STATS 16B- More chi squared tests

Question 1

Anecdote

Answer 1

• I went to Balti King last night and was sick afterwards- I think it was food poisoning
• 3 people state they had food poisoning

Question 2

Balti King replies

Answer 2

• Lots of people ate here last night and were not sick- therefore it cannot possibly be food poisoning
• There is a bug going around anyway it is nothing to do with the food- lots of people are sick all the time

Question 3

A researchers view

Answer 3

• How many people were sick after going to Balti King last night
• How many people were sick last knight but did not go to Balti King
• How many people were not getting sick but went to the Balti King
• How many people were not sick but didn’t go to the Balti King

Question 4

Any relationship between the variables

Answer 4

• Null hypothesis: there is no relationship between being ill and eating at balti king- need to know how many weren’t sick and did not go

Question 5

What might we expect

Answer 5

• Balti king yes and sick
  
  • 20 x 35 / 100 = 7
• Balti king YES and NOT sick
  
  • 20 x 65 / 100 = 13

Question 6

But is this difference significant

Answer 6

The Chi-squared test

• Compares observed and expected frequencies
  
  • Subtracts one from the other
• Squares the difference (to avoid problems of polarity (+/-)
• Divide each squared difference by the expected value for the cell (since a big difference is less noteworthy in a larger sample)
• Chi-squared statistic
• The calculated statistic can then be compared to critical values in tables according to the degrees of freedom to calculate significance
  
  • See later for df calculation

Question 7

Calculations

Answer 7

Question 8

SPSS output

Answer 8

Question 9

Reporting the result

Answer 9

• A chi-squared test of association suggested that there was a significant association between having eaten at Balti King and having been ill
• (Chi= 17.58, df= 1, p<0.001)
• The data suggest that those who had eaten at Balti King were more likely to have also been ill
• Note that association doesn’t imply causation

Question 10

Summary

Answer 10

• Chi-square can be used to test for independence between 2 variables with nominal data and where each participant can be in only one category (i.e. frequency counts)
• It compares the observed data with the data that would be expected if there were no relationship between the variables

Question 11

Other points

Answer 11

• In 2x2 tables, frequencies should be >5
  
  • (Or not more than 25% of cells <5 in larger tables)
• In 2x2 tables fisher’s exact probability test can be used if this assumption is broken- it’s less sensitive to small expected frequencies