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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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**PARAMETRIC VERSUS NONPARAMETRIC STATISTICS**Heibatollah Baghi, and Mastee Badii**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 )**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.**Spearman Rank Correlation**• The Spearman rank correlation is used when: • Distribution assumptions required by Pearson r are in question • Small sample size**Example**• X: The student’s popularity measure • Y: The student’s average academic achievement • Research questions : Is popularity related to achievement ?**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**Calculation of Spearman Rank Correlation**Spearman rank correlation**Continued**Calculation of Spearman Rank Correlation Difference between ranks**Continued**Calculation of Spearman Rank Correlation Number of cases**Continued**Calculation of Spearman Rank Correlation X: The student’s popularity measure Y: The student’s average academic achievement**Continued**Calculation of Spearman Rank Correlation**Continued**Calculation of Spearman Rank Correlation**Continued**Calculation of Spearman Rank Correlation**Continued**Calculation of Spearman Rank Correlation**Continued**Calculation of Spearman Rank Correlation**Continued**Calculation of Spearman Rank Correlation**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**Continued**When to Use Which Test**Continued**When to Use Which Test**Take Home Lesson**Spearman Rank Correlation can be used on ordinal data

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