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duke_notes [2025/11/10 20:43] – adminduke_notes [2025/11/17 21:46] (current) – admin
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 [[https://stats.libretexts.org/Bookshelves/Introductory_Statistics/OpenIntro_Statistics_(Diez_et_al)./06%3A_Inference_for_Categorical_Data | Inference for Categorical Variables]] [[https://stats.libretexts.org/Bookshelves/Introductory_Statistics/OpenIntro_Statistics_(Diez_et_al)./06%3A_Inference_for_Categorical_Data | Inference for Categorical Variables]]
 +
 +===== General Tips =====
 +
 +  * if you can, pick a continuous outcome over a binary outcome
 +    * Why? For a binary outcome, you'll need a much larger sample size. Continuous outcomes also allow more precision.
 +  * logistic regressions stink!
 +
 +logistic regression = linear model for the log-odds of the outcome
 +
 +=== analyzing relationship between categorical outcome and a continuous covariate ===
 +
 +===effect modification vs confounding===
 +
 +if we don't take effect modification into account, we get an over-generalized estimate of the relationship between the outcome and the exposure for the entire co-hort
 +
 +  * Breslow-Day Test examines if evidence of a differential association between two variables across the level of a third variable
 +    * similar limitations to Cochran-Mantel-Haenszel test
 +
 +==== Cochran-Mantel_haenszel test ====
 +
 +  * limitations
 +    * can only adjust for one variable at a time
 +
 +looks at two binary categorical variables while adjusting for the value of a third categorical variable
  
 ==== Parametric One-Sample Inference of Categorical Variables==== ==== Parametric One-Sample Inference of Categorical Variables====
  
-    * one-sample proportion test +  * one-sample proportion test 
-      * do NOT use Yate's continuity, so specify: +    * do NOT use Yate's continuity, so specify: 
-      *  +      * prop.test(..., correct = FALSE) 
- <code>prop.test(..., correct = FALSE)</code>+ 
 +  * $\Chi^2$ goodness of fit test 
 +    * to ensure sufficient sample size: $n \cdotp_{0} > 5$ 
 +    * don't use continunity corrections! 
 +      * chisq.test(..., correct = FALSE) 
 + 
 +**NOTE**: //one-sample single proportion test// gives a 95% CI -- $\Chi^2$ does not! 
 + 
 +==== Types of Probabilites ===
  
-    * $\Chi^2$ goodness of fit test +[[https://sites.nicholas.duke.edu/statsreview/jmc/ | Joint, Marginal and Conditional Probabilities]]
  
   * QI   * QI
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