Merge branch 'main' into LT1

.gitignore

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 .Ruserdata
 /_site/
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+.DS_Store

Comp/r-sas_chi-sq.qmd

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+---
+title: "R/SAS Chi-Squared Comparision"
+---
+
+Chi-Squared test is a hypothesis test for independent contingency tables, dependent on rows and column totals. The test assumes:
+
+-   observations are independent of each other
+
+-   all values are 1 or more and at least 80% of the cells are greater than 5.
+
+-   data should be categorical
+
+The Chi-Squared statistic is found by:
+
+$$
+\chi^2=\frac{\sum(O-E)^2}{E}
+$$
+
+Where O is the observed and E is the expected.\
+For an r x c table (where r is the number of rows and c the number of columns), the Chi-squared distribution's degrees of freedom is (r-1)\*(c-1). The resultant statistic with correct degrees of freedom follows this distribution when its expected values are aligned with the assumptions of the test, under the null hypothesis. The resultant p value informs the magnitude of disagreement with the null hypothesis and not the magnitude of association
+
+For this example we will use data about cough symptoms and history of bronchitis.
+
+```{r}
+
+bronch <- matrix(c(26, 247, 44, 1002), ncol = 2)
+row.names(bronch) <- c("cough", "no cough")
+colnames(bronch) <- c("bronchitis", "no bronchitis")
+```
+
+To a chi-squared test in R you will use the following code.
+
+```{r}
+chisq.test(bronch)
+```
+
+To run a chi-squared test in SAS you used the following code.
+
+```{SAS}
+#| eval: false
+proc freq data=proj1.bronchitis;
+tables Cough*Bronchitis / chisq;
+run;
+```
+
+The result in the "Chi-Square" section of the results table in SAS will not match R, in this case it will be 12.1804 with a p-value of 0.0005. This is because by default R does a Yate's continuity adjustment. To change this set `correct` to false.
+
+```{r}
+chisq.test(bronch, correct = FALSE)
+```
+Alternatively, SAS also produces the correct chi-square value by default. It is the "Continuity Adj. Chi-Square" value in the results table.