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Goodness of Fit

  • This presentation was given by Aneta Siemiginowska at the 4th International X-ray Astronomy School (2005), held at the Harvard-Smithsonian Center for Astrophysics in Cambridge, MA.  

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  • This presentation is a part of a series of lessons on the Analysis of Categorical Data. This lecture covers the following: partial/conditional tables, confounding, types of independence (mutual, joint, marginal, and conditional), identifiability constraints, partial odds ratios, hierarchical log-linear model, pairwise interaction log-linear model, conditional independence log-linear model, goodness of fit, and model building.

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  • This presentation is a part of a series of lessons on the Analysis of Categorical Data. This lecture covers the following: maximum likelihood estimation for logistic regression, sample size requirements for approximate normality of the MLE’s, confidence intervals, likelihood ratio statistic, score test statistic, deviance, Hosmer-Lemeshow goodness-of-fit statistic, the Hosmer-Lemeshow statistic, parameter estimates, scaled/unscaled estimates, residuals, grouped binomials, and model building strategies.

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  • This presentation is a part of a series of lessons on the Analysis of Categorical Data. This lecture covers the following: iterative solutions to non-linear equations, score equations for exponential class variables, Newton-Raphson vs. Fisher’s Scoring, Logistic Regression for an R × 2 tables, saturated model, odds ratios when rows are not ordinal, goodness of fit, likelihood ratio statistic for nested models, and residuals.

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  • This presentation is a part of a series of lessons on the Analysis of Categorical Data. This lecture covers the following: multinomial distribution, LaGrange multipliers, Exact Multinomial Test (EMT), the Pearson statistic, and goodness of fit.

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  • There are more than a dozen different fit statistics researchers use to assess their confirmatory factor analyses and structural equation models. Here we have assembled a list of the most popular fit statistics used and recommended cut-offs that indicate a good fit. 

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  • A video to teach about the uses of the Chi-squared statistic for goodness-of-fit and independence. The concept and lyrics are by Scott Crawford of University of Wyoming. The video won an honorable mention in the 2015 A-mu-sing contest. The music in the video is the Stevie Wonder hit "Signed Sealed Delivered I'm Yours."
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  • A statistics scramble that might be used in teaching goodness-of-fit significance tests. A set of five anagrams must be solved to reveal the letters that provide the answer to the clue in the cartoon. The cartoon was drawn by British cartoonist John Landers based on an idea by Dennis Pearl. Free for use on course websites, or as an in-class, or out-of class exercise.

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  • This is my take on the ubiquitous M&Ms counting activity. Each student records the color proportions in a fun-size bag of M&Ms. We pool the class data and run a Chi-Square goodness-of-fit test to determine whether or not the color proportions match those claimed on the manufacturer's website. We consistently find that the proportions do not match. The blue M&Ms, in particular, are underrepresented. This activity also includes a review of the 1-proportion z confidence interval.

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  • Song about the pleasure of teaching statistics when the class is engaged. May be sung to the tune of John Lennon and Paul McCartney's 1963 song "I Want to Hold Your Hand." Lyrics by Armin Schwartzman (December, 2003). This song is part of the "Stanford Statistics Songbook" found at www.bscb.cornell.edu/~hooker/StanfordStatisticsSongbook.pdf Free to use for non-commercial educational purposes. Contact author to use in publications or for commercial purposes. Musical accompaniment realization and vocals are by Joshua Lintz from University of Texas at El Paso.

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