Logistic vs Gaussian

Logistic normal distribution. Logistic vs Gaussian. There is very little difference between the Logistic function and the Gaussian function: The logistic function is a little thicker at the tail which is good as subjects tail are usually a little thicker than expected due to mistakes. Most older books on psychometric methods only mention the Gaussian function. The reason is that until recently, computers could not fit models very well, and it was easier to use easily accessible Gaussian cummulative function tables. Older books motivated the use of the Gaussian function with the following model: A subject observes a feature theta. The perception process adds some Normal noise. The subject then uses a step Decision cutoff. Any reading (theta + noise) above the cutoff results in a yes response, any reading under the cutoof results in a no response. Proba(Subject chooses a yes response / theta) = Proba(theta + noise > threshold / theta) = Proba(noise > threshold -theta / theta) = Normal cumulative function(theta-threshold) According to this model then, the data should follow a normal cumulative function curve. However, through a similar reasoning, if we assumed that the noise followed a logistic distribution, the probability of choosing a yes response would become a logistic cumulative function. The two functions are so similar that they cannot be distinguished with typical data set sizes.