Unit 13-1 - Chi-square test Chi-square or 2 test fair...

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Chi-square test Chi-square test or χ 2 test
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What if we are interested in seeing  if my “ crazy crazy ” dice are considered  “fair”? What can I do?
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Chi-square test Chi-square test Used to test the  counts counts  of categorical  data Three Three  types Goodness of fit (univariate) Independence (bivariate) Homogeneity (univariate with two  samples)
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χ χ 2 2 distribution – distribution –   df=3 df=5 df=10
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χ χ 2 2 distribution distribution Different  df  have different curves Skewed  right As df increases, curve shifts toward  right & becomes more like a  normal  normal  curve curve
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χ χ 2 2 assumptions assumptions SRS SRS – reasonably random sample Have  counts counts    of categorical data & we expect  each category to happen at least once Sample size Sample size  – to insure that the sample size  is large enough we should expect at least five in  each category. ***Be sure to  list expected counts !! Combine these together: All expected counts are at least 5.
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χ χ 2 2 formula formula ( 29 - = exp exp obs 2 2 χ
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χ χ 2 2 Goodness of fit test Goodness of fit test Uses univariate data Want to see how well the  observed   counts “fit” what we  expect  the  counts to be Use  χ χ 2 2 cdf function cdf function  on the  calculator to find  p-values p-values Based on df – Based on df – df = number of df = number of categories categories - 1 - 1
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Hypotheses – written in words Hypotheses – written in words H 0 : the observed counts equal the         expected counts H a : the observed counts are not        equal  to the expected counts Be sure to write in context!
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Let’s test our dice! Let’s test our dice!
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Does your zodiac sign determine how successful you will be? Fortune magazine collected the zodiac signs of 256 heads of the largest 400 companies. Is there sufficient evidence to claim that successful people are more likely to be born under some signs than others?
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