Chi Square Tests

1. Chi Square Tests

2. What is the Chi square test? • Chi square is a statistical test that compare actual results with expected results. • If the results of an experiment are realy close to the numbers you expected, the Chi square test will confirm that “there is no significant difference between actual and expected results”. • This means that your prediction (hypothesis) was correct.

3. What is the Chi square test? • If the results of an experiments are different from the numbers you expected, the Chi square test will confirm that “there is a significan difference between actual and expected results.” • This means that your prediction (hypothesis) was NOT correct.

4. Chi Square test from Instructions • Chi Square = (expected-actual)2+ (expected –actual)2 expected expected • Hitchhiker’s Thumb Regular Thumb • Actual 97 Actual 101 • Expected 99 Expected 99 • Do actual results match expected results?

5. Chi Square test from Instructions • Chi Square = (expected-actual)2+ (expected –actual)2 expected expected (2)2 + (-2)2 99 99

6. Chi Square test from Instructions • Chi Square = (expected-actual)2+ (expected –actual)2 expected expected 4 + 4__ = 0.04 + 0.04 = 0.08 99 99

7. Chi Square test from Instructions • Chi Square = (expected-actual)2+ (expected –actual)2 expected expected Chi Square = .08 • Is this number Less than or Greater than 3.84? • 3.84 is a number from a statistical chart. • 2 groups in experiment, compare Chi square to 3.84 • 3 groups in experiment, compare Chi square to 5.99 • 4 groups in experiment, compare Chi square to 7.82

8. Chi Square test from Instructions • Chi Square = .08 • This number is LESS THAN 3.84. • Therefore, there is no significant difference between our expected result and our actual result. Our prediction was correct.

9. Chi Square test from Homework • Chi Square = (expected-actual)2+ (expected –actual)2 expected expected • Hitchhiker’s Thumb Regular Thumb • Actual 1 Actual 27 • Expected 7 Expected 21 • How do we know the “expected” number?

10. Chi Square test from Homework • Chi Square = (expected-actual)2+ (expected –actual)2 expected expected • Hitchhiker’s Thumb Regular Thumb • Actual 1 Actual 27 • Expected 7 Expected 21 • Figure out what percentage of people you PREDICT will have hitchhiker’s thumb. Let’s guess 25%

11. Chi Square test from Homework • Chi Square = (expected-actual)2+ (expected –actual)2 expected expected • Hitchhiker’s Thumb Regular Thumb • Actual 1 Actual 27 • Expected 7 Expected 21 • What number is 25% of the TOTAL? • 25% of 28 is 7 75% of 28 is 21

12. Chi Square test from Homework • Chi Square = (expected-actual)2+ (expected –actual)2 expected expected (1-7)2 + (27-21)2 7 21

13. Chi Square test from Homework • Chi Square = (expected-actual)2+ (expected –actual)2 expected expected (-6)2 + (6)2 7 21

14. Chi Square test from Homework • Chi Square = (expected-actual)2+ (expected –actual)2 expected expected 36 + 36__ = 5.14 + 1.7 = 6.84 7 21

15. Chi Square test from Homework • Chi Square = 6.84 • This number is GREATER THAN 3.84. • Therefore, there is a significant difference between our expected result and our actual result. Our prediction was not correct.

16. Practice Chi Square Test • Smallville has 120 members who have cystic fibrosis. • The same town has 325 people who have no symptoms of cystic fibrosis. • How many people are in the population? • What is the OBSERVED number of people with CF? • What is the EXPECTED number of people with CF?

17. Chi Square test • Our hypothesis is that 25% of all people in Smallville will have CF disease. • Does our expected number match your actual number?