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DICE! You are going to make your own and then we are going to test them (later) to see if they are fair!
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Chapter 11 Chi-Squared (Categorical Data)
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Chi-Squared The chi-squared goodness of fit test allows us to determine whether a hypothesized distribution seems valid. (multiple variables in a distribution – not just one) Two types: Chi-squared for homogeneity – tells us whether the distributions differ when there is a treatment/experiment involved. Chi-squared for association – tells us whether the distributions differ in an observational study.
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Chi-Squared Statistic
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Carrying Out a Test
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The chi-squared test statistic compares observed minus expected COUNTS. Don’t try to perform calculations with observed minus expected proportions in each category! The checking large sample size condition, be sure to examine the EXPECTED counts, not the observed counts.
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When were you born? Are births evenly distributed across the days of the week? The one-way table shows results of a random sample of 140 births from local records. Do these data give significant evidence that local births are not equally likely on all days of the week? DaysSunMonTuesWedThursFriSat Births13232420271815
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State: Plan:
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Do: Conclude:
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Follow-Up Analysis When you reject your null hypothesis…you need to follow up by looking at individual components to see which values are the biggest contributors – or helped to push your data far enough to reject. These components show which terms contribute most to the chi-squared statistic.
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Homework Pg 692 (1-9 odd, 11, 15, 19-22) Let’s do #11 together!
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#11
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