Using chi square wisely
- 1. Using Chi-Square Both chi-square tests are calculated the same ways and provide the same information, but answer two very different questions… Chi-square test for homogeneity tests whether the distribution of a categorical variable is the same for each of several populations or treatments. Chi-square test for association/independence tests whether two categorical variables are associated in some population of interest. It is common to see questions asking about association that require a test for homogeneity and questions asking about differences between proportions of variables when a test for association is required.
- 2. Using Chi-Square Instead of paying attention to how the question is asked…. look at how the data is produced If the data came from two or more independent random samples or treatment groups in a randomized experiment – do a chi-square test for homogeneity If the data came from a single random samples, with the individuals classified according to two categorical variables – do a chi-square test for association/independence
- 3. Using Chi-Square Are men and women equally likely to suffer lingering fear from watching scary movies as children? Researchers asked a random sample of 117 college students to write narrative accounts of their exposure to scary movies before the age of 13. More than one-fourth of the students said that some of the fright symptoms are still present when they are awake. Fright Symptoms Male Female Total Yes 7 29 36 No 31 50 81 Total 35 79 117 Expected Counts are printed below observed counts & chi-square contributions are below expected counts MALE FEMALE Total Yes 7 11.69 1.883 29 24.31 0.906 36 No 31 26.31 0.837 50 54.69 0.403 81 Total 38 79 117 Chi-Sq = 4.028, DF = 1, P-value = 0.045
- 4. Using Chi-Square Explain why a chi-square test for association/independence and not a chi-square test for homogeneity should be used. Fright Symptoms Male Female Total Yes 7 29 36 No 31 50 81 Total 35 79 117 Expected Counts are printed below observed counts & chi-square contributions are below expected counts MALE FEMALE Total Yes 7 11.69 1.883 29 24.31 0.906 36 No 31 26.31 0.837 50 54.69 0.403 81 Total 38 79 117 Chi-Sq = 4.028, DF = 1, P-value = 0.045
- 5. Using Chi-Square Researchers decided to use the null hypothesis H0: gender and ongoing fright symptoms are independent in the population of interest. State the correct alternative hypothesis. Fright Symptoms Male Female Total Yes 7 29 36 No 31 50 81 Total 35 79 117 Expected Counts are printed below observed counts & chi-square contributions are below expected counts MALE FEMALE Total Yes 7 11.69 1.883 29 24.31 0.906 36 No 31 26.31 0.837 50 54.69 0.403 81 Total 38 79 117 Chi-Sq = 4.028, DF = 1, P-value = 0.045
- 6. Using Chi-Square Interpret the P-value in context. What conclusion would you draw at a α = 0.01 Fright Symptoms Male Female Total Yes 7 29 36 No 31 50 81 Total 35 79 117 Expected Counts are printed below observed counts & chi-square contributions are below expected counts MALE FEMALE Total Yes 7 11.69 1.883 29 24.31 0.906 36 No 31 26.31 0.837 50 54.69 0.403 81 Total 38 79 117 Chi-Sq = 4.028, DF = 1, P-value = 0.045
- 7. Using Chi-Square We can turn quantitative variable in a categorical variable by grouping intervals of values (quantities) together (think about histograms) Tax income brackets Income City 1 City 2 Under $10,000 70 62 $10,000 to $19,999 52 63 $20,000 to $24,999 69 50 $25,000 to $34,999 22 19 $35,000 or more 28 24
- 8. Using Chi-Square Large Sample Size condition Observed Counts: Expected Counts: Pg. 721 Living Arrangements 19 20 21 22 Totals Parents’ Home 324 378 337 318 1357 Another Person’s Home 37 47 40 38 162 Your Own Place 116 279 372 487 1254 Group Quarters 58 60 49 25 192 Other 5 2 3 9 19 Total 540 766 801 877 2984 Living Arrangements 19 20 21 22 Totals Parents’ Home 245.57 348.35 364.26 398.82 1357 Another Person’s Home 29.32 41.59 43.49 47.61 162 Your Own Place 226.93 321.90 336.61 368.55 1254 Group Quarters 34.75 49.29 54.51 56.43 192 Other 3.44 4.88 5.10 5.58 19 Total 540 766 801 877 2984