$1.$ Confusion matrix

Confusion matrices are confusing. Here is an exercise that looks fairly simple. $..$

In the literature, confusion matrices are presented in various ways. Schleimer et $(2023)$ analyze how good are Washington State criminal codes in terms of telling if a crime involved or did not involve firearms.

They manually review $5000$ cases, and compare the results with criminal codes. Their confusion matrix $($attached picture$)$:

$($Table $1$ Sensitivity and negative predictive value of firearm$-$related cases, all cases$)$

Answer the following questions based on the table:

$1.$ What are the actual and what are the predicted values in this context?

$2.$ Does the CM have actual values in rows, or predicted values in rows?

Hint: Here $$No$.$ means $$number$($note the period$),$ it is not $$no$!$

$3.$ Does the CM have positive values first or negative values first?

$4.$How many false positives and false negatives are reported?

$5.$Show the CM using the convention as used in the Lecture Notes: actual in rows, negatives first.

$6.$ In the table they report NPV $=93\mathrm{.}2\%$ and Se $=17\mathrm{.}6\%.$What do these numbers mean?

$7.$ Compute precision, recall, and F $-$score, based on the numbers $($the counts$)$ in the CM