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Lecture 8

# Lecture 8 - Feb 1.doc

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McGill University

Psychology

PSYC 305

Heungsun Hwang

Winter

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PSYC305 Lecture 8 - Feb. 1
One-Way ANOVA:
• Assume all three populations all have the same variances
Assessing Normality:
• Look at descriptive statistics
Skewness ≃ 0
•
• > 0 - positively/right skew
• < 0 - negative/left skew
• Look at their standard errors
• If it is normally distribution, there is no skewness
If it is skewed, technically you can’t apply the one-way ANOVA
•
• Construct charts
• Separate histograms for each group to assess normality
• It doesn’t have to be perfect, just roughly symmetric
• Evaluate a normal quantile plot (or normal probability plot)
Sort observations from smallest to largest
•
• Calculate the z-scores of the sorted observations
• Plot the observations against the corresponding z-scores
• If the data are closed to normal, then the points will lie close to some straight
line
Statistical tests of normality:
•
• The Kolmogorov-Smirnov (K-S) test
• The Shapiro-Wilk test
• Compares sample scores to a set of scores generated from a normal distri-
bution with the sample means and standard deviation •If the test is non-significant (p > .05), the distribution of the sample is the
same as a normal distribution
• Limitation of the normality tests
• It is very easy to give significant results when sample size is large
• You use these tests, but plot your data as well
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Histogram & Normal Quantile Plot - Price Promotion Data:
Assessing Homogeneity of Variance: Serious violation of this assumption tends to inflate the observed value of the

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