Ttests and Nonparametric

1
Chapter 6

• T-tests and Nonparametric
• Comparisons

2
One sample t-test

• A random sample of 5 stock prices is obtained
• 28.37 7.5 75.37 13.62 14.75
• We want to test the claim that the mean stock
• price is significantly different from 50.

3

• data stock
• input prices
• datalines
• 28.37
• 7.5
• 75.37
• 13.62
• 14.75
• proc ttest datastock H050
• var prices
• run

4
Two sample t-test

• Two species of butterflies
• are to be compared
• based on their wing size.
• Are their mean wing sizes
• significantly different?

5
Population of Species 1 Butterflies
6

• If , then we will use a 2 sample
  pooled
• t-test to test the equality of the means.
• If , then we will use a 2 sample
  t-test to
• test the equality of the means.

7

• data bflies
• input species wingspan
• datalines
• species1 6
• species1 4
• species1 7
• species1 3
• species2 6
• species2 9
• species2 6
• If the species names arent sorted
  alphabetically
• you need to do so before running proc ttest
• proc ttest databflies
• class species
• var wingspan
• run

8
Wilcoxon Test

• One and two sample t-tests assume the data
• comes from a normal population. If the sample
• size is large, we may still use the t-tests even
  if
• the data didnt come from a normal distribution.
• But when the sample size is small, the t-tests
• arent appropriate when the data doesnt come
• from a normal distribution.

9

• data bflies
• input species wingspan
• datalines
• species1 6
• species1 4
• species1 7
• species1 3
• species2 6
• species2 9
• species2 6
• proc npar1way databflies
• class species
• var wingspan
• exact wilcoxon
• run

10
Paired t-test

• Four people are selected
• for a headache study.
• Each takes 2 drugs and
• the time it takes to relieve
• a headache is recorded.
• We want to know if there
• is a difference between
• how fast each drug
• relieves a headache.

11

• data headache
• input druga drugb
• diffdruga-drugb
• datalines
• 20 18
• 40 36
• 30 30
• 45 46
• proc ttest H00
• var diff
• run