Convert ability (in W scores by default) to relative proficiency index
Usage
rpi(
x,
mu = 500,
scale = 20/log(9),
criterion = 0.9,
reverse = FALSE,
interpretation = FALSE
)Arguments
- x
numeric vector of ability scores
- mu
numeric vector of ability scores of reference group
- scale
number vector of scaling factor. The default value (
log(9) / 20) assumes that x and mu are W scores.- criterion
numeric proficiency criterion (between 0 and 1, exclusive)
- reverse
boolean. If TRUE, the criterion refers to the proficiency of the person instead of the proficiency of the peer group. In other words, the role of the x and mu are reversed.
- interpretation
If TRUE, the rpi's print method will provide an interpretation of the relative proficiency.
Examples
# What is the probability a person with a W score of 540 can pass
# an item that a person with a 500 W score can pass with a
# probability of .90?
rpi(x = 540, mu = 500, criterion = .9)
#> 0.9986301
# Same as above but with an interpretive statement
rpi(x = 540, mu = 500, criterion = .9, interpretation = TRUE)
#> When a same-age peer of average ability has a .90 probability of answering an item correctly, this person has a .999 probability of answering it correctly.
# When a person with a W score of 540 has a .9 probability of
# passing an item, what is the probability that a person with a W
# score of 500 will pass it?
rpi(x = 540, mu = 500, criterion = .9, reverse = TRUE, interpretation = TRUE)
#> When this person has a .90 probability of answering an item correctly, a same-age peer of average ability has a .10 probability of answering it correctly.