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Quntative Data Analysis SPSS Exploring Assumptions

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Presentation on theme: "Quntative Data Analysis SPSS Exploring Assumptions"— Presentation transcript:

1 Quntative Data Analysis SPSS Exploring Assumptions

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

3 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)

4 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

5 Analysis by groups

6 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

7 SPSS window

8 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

9 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

10 Hartley’s FMax test

11 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

12 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

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

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