2. A dose-response study gives the following proportions of response: | Dose | Responded | Total | Proportion | |---|---|---|---| | 2 | 1 | 5 | 0.20 | | 4 | 3 | 5 | 0.60 | | 6 | 4 | 5 | 0.80 | Compute the logit transformation of each proportion. What is the main purpose of using Probit transformation in biological assays?
Answer (1)
To compute the logit transformation of each proportion, we use the formula for the logit:
logit ( p ) = ln ( 1 − p p )
where p is the proportion.
For the dose of 2 with a proportion of 0.20:
logit ( 0.20 ) = ln ( 1 − 0.20 0.20 ) = ln ( 0.80 0.20 ) = ln ( 0.25 ) ≈ − 1.386
For the dose of 4 with a proportion of 0.60:
logit ( 0.60 ) = ln ( 1 − 0.60 0.60 ) = ln ( 0.40 0.60 ) = ln ( 1.5 ) ≈ 0.405
For the dose of 6 with a proportion of 0.80:
logit ( 0.80 ) = ln ( 1 − 0.80 0.80 ) = ln ( 0.20 0.80 ) = ln ( 4 ) ≈ 1.386
The main purpose of using a probit transformation in biological assays is to model the relationship between dose and response. Probit analysis assumes that there is a normal distribution of the response to the dose, and the transformation allows us to linearize the dose-response curve. This makes it easier to estimate effective doses, compare different treatments, and understand variations in biological responses effectively.
