Z-test with 2 samples

Does Matlab calculate the Z-test with 2 samples?

[Scott Callahan]

Visit my page for a 2 sample z test function I created.

Answer 1

[Wayne King]

Why not use the two-sample t-test? I think there are very few situations in which the two-sample z-test is going to give you something the two-sample t-test will not.

For example, as far as I know, the z-test means that you know the (population) standard deviation of the samples. That is pretty restrictive.

But you can easily define a two-sample z-test

function zval = ztest2(x,y,mux,muy,varax,vary)
% x - sample 1
% y - sample 2
% mux - mean of x to be used in difference. If you are not testing a
% specific difference, use mux = 0
% muy - mean of y. If you are not testing a
% specific difference, use muy = 0
% varx - variance of x
% vary - variance of y
    Nx = length(x);
    Ny = length(y);
  zval = ((mean(x)-mean(y))-(mux-muy))/sqrt(varax/Nx+vary/Ny);
  end

Save ztest2.m in a folder on the MATLAB path and try

   x = 4+randn(100,1);
   y = randn(100,1);
   zval = ztest2(x,y,0,0,1,1);
   % now use
   zval1 = ztest2(x,y,4,0,1,1);

[Sonja Brett]

I am having issues with the t-test because I am using large sample sizes (20,000). My p-values are coming up as 0 or 1, no decimals even when changing to format long. I believe it is because the t-test is designed for smaller sample sizes. I would like to compare the same population (large large sample size) before and after treatment, which would be a paired z-test.

[raym]

After we get zval, how to get p-value?

[raym]

This is my modified function

function zval = ztest22(x,y,mux,muy,varx,vary)
if ~nargin
    x = rand(10000,1);
    y = 1+rand(10000,1);
end
%%
% x - sample 1
% y - sample 2
% mux - mean of x to be used in difference. If you are not testing a
% specific difference, use mux = 0
% muy - mean of y. If you are not testing a
% specific difference, use muy = 0
% varx - variance of x
% vary - variance of y
if ~exist('mux','var');mux=0;end
if ~exist('muy','var');muy=0;end
if ~exist('varx','var');varx=std(x);end
if ~exist('vary','var');vary=std(y);end
%%    
Nx = length(x);
Ny = length(y);
zval = ((mean(x)-mean(y))-(mux-muy))/sqrt(varx/Nx+vary/Ny);
end