Re: Which calculator can do a "normal probability plot"?

[Prev][Next][Index][Thread]

Re: Which calculator can do a "normal probability plot"?

Penser asked:

>Anyone know which calculator can do a "normal probability plot"?  I have
>a TI-86 with the advance stats module, but I don't see how it can do it.  If
>no calc can do it, any suggestions on how to program it?

Below is the basic idea, based on a quick scan of my Minitab manual.  This
can be turned into a program for (presumably) ANY of the TI calculators --
it does not use any heavy-duty statistics functions.  (I had assumed that
at least an inverse-cdf for the normal distribution would be needed, but a
nifty approximation mentioned in the Minitab manual takes care of that part
of the computation.)

Penser also wrote:
>Probability plotting typically uses special graph paper, known as
>probability paper, that has been designed for the hypothesized distribution.

The method below doesn't require any special paper :-)  (Has anyone out
there actually made a quantile plot by hand?)

Suppose the data are in a list we shall call xlist.  (TI-81s don't actually
have list variables, but I think this will work if the data is in the
statistics xlist.)  Let n be the number of data points.

1. Sort xlist in order from smallest to largest.  (All calculators have
some sort of list-sorting command.)

2. for i=1 to n
     (i-3/8) / (n+1/4) -> p
     *** "->" is the store key.
     4.91 (p^0.14-(1-p)^0.14) -> ylist(i)
     *** This is the approximation of invcdf(p).
   next i  (that is "End" or "EndFor", in TI-Basic)

3. Make a scatterplot of xlist vs. ylist.

(This last step reflects my preference to put xlist -- the variable being
studied -- on the vertical axis and ylist -- the theoretical quantiles --
on the horizontal axis.  The quote below from the Instructor's Guide to
Moore and McCabe's _Introduction to the Practice of Statistics_ gives my
rationale.)

----Quoted material begins
Note that software packages that create quantile plots may differ in
what variable is put on each axis.  Plots in the book [IPS] place the
variable being studied on the vertical axis, and the $z$ score on the
horizontal axis.  One benefit of this arrangement is that we can
interpret the plot in a natural way: if (e.g.)\ the upper right part of
the plot bends down (below the line), we can interpret it by saying,
``The high values of the variable are lower than they `should' be [to
be from a normal distribution]." (This is natural,
since the {\em high} part of the plot is {\em below} the line.)
Likewise, if the lower left part of the plot bends up, we can say,
``The low values of the variable are too high [to be from a normal
distribution]."
----Quoted material ends

If anyone actually turns this into a program (for any calculator), I'd be
interested in a copy.  (I'll probably tackle the problem myself, when I
have time.)

Darryl K. Nester                E-mail: mailto:nesterd@bluffton.edu
Assoc. Prof. of Mathematics        WWW: http://www.bluffton.edu/~nesterd
Bluffton College                 Phone: 419-358-3483
Bluffton, OH  45817-1704           Fax: 419-358-3232
References: