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**Quntative Data Analysis SPSS Exploring Assumptions**

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

Normal distribution Parametric test --- Nonparametric data = Wrong Conclusion Why? Test Selection Be a Critic Impress your seniors

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**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)

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**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

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Analysis by groups

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**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

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SPSS window

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**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

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**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

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Hartley’s FMax test

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**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

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**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

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**What Else Evils of Transformation Non-parametric tests Robust methods**

Trimmed mean Bootstrap

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