Talk:Probit

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[edit] Percentile

shouldn't the graph's x-axis be in percentile and not in probability? The range of CDF is percentile (0,1) = (0th percentile, 100th percentile), whereas the range of normal distribution is probability (0,1) = (0%,100%). Since the probit is the CDF inverse, it's domain is CDF's range, which is in percentile, not probability. Thoreaulylazy 15:20, 3 October 2006 (UTC)

The range of the CDF in the graph is probability, right? However, this is an article about the probit, not the normal CDF, so it should probably remain a map from [0,1] to [-Inf, Inf]. --Pdbailey 00:49, 4 October 2006 (UTC)

I agree that Probit is a map from [0,1] to [-Inf,Inf], the problem is that [0,1] can be interpreted as 0% to 100% or 0th percentile to 100th percentile. The correct interpretation should be percentile not probability. An article about the probit function should be consistent with an article on the CDF function because they are inverses of each other. That is, the domain and range for CDF becomes the range and domain for Probit. The complication on whether to use "percentile" or "probability" stems from the fact that a percentile is a form of probability, "the probability that a random sample from the set is BELOW". That is, it is equivalent to say (a) a student John is ranked 70th in a class of 100, as it is to say (b) a random student from the class has a 70% probability of having a lower rank than John. Most statisticians, however, would simply say "John is at 70th percentile" -- no statistician would ever say "John is at 70% probability" (although they might say, if they're trying to be unnecessarily wordy, "a random student from the class has a 70% probability of being below John"). Thus, knowing the mean test score (M) and the standard deviation (D), we can infer John's score as M + D*Probit(.7). The domain of the Probit function is clearly percentile (.7 = 70th percentile). -- Thoreaulylazy 18:41, 7 December 2006 (UTC)