Unformatted text preview: tic Chisquare ∑
j (O j − E j ) Ej 2 where sum is over each category. Each squared difference is weighted by the Each
inverse of expected frequency, Ej. Distribution under the null hypothesis of no difference hypothesis
If Os and Es are all “big” (>5) the Chisquare If and are statistic has a χ 2 distribution with J1 df (J=5 in the above example). in Test of smoking patterns Test Calculate χ2obs Calculate Determine df (J1 where J is number of Determine
categories) categories) Choose significance level (e.g., α=.05) Choose =.05) Look up χ 2crit Table C.7, p. 504. Look crit Table If χ2obs > χ 2crit then reject the hypothesis If
that recent smoking pattern is the same as previous. previous. If χ2obs < χ 2crit then don’t reject the If Calculations Calculations
A0 A1 A2 A3 A4 Total Observed 406 164 189 78 26 863 Expected 371.09 146.71 207.12 86.3 51.78 863 (OE)2/E 3.28 2.04 1.59 0.80 12.84 20.54 •χ 2obs = 20.54, df = 51 = 4 •χ 2crit(4) =9.48 •Since χ 2obs > χ 2crit(4) reject H0. Therefore we conclude that smoking patterns have changed. Comparison involving two variables Comparison
Adult female TV characters by hair color and career level Hair Color
Blonde Dark Career Professional Career Level Level
Nonprofessional 36 24 48 72 Raw data Raw B1 B2 total B1 B2 total A1 36 24 60 A1 A2 48 72 120 A2 total 84 96 180 total 84 96 180 84*60/180 84*120/180 96*60/180 96*120/180 60 120 Expected values under independence independence B1 B2 total A1 84*60/180 96*60/180 60 A2 84*120/180 96*120/180 120 total 84 96 180 B1 B2 total A1 28 32 60 A2 56 64 120 total 84 96 180 Chisquare table Chisquare Also called a rowsbycolumns Also
contingency table contingency Each data point fits into one cell Row and column totals are called Row marginals marginals We use marginals to calculate expected We marginals expected cell totals, and compare to observed cell observed totals totals Expected Values Expected
Hair Color
E = row marg.*col marg. total responses Blonde Dark Marginals Career Professional O = 36 Career Level Level E = 28 NonO = 24 professional E = 32
Marginals O = 48 E = 56 O = 72 E = 64 120 84 96 N = 180 60 Chisquare test Chisquare
χ = ∑∑
2 i =1 j =1 c r (Oij − Eij ) Eij
2 2 (36 − 28) (24 − 32) χ= + + 28 32 2 2 (48 − 56) (72 − 64)...
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 '07
 Nezami,Borovay
 OS, Nonparametric statistics, A1 A2 A3, A2 A3 A4, chisquare test chisquare

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