Lecture 15 Chi-Square

Lecture 15 Chi-Square - ChiSquare Lecture 15 Today...

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Chi-Square Lecture 15
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Today • Introduction to non-parametric tests • Chi square  – Test of independence – Test of goodness of fit • (Not covered in this course)
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Non-Parametric Statistics • Up to this point, we have used  parametric  statistics . – Normal distribution (Z scores), t tests, F test • An alternative:  non-parametric statistics – You don’t know the population variance ( σ ) – You don’t meet the assumptions for F and t tests  (not normally distributed) – Data are frequency counts or ranks
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Comparing Parametric & Non- parametric Tests • Similarities: – Both use null hypothesis testing logic – Both require random assignment to groups • Differences: – Assumptions – Interpretation
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Some non-parametric tests • Chi Square – Test of independence – Test of goodness of fit • Mann-Whitney U, Wilcoxon matched-pairs sign  ranks T, Wilcoxon-Wilcox comparisons Spearman r s • Randomization Tests • AND many others (logistic regression, survival  analysis, growth curve analyses…)
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Chi Square • Used with  frequency counts  in categories • Comparing  observed  frequencies to  expected   frequencies • Uses a  chi square distribution  of values • Two types – Test of  independence – Test of  Goodness of Fit
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Frequency Counts Favorite Food Pizza Chocolate Gender Males 18 6 Females 4 20 In cells: Frequency (# of people), rather than means
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Observed frequencies (O) – Actual count of events in a category Expected frequencies (E) – Theoretical frequency based on the null hypothesis – These are the values we’d expect to see if the null  hypothesis is true
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Chi Square Test • We compare the observed and expected frequencies  using a chi square test χ ² = (O – E) ² E O = Observed Frequency E = Expected Frequency
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Chi Square Distribution • Theoretical  distribution • Changes as df  changes • Positively skewed  (no negative values)
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Chi Square Distribution • For critical values, use 
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This note was uploaded on 05/25/2010 for the course PSYC 11 taught by Professor Ryne during the Spring '10 term at UC Riverside.

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Lecture 15 Chi-Square - ChiSquare Lecture 15 Today...

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