Statistics One Lecture 21 Assumptions Revisited 1
Statistics One
Lecture 21 Assumptions Revisited
1
Two segments
• Assumptions • Transformations
2
Lecture 21 ~ Segment 1
Assumptions
3
Review of main assumptions
• Correlation • Normal distribution in X and Y • Linear relationship between X and Y • Homoscedasticity
• Plot histograms and scatterplots • Print summary statistics
Review of main assumptions
• Regression • Normal distribution in Y • Linear relationship between X and Y • Homoscedasticity • Correlations among predictor variables all < .80 • No multicolinearity
• Plot histograms and scatterplots and residuals • Print summary statistics
Review of main assumptions
• t-tests • Normal distribution in Y (DV) • Homogeneity of variance • Equivalent sample size
• Levene’s test
Review of main assumptions
• Between groups and Factorial ANOVA • Normal distribution in Y (DV) • Homogeneity of variance • Equivalent sample size
• Levene’s test
Review of main assumptions
• Repeated measures ANOVA • Normal distribution in Y (DV) • Sphericity assumption • Homogeneity of variance • Homogeneity of covariance
• Equivalent sample size
• Levene’s test • Mauchly’s test
Review of main assumptions
• Chi-square • Independence • Adequate expected cell counts
Review of main assumptions
• Two primary constraints of the assumptions • Normal distribution in Y (DV) • Linear relationship between predictor variables
and outcome variable (see Lecture 23)
Review of main assumptions
• Normal distribution in Y (DV) • How to test • Histograms and summary statistics • Q-Q plots • Empirical tests, such as D’Agostino’s K2 test
Review of main assumptions
• Normal distribution in Y (DV) • How to test • Histograms and summary statistics
• Look for extreme skew and/or kurtosis and/or outliers (for example, cases +/- 3 SDs from the mean)
• Rule of thumb is (skew > 3) and/or (kurtosis > 10) indicates a non-normal distribution
Positive skew with outliers
Positive skew
Review of main assumptions
• Normal distribution in Y (DV) • How to test • Q-Q plot
• A plot of the sorted values from the data set against the expected values of the corresponding quantiles from the standard normal distribution.
• If the distribution is normal then the plotted points should approximately lie on a straight line.
Normal distribution
Positive skew
Segment summary
• The inferential statistics covered in this course involve several assumptions
• Two primary assumptions – Normal distribution in the outcome Y (DV) – Linear relationship between predictors and Y
Segment summary
• Normal distribution in Y (DV) • How to test • Histograms and summary statistics • Q-Q plots • Empirical tests, such as D’Agostino’s K2 test
END SEGMENT
20
Lecture 21 ~ Segment 2
Transformations
21
Transformations • If a distribution is not normal then it is sometimes possible
to transform the data in an attempt to make the distribution normal
• A transformation is a single function applied to all data points in the distribution (for example, square root)
• The rank order of cases should remain the same but the distance between cases may change
Transformations
• Most common transformations for positive skew • Square root • Logarithm • Inverse
Transformations
Transformations
• Most common transformations for negative skew • Reflect and Square root • Reflect and Logarithm • Reflect and Inverse
Transformations
Positive skew
Skew = 3.05 Kurtosis = 9.26
Square root transform
Skew = 2.86 Kurtosis = 7.91
Log transform
Skew = 2.69 Kurtosis = 6.75
Negative skew
Skew = -3.36 Kurtosis = 11.73
Reflect and square root
Skew = 2.58 Kurtosis = 6.62
Reflect and log
Skew = 1.59 Kurtosis = 2.92
Segment summary
• If a distribution is not normal then it is sometimes possible to transform the data in an attempt to make the distribution normal
Segment summary
• Most common transformations for positive skew • Square root • Logarithm • Inverse
Segment summary
• Most common transformations for negative skew • Reflect and Square root • Reflect and Logarithm • Reflect and Inverse
END SEGMENT
36
END LECTURE 21
37