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Subject: Re: [office-formula] ZTEST

• From: Stefan Nikolaus <stefan.nikolaus@kdemail.net>
• To: office-formula@lists.oasis-open.org
• Date: Fri, 9 Feb 2007 12:56:09 +0100

```On Friday 09 February 2007 00:44:16 Andreas J. Guelzow wrote:
> I just had a look at the ZTEST description. Considering the 2 argument
> version, the description seems to differ from what OOo and GNumeric
> implements (and according to what the description itself says also what
> Excel does.)
>
> I can't confirm what Excel does (it doesn't run under Linux so it is not
> available to me) but OOo and Gnumeric calculate the onesided p-value for
> the z-test.

Hmm, Calc's help claims, that it computes the two-tailed test. I've interpret
this as: it uses both tails of the distibution to compute the value.
Calc's code look like this:
PushDouble(0.5 - gauss((mue-x)/sqrt(sigma/rValCount)));
Which shows, that it tries to use the onesided p-value and also tries to
implement the one-tailed test, because I see not doubling of the value in the
contextual code.
gauss() is the method returning the value for GAUSS (what a surprise ;-) ).
And that is defined as NORMDIST(x)-0.5. NORMDIST(x) returns the value of the
normal distribution pdf (!) at position x. Is that what you call the p-value?
I think not. You want the value of the cdf! Otherwise, it makes no sense at
all (AFAICT).

And if you want to calculate the one-tailed test, make sure, that you don't
make the same error as Excel: It takes the value of the cdf at the position
of the signed (!) z value. If z is negative, this results in a wrong value.

> The three-argument version yields significantly different values between
> OOo and Gnumeric and I haven't quite determined yet which values that
> are.
>
> Am I correct in assuming that our function descriptions ought to be
> close to at least some implementation?

The upcoming KSpread 2.0 implements it exactly this way. ;-)
The z-Test is not arbitrarily definable. AFAIK, the z-Test is a well defined
method in statistics. To use the name ZTEST and differ from this definition
is not acceptable, even not for compatibility reasons. If you define the one-
or two-tailed test, is only a matter of taste.
Calc's help claims to implement the two-tailed test, but it actually
implements the one-tailed test and gets it wrong.
Gnumeric claims to calculate the one-tailed test. It produces the same values
as Calc, which are wrong.
Excel claims to calculate the one-tailed test, but gets it wrong for negative
z values.
KSpread claims to implement the two-tailed test, and gets it right (this
statement is biased ;-) ).

Regards,
Stefan

--
Stefan Nikolaus
humba, humba, tätärää, tätärää, tätäräää ;-)
```

PGP signature

• References:
• ZTEST
• From: "Andreas J. Guelzow" <aguelzow@math.concordia.ab.ca>

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