Quntative Data Analysis SPSS Exploring Assumptions

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

Assumptions of parametric tests 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)

Normality 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

Analysis by groups

Test of 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

SPSS window

Homogeneity of variance 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

Test of HV Levene’s test Hartley’s Fmax (Variance ratio) 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

Hartley’s FMax test

Dealing with outliers 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

Dealing with non-normality and unequal variances 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

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