using chi square wisely
DESCRIPTION
Knowing which chi-square test to use whenTRANSCRIPT
Using Chi-SquareBoth 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.
Using Chi-SquareInstead 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
Using Chi-SquareAre 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 countsMALE FEMALE Total
Yes7
11.691.883
2924.310.906
36
No31
26.310.837
5054.690.403
81
Total 38 79 117 Chi-Sq = 4.028, DF = 1, P-value = 0.045
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 countsMALE FEMALE Total
Yes7
11.691.883
2924.310.906
36
No31
26.310.837
5054.690.403
81
Total 38 79 117 Chi-Sq = 4.028, DF = 1, P-value = 0.045
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 countsMALE FEMALE Total
Yes7
11.691.883
2924.310.906
36
No31
26.310.837
5054.690.403
81
Total 38 79 117 Chi-Sq = 4.028, DF = 1, P-value = 0.045
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 countsMALE FEMALE Total
Yes7
11.691.883
2924.310.906
36
No31
26.310.837
5054.690.403
81
Total 38 79 117 Chi-Sq = 4.028, DF = 1, P-value = 0.045
Using Chi-SquareWe 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
Using Chi-SquareLarge Sample Size condition
ObservedCounts:
Expected Counts:
Pg. 721
Living Arrangements 19 20 21 22 TotalsParents’ 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 TotalsParents’ 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