In ESunRoc/STT218: University of Rochester Statistics 218 Functions

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library(URStat218)

All notes in the vignettes of this package are adapted from Dr. Joseph Ciminelli's fall 2019 section of Statistics 218. For a more complete version of the material herein contained, please reference the notes, attend the lectures, or ask Dr. Ciminelli himself.

2x2 Contingency Tables

We begin by taking a contingency table on X and Y, where the rows are fixed:

|X (Explanatory)|Y(Response) | | | |:--: |:--: |:--: |:--: | | |1 |2 | Total | |1 | $n_{11}$ | $n_{12}$ | $n_{1+}$ | |2 | $n_{21}$ | $n_{22}$ | $n_{2+}$ |

For this 2x2 table, we have two independent binomial proportions, one for each level of X: $$n_{11} \sim Binom(n_{1+},p_{1|1})$$ $$n_{21} \sim Binom(n_{2+},p_{1|2})$$ Ultimately, we wish to test the significance of the difference in the two groups' proportions. If there is a significant difference, we conclude X and Y to be significantly associated, while the opposite leads to a correspondingly opposite conclusion.
As we are testing for independence, with unknown probabilities $p_{1|1}$ and $p_{1|2}$, we test against a null hypothesis of $H_0: p_{1|1} =p_{1|2}$; that is, that the proportions are independent and equal. Of the methods available to us, we note that R has built-in support for a difference-of-proportions test. We discuss in greater detail Relative Risk and Odds Ratio tests, as this package creates functions for them.

ESunRoc/STT218 documentation built on Jan. 14, 2020, 2:39 a.m.