GEA1000 chapt 2 rates and categorical variables

what the heck is this mod bro

what is the type of variable that is focused in rate

categorical variables

what is rate

• fraction

• proportion

• percentage

what bar plots can be made from categorical variables

• dodged bar plot

• stacked bar plots

what is the best bar plot for categorical variables

100% stacked bar plot

what is a marginal rate / proportion

calculations made by using 2 numbers in the margin of the table that relate to just one of the categorical values

what is a conditional rate / proportion

when a variable is limited only to a population that had X

(eg what is the proportion of A given that A got X)

what is a joint rate / proportion

when a variable is looked at amongst the total observations

eg what is the proportion of A(subjects) who did X (variable) and got C (result) → look at only the number that falls under both X and C

what are the types of relationships between type of treatments and outcome of the treatment

• positive association

• negative association

what is the association when rate (A | B)

association absent between A and B

what is the association when rate (A | B）> rate(A | NB)

positive association between A and B

what is the association when rate (A | B) < rate (A | NB)

negative association between A and B

what are the rates that can show positive association

• rate (A | B) > rate (A | NB)

• rate ( B | A) > rate ( B | NA)

• rate (NA | NB) > rate (NA | B)

• rate (NB | NA) > rate (NB | A)

what are the rates that can show negative association

• rate (A | B) < rate (A | NB)

• rate (B | A) < rate (B | NA)

• rate (NA | NB) < rate (NA | B)

• rate (NB | NA) < rate (NB | A)

what are 2 rules that govern rate

• symmetry rule

• basic rule on rates

what is the symmetry rule

• rate (A | B) > rate (A | NB) ⇔ rate (B | A) > rate (B | NA)

• rate (A | B) < rate (A | NB) ⇔ rate (B | A) < rate (B | NA)

• rate (A | B) = rate (A | NB) ⇔ rate (B | A) = rate (B | NA)

why is this the case for the relationship 1 and 2

rate (A | B) > rate (A | NB) → positive association between A and B → more likely to see A when B is present as compared to when B is absent = more likely to see B when A is present as compared to when A is absent → rate (B | A) > rate (B | NA)

what is the basic rule on rates

• the overall rate (A) will always lie between rate (A | B) ad rate (A | NB)

what are the consequences of basic rule on rates

1. the closer rate (B) is to 100%, the closer rate (A) is to rate (A | B)

2. if rate (B) = 50%, then rate (A) = [rate (A | B) + rate (A | NB)]/2

3. if rate (A | B) = rate (A | NB), then rate (A) = rate (A | B) = rate (A | NB)