Talk:Probit

message: 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)
replies: text: 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)
replies: text:  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)
replies: text: Refer also to the articles on rankit and Q-Q plot. DFH 19:23, 29 January 2007 (UTC)
thread_title:  Percentile 

message: Couldn't this article have a simpler summary? The lingo used in this article suggests to me that anybody who understood it would probably know what a probit was already anyway. —The preceding unsigned comment was added by 195.194.178.251 (talk) 09:46, 12 January 2007 (UTC)
thread_title:  Summary is a bit heavy 

message: 1.  There is a problem with identifying your readers, and writing appropriately.  One reader might be an EPA manager with one course in statistics, who has heard that the scientists are using "LD50s" which are computed using something called "probit analysis." Another may be a statistician who thinks "wonder what Wikipedia has on probit."  
2.  Looks like this is mostly about math.  You probably want to think about subject-matter motivation.  Important areas of application include psychometrics, econometrics, and toxicology.  A conventional toxicological explanation is based on a lognormal distribution of tolerances, where the tolerance of a single organism is the dose just high enough to elicit a particular type of "response" (not necessarily death).  
3.  I think it would be good to include some more about statistical inference, including some interesting history.  The linear relation between probit of expected response and the predictor is very often taken by the statistically naive as an indication that inference is a case of ordinary linear regression.  In fact, maximum likelihood estimation is pretty standard.  Historically, it seems you could about say that probit is the original "generalized linear model."  The scoring algorithm used in glm comes from an appendix of Bliss paper, written by R.A. Fisher.  
4.  Possible links are bioassay, toxicology, generalized linear models, R.A. Fisher.     
Dfarrar 04:37, 20 February 2007 (UTC)
replies: text: Bliss's 1934 paper in Science simply says "These arbitrary probability units have been termed 'probits' and are given above in an abbreviated table". He gives no further explanation of the motivation for the term. "Probability of Insect Toxicity" gives 0 hits on Google. Smells like a backronym to me. --Qwfp (talk) 13:26, 29 August 2009 (UTC)
thread_title:  Needs More History and Motivation 

message: I think this should be limited pretty much to defining the probit function and alluding to the important uses.  Additional detail on probit modeling should probably go under probit model.  I hope my additions conform to that suggestion. 
I suggest finding some links related to the material I just put in on diagnosing deviation from normality. Thanks for the nice details on Bliss's work.  Dfarrar 03:51, 31 March 2007 (UTC)
replies: text: I could live with merging this into probit modeling. Thanks for pointing out the QQ plot article.Dfarrar 00:29, 2 April 2007 (UTC)

text: Richard, Could you provide the text of reference 14? Also, why do you think that belongs here and not at probit model? Pdbailey 16:18, 8 April 2007 (UTC)
thread_title:  what goes here vs. what goes under [[probit model]] 

message: I think the erf stuff is fairly technical and needs some generally acceisible statement of it's significance.  Here it is:
"The probit function may be expressed in terms of the inverse of the error function:
:\Phi^{-1}(p)=\sqrt{2}\,\operatorname{erf}^{-1}(2p-1)
As a student, the error function inverse is how probits are described and introduced to us, as we learn about the error function in basic courses. I personally think it would be useful to have it on there Geeeeeeek (talk) 17:15, 12 May 2016 (UTC)
thread_title:  here is the deleted erf() stuff