1. 1.8 Critical Analysis: Outliers

2. 1.8.1 Driving Test Scores
School is making assumption that the correlation between instructional hours and test scores is indication of instructor’s teaching skills
Difficult to prove definitively
Reasonable if school has found instructors have consistently strong correlations between time spent with their students and students’ test scores

3. Analysis: Number of hours is independent variable
Scatterplot indicates strong positive linear correlation
Linear regression analysis
yields line of best fit:
y = -0.13x + 80 and r = -0.05!
virtually zero linear correlation
line of best fit has negative slope:
less time instructing -> better test scores?
Scatterplot looked favourable, but regression analysis suggests that instructor’s lessons had no positive effect on students’ test results

4. Funny Data? Outlier at (20, 45) Look at residual plot.
Substantially below the others
suggests special circumstance
may have caused abnormal
result on test
Illness, emotional upset, really bad driver!
Could have been a typo!
Bad regression model?
Reasonable to exclude this data point when evaluating the driving instructor

5. Removing outlier and repeating analysis
y = x ,
r = 0.93
Strong positive linear
correlation between
instructional hours and test
result
Instructor may be an effective teacher after all

6. Note: Outlier had dramatic effect on regression analysis because
Distant from other data points
Sample size quite small
To do a proper evaluation, need
Larger set of data
More information about the outlier

7. Outliers Can skew regression analysis
Could also simply indicate that data really do have large variations
Comprehensive analysis of a set of data should
Look for outliers
Examine their possible causes
Examine their effect on analysis
Discuss whether they should be excluded from calculations
Outliers have less effect on larger samples