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Assumptions……………Seriously..! Assumptions of parametric data Normal distribution Parametric test --- Nonparametric data = Wrong Conclusion Why? Test Selection.

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Presentation on theme: "Assumptions……………Seriously..! Assumptions of parametric data Normal distribution Parametric test --- Nonparametric data = Wrong Conclusion Why? Test Selection."— Presentation transcript:

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2 Assumptions……………Seriously..! Assumptions of parametric data Normal distribution Parametric test --- Nonparametric data = Wrong Conclusion Why? Test Selection Be a Critic Impress your seniors

3 Four basic assumptions Normally distribution Different meaning in different context Sampling distribution/error distribution Homogeneity of variance Same variance of data Groups comparison (same variance of groups) Correlational design (stable variance of a variable across all levels of other variable) Interval data Independence Participants data independent of each other and uncorrelated errors (correlational desgin) Between conditions non-independent b/w participants independent (Repeated Measure design)

4 Frequency distribution Values of skewness and kurtosis (Sig s = s/s.e P–P plot (Analyze Descriptives P-P plot cumulative probability of a variable against the cumulative probability of a particular distribution Z-score of rank orders of data against their own z-scores A diagonal distributed data Normal distribution

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6 Kolmogorov–Smirnov test (K–S test) Shapiro–Wilk test (more power than K-S) Analyze descriptive statistics explore Normality Plots with tests Non-significant (p >.05) = Normal Distribution Reporting results: D(df) = test-statistic, p >.05 D = (Symbol for K-S), df = degree of freedom (sample size), test-statistic = K-S Statistic Limitations Large sample sizes Always Significant

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8 Equal variance In groups data – at least one variable is categorical All groups have equal variance In correlation – both or all variables are continuous A variable has equal variance for all levels of other

9 Levenes test Analyze descriptive statistics explore Spread vs. level with Levenes test Non-significant (p >.05) = Equal Variance Reporting results: F(df1, df2) = 7.37, p <.01. F = (Symbol for Levenes test), df = degree of freedom (categories, sample size), test-statistic = F Statistic Hartleys F max (Variance ratio) VR= largest group variance/the smallest Smaller than the critical values

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11 Remove the case Transform the data Change the score (a lesser evil) The next highest score plus one X = (z × s) + X = (mean + 3sd) The mean plus two standard deviations

12 Transforming data Doesnt change relationship b/w variables Changes difference b/w variables Choosing a transformation trial and error Levenes test (Use Transformed option) Types: Log transformation (log(Xi)) Square root transformation (Xi) Reciprocal transformation (1/Xi) Reverse score transformations

13 Evils of Transformation Non-parametric tests Robust methods Trimmed mean Bootstrap


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