[[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====

  * one-sample proportion test
    * do NOT use Yate's continuity, so specify:
      * prop.test(..., correct = FALSE)

  * $\Chi^2$ 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 ===

[[https://sites.nicholas.duke.edu/statsreview/jmc/ | Joint, Marginal and Conditional Probabilities]]

  * QI
    * [[https://www.squire-statement.org/index.cfm?fuseaction=page.viewPage&pageID=471&nodeID=1 | SQUIRE 2.0 for QI Reporting]]
    * <todo>Stepped-wedge trial</todo>
      * [[https://en.wikipedia.org/wiki/Stepped-wedge_trial | Link]]
  * Linear regression
    * [[https://en.wikipedia.org/wiki/Q%E2%80%93Q_plot | Q-Q plot]]
    * plot of residuals
    * [[https://en.wikipedia.org/wiki/Cook's_distance | Cook's Distance]]
    * these are different!
      * correlative
      * descriptive
      * predictive
      * associative
  * confounding vs. effect modification

__to assess a paired difference__
  * create histogram
  * plot as box plot
  * make [[https://en.wikipedia.org/wiki/Q%E2%80%93Q_plot | Q-Q plot]]