You persist in repeating your original request in your original phrasing, with no elaboration(s) that might resolve the ambiguities therein.
On Sat, 10 Nov 2001, Mark T wrote: > On Fri, 09 Nov 2001 Rich Ulrich <[EMAIL PROTECTED]> wrote: > > > On Thu, 8 Nov 2001 Mark T <[EMAIL PROTECTED]> wrote: > > > What are the formulae for calculating the mean to z, larger > > > proportion and smaller proportion of a z-score (standardised score) > > > on a standard normal distribution? I know about tables listing > > > them all, but I want to know how to work it out for myself :o) > > Do you want the calculus, or just a numerical approximation? > > > > For starters, in my stats-FAQ, see > > > > http://www.pitt.edu/~wpilib/statfaq/gaussfaq.html > Thanks for your reply. Ummm, unfortunately I don't understand this :o) Not surprising. > I am by no means a mathematician. I am studying psychology and 1/4 of > my course is statistics *for psychology*, ie it's pretty basic without > any of the advanced stuff (I hope!). A pity, if true. Adequate practice of psychology requires considerably more than a minimum knowledge -- and understanding! -- of statistics. > All I want to know, for interest's sake, is how one calculates the > mean to z, Yes, you said that before. In the same words. For the sake of (possibly) furthering the conversation, I will assume that what you meant was something like "Given a value x of a variable X, which has a known mean, how does one convert x to z?" (Your language admits of several other possible meanings, but I'll leave it to you to clarify what you intended, if it wasn't what I've conjectured (and if you can).) The formula you request, for this purpose, converts x to z: z = (x - mean)/sd where "sd" is the known standard deviation of the variable X. Now, I'm sure your statistics instruction includes this equation; it follows that the question you really want to ask is (probably) something else. In which case we all await with interest your clarification. > larger proportion and smaller proportion of a standardised score, > without having to read through a long list of numbers. Hmm. Numbers scare you, do they? There are essentially three ways of going about this part: 1. Look the proportions up in a table of the standard normal distribution, which by your account you are apparently too lazy to do. Sounds as though you're being inefficient, by the way: there's no need to "read through a long list of numbers", only to look up a single number in the table (the other proportion you can get by subtracting from 1.) 2. Use convenient statistical software (MINITAB, SAS, SPSS, a TI-83 calculator, etc.) to calculate the proportions by numerical approximation. This of course does not satisfy your request for "the formulae". 3. Start with the mathematical expression for the density function of a standard normal distribution, and integrate it from minus infinity to z. Which is what Rich was referring to when he asked if you wanted the calculus. Again, by your account you haven't the mathematics for this; especially as the integral in question does not exist in closed form. (Which, of course, is precisely the reason why tables were constructed in the first place, to avoid a _very_ tedious computational chore every time one had a value of z for which proportions, or probabilities, were needed.) > Forgive me if that was covered in your FAQ, but I couldn't see > it! Perhaps you could point me in the direction of the formulae? Forgive me if my candour is uncomfortable, but this sounds to me very like asking a sorcerer for the spell(s) you think he uses. Do you want a magic wand also, and perhaps a cloak of invisibility? I am reminded of the time, years ago, when the mother of a high-school student telephoned me for assistance in a problem the boy had been set by his math teacher. (I noticed at the time that it wasn't the _boy_ who called me.) He'd been asked to figure out the possible scores one could get in a hand at cribbage (or perhaps to explain why a score of 19 is not possible -- I don't remember precisely). Mother was sure there must be a "formula" for doing this (she evidently looked on mathematics as you do, as a domain wholly of magic and populated by sorcerers), and was audibly disappointed to be told "The only way to do this is to enumerate the possible hands". -- DFB. ------------------------------------------------------------------------ Donald F. Burrill [EMAIL PROTECTED] 184 Nashua Road, Bedford, NH 03110 603-471-7128 ================================================================= Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =================================================================
