = 0.738 • Calculated rRanks is less than critical value • The relation between Popularity and academic achievement is not statistically significant

  18. When to Use Which Test

  19. Continued When to Use Which Test

  20. Continued When to Use Which Test

  21. Take Home Lesson Spearman Rank Correlation can be used on ordinal data

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