## How to conduct z test

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Occasional Contributor
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# How to conduct z test

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Solution
‎10-11-2017 11:29 AM
Super User
Posts: 19,851

## Re: How to conduct z test

There isn't much Z test information out there because it's rarely used and rarely applicable. For large N the T-Test will approximate the Z-Test quite closely, almost exactly as you get to large Ns.

If you check the T-Test documentation, the first example shows how to perform a t-test with summary statistics.

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## Re: How to conduct z test

Occasional Contributor
Posts: 19

## Re: How to conduct z test

Hi Reeza,

Sorry, my question didnt give much clarification. I want to know a proc by which z test can be conducted as like for t-test there is a proc ttest.

Super User
Posts: 19,851

## Re: How to conduct z test

I don't think there is one. A z test is only appropriate if you have the full population, which is rare, and at large numbers they'll give the same results anyways.

What kind of Z test do you need? There are some examples of people having hardcoded data steps to do this, but it's rare for a reason.

SAS Super FREQ
Posts: 3,755

## Re: How to conduct z test

What are the data and what question are you trying to answer?

The only z test that I can think of that is used in practice is the test for difference between two proportions. You can conduct that test by using PROC FREQ, as shown by Usage Note 22561.

Posts: 1,931

## Re: How to conduct z test

Arun_shSAS wrote:

Hi Reeza,

Sorry, my question didnt give much clarification. I want to know a proc by which z test can be conducted as like for t-test there is a proc ttest.

This really doesn't give us useful information. Can you state what hypothesis you are trying to test, and what your data is, and what distribution you have, and things like that? Just start from scratch, and describe the ENTIRE WHOLE COMPLETE problem for us, leaving nothing out, and do not be stingy with words.

Valued Guide
Posts: 684

## Re: How to conduct z test

If you are trying to compare two means with a z test, you can just trick PROC MIXED into doing this, because a t distribution with infinite df is equivalent to a standard normal distribution. If you have data in long form, with a separate record for the treatment and control (as an example, with a variable called treat for identifying treatment (say 0 for control and 1 for treated), you can use:

proc mixed data=...;

class treat;

model y = treat / ddf = 10000 solution;

run;

The Solution output gives the "t statistic", but with df=10000, this is really giving you a z test for the mean difference. Of course, this would be very misleading if you have a small number of observations.

SAS Super FREQ
Posts: 3,755

## Re: How to conduct z test

Please provide details about what problem you are trying to solve. Do you want

1. A z-test for a one-sample mean for which the population mean and variance are known? (textbook problem)

2. A z-test for comparing the means of two samples for which the population variances are known? (textbook problem)

3. A z-test for the difference of proportions?

4. Something else?

Contributor
Posts: 24

## Re: How to conduct z test

Hi, Rick,

I have also been trying to find documentation on what procedure to run and what attributes to specify for a one-sample z-test. I was wondering if you could help me figure this out?

In my dataset, I have data on 58 people, so the standard deviation, mean and distributions are all known. My data is being compared to the U.S. population norm data collected by a survey company. The only thing that is known from their data is the mean and the standard deviation. So I would like to run a one-sample z-test that compares my mean against theirs with the null hypothesis being: "There is no difference in the means between the two populations". A couple of questions:

1. The standard deviation needs to be known for which population, or is it both of them?

2. Why is it so difficult to find a tutorial on this via Google? Any time I find anything regarding doing a z-test, I mostly get t-test instructions instead, or, if I do get a z-test instructions, I get tutorials on knowing the variance and not specifically how to do a z-test in SAS, but by-hand calculations instead. And if I do get an SAS tutorial, there is nothing said in any example about inputting anything about the variance for PROC FREQ (I'm assuming this is the z-test). So, I gather from your questions, that you have to know the variance for a z-test, then why isn't it talked about in tutorials or specified in PROC FREQ examples, like h0 is?

Confused!!!

Solution
‎10-11-2017 11:29 AM
Super User
Posts: 19,851

## Re: How to conduct z test

There isn't much Z test information out there because it's rarely used and rarely applicable. For large N the T-Test will approximate the Z-Test quite closely, almost exactly as you get to large Ns.

If you check the T-Test documentation, the first example shows how to perform a t-test with summary statistics.

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