Assumptions……………Seriously..! Assumptions of parametric data

◦ Normal distribution Parametric test --- Nonparametric data

= Wrong Conclusion Why? Test Selection Be a Critic Impress your seniors

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)

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

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

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

Levene’s test◦ Analyze descriptive statistics explore◦ Spread vs. level with Levene’s test

Non-significant (p > .05) = Equal Variance◦ Reporting results:

F(df1, df2) = 7.37, p < .01. F = (Symbol for Levene’s test), df = degree of freedom

(categories, sample size), test-statistic = F Statistic Hartley’s Fmax (Variance ratio)

◦ VR= largest group variance/the smallest◦ Smaller than the critical values

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

Transforming data◦ Doesn’t change relationship b/w variables◦ Changes difference b/w variables

Choosing a transformation◦ trial and error◦ Levene’s test (Use Transformed option)

Types:◦ Log transformation (log(Xi))◦ Square root transformation (√Xi)◦ Reciprocal transformation (1/Xi)◦ Reverse score transformations

Evils of Transformation Non-parametric tests Robust methods

◦ Trimmed mean◦ Bootstrap