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