1. Chi-square test

2. Data Statistics Continuous measurement: Interval Mean Categorical measurement: NominalFrequency, count, proportion One-way chi-square test counts the number of subjects falling into different categories of a variable and determines whether the distribution or pattern of the counts in different categories differs from that expected by the null hypothesis Two way chi-square test counts the number of subjects falling into different categories of two variables and determines whether the distribution or pattern of the counts in different categories of one variable is related to (your hypothesis) or independent from (null hypothesis) that of the other variable.

3. Examples Hypothesis: The marketing campaign of Pepsi has increased its market share Expected frequency distribution Observed frequency distribution Historical market shares CokePepsiOther 50%30%20% Current market shares CokePepsiOther 40%50%10%

4. Hong Kong has more high-IQ people than the normal distribution 70 85 100 115 130 34% 16% 50% 20% 10% Expected IQ distributionHK IQ distribution

5. 0 5 10 15 20 25 30 35 40 1 df 6 df 10 df 20 df 22 df = number of categories minus one

6. Movie ActionHorrorDramaComedyTotal Observed4581532 Expected888 832 df = J – 1 = 4 – 1 = 3   0.05  2 = 9.25  2 (3,.05) = 7.81 Reject Null

7. E  5, df  2 E  10, df = 1 Yates’s correction, 1.Subtract.5 from the observed frequency if the observed frequency is greater than the expected frequency; that is, if O>E, subtract.5 from O. 2. Add.5 to the observed frequency if the observed frequency is less than the expected frequency; that is, if O<E, add.5 to O.

8. Movie Choices SexActionHorrorDramaComedyTotal Male108345 9417564 Female 8 1225360333 Total11635734777897 (73) (43) (224) (133) (218) (129) (48) (29)  2 observed = 16.78 + 28.48 + 265.36 + 110.08 + 70.53 + 119.19 + 20.02 + 33.13 = 463.37 Reject Null  2 = 463.37  2 (3,.01) = 11.34 df = (r – 1)(c – 1) = (4-1)(2-1) = 3  <.01

9. Answers to Homework 4: Economy has changed undergraduate major choices Past five years record: ScienceSocial ScienceMedicineArts 30%20%40%10% You took a random sample 110 second year students and their majors are distributed: ScienceSocial ScienceMedicineArtsTotal 23322431110 Observed 33224411 Expected df = k – 1 = 4 – 1 = 3

10.  2 = 53.03  2 (3,.01) = 11.34 Reject Null

11. Answer to h4: There is a relationship between gender and major choices ScienceSocial ScienceMedicineArtsTotal 525151560 Female 51515 540 Male 10 403020100 ScienceSocial ScienceMedicineArtsTotal 5 /625 / 2415 /1815 /1260 Female 5/ 415 / 1615 /12 5 / 8 40 Male 10403020100 df = (r – 1)(c – 1) = (4 – 1)(2 – 1) = 3

12.  2 = 3.65  2 (3,.01) = 11.34 Do not reject Null.