Unformatted text preview: + = 6.43 56 64
2 2 Hypothesis testing Hypothesis H0: The row and column variable are The
independent in the population. independent The job level of the character is independent The of the hair color of the character. of H1: The row and column variables are The
related in the population. related The job level of the character is related to the The hair color of the character. hair Hypothesis testing Hypothesis Look up critical value at alpha of 0.05 or Look
0.01 (Table C.7, p. 504). 0.01 df = (r1)(c1) If χ2obs > χ2crit then reject H0, accept H1 If If χ2obs < χ2crit then fail to reject H0, do not If do
accept H1 accept Example results Example χ2obs = 6.43 χ2crit = 3.84 (df = 1, α = 0.05) Reject H0, accept H1. There is a relationship between job level There
and hair color of a TV character. and Example 2 Example Are firstborn Are
children more creative than laterborn children? children? Creativity Top Creativity Top
test score 1/3 test 1/3 Birth Order Firstborn Laterborn 47 29 35 36 Middle 29 Middle 1/3 1/3 Bottom 24 Bottom 1/3 1/3 Hypotheses Hypotheses H0: distribution of creativity scores is the distribution the same for first and later born H1: distribution of creativity scores is distribution
different for first and later born different Expected Scores Expected
E = row marg.*col marg. total responses Birth Order Firstborn LaterRow Row born Marginal Marginal Creativity Creativity test score test O=47 E= Middle 1/3 O=29 E= Bottom 1/3 O=24 E= Column Column 100
Marginal Marginal Top 1/3 O=29 E= O=35 E= O=36 E= 100 76 64 60 200 Birth order example Birth χ2obs= 7.22 df=(31)*(21)=2 χ2crit= 5.99 Reject H0 that birth order and creativity are
independent. independent. Rank tests Rank Continuous data. Rank them. Test is a function of the ranks. Rank tests Rank Spearman correlation (test that r=0) MannWhitney U Wilcoxon Rank tests: When to use Rank Continuous (interval or ratio) data Normality assumption doesn’t hold Equal variance assumption doesn’t hold MannWhitney U test MannWhitney Use with: Twofactor betweensubjects design At least ordinal measurement (so the values At can be “ranked”) can This is the “nonparametric” version of the ttest for two independent groups. Schro...
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 '07
 Nezami,Borovay
 OS, Nonparametric statistics, A1 A2 A3, A2 A3 A4, chisquare test chisquare

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