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nonparametric statistics. nonparametric Chi-square tests Chi-square The purpose of χ 2 is to evaluate if the The “pattern” created by categorical data is typical. typical. Two common applications of χ 2 test are: Test whether the data fit a particular Test distribution. distribution. Test a H0 about whether one variable is related to the other. related Chi-Square Test Chi-Square Analysis of frequency data Between-subjects design Between-subjects (not within-subject) (not Scores are nominal – frequency of Scores event occurring or not event Example 1: Do Data have certain pattern? certain We observe cigarette We
smoking of a random sample of 863 men 40-50 years old. years
Observed freq A0=None A1=one pack A2=Two pack A3=Three pack A4=Four or more Total 406 164 189 78 26 863 Relative freq A0 A1 A2 A3 A4 Total 0.43 0.17 0.24 0.10 0.06 1.00 We have the following We
frequency table, and also frequency the relative frequency on relative cigarette smoking for men at that age group 10 years ago. ago. Question Question Are the “observed numbers” of men by Are
“cigarette use category” (A1-A4) consistent with those “expected” based on the frequencies from ten years ago? the Calculate age group expecteds based on 863 total subjects based
A0 A1 A2 A3 A4 Total Relative freq 0.43 0.17 0.24 0.10 0.06 1 Calculation 863* 0.43 863* 0.17 863* 0.24 863* 0.10 863* 0.06 863 Expected 371.09 146.71 207.12 86.3 51.78 863 Example 1 To see if the cigarette To
use habits of American men in the 40-50 age group are the same now as they were 10 years ago, we can compare the difference between the obtained vs. expected frequency.
Observed A0 A1 A2 A3 A4 406 164 189 78 26 863 Expected 371.09 146.71 207.12 86.3 51.78 863 Observed vs. Expected Frequency Observed O is Observed (or Obtained) frequency Observed E is Expected frequency, with Ej =N× Pj . Expected Compare Os to Es. Statistical question is whether the Statistical
differences are likely or unlikely to be due to chance. to Chi-square test statis...
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