Z score to p values

I have a large matrix 1xN containing z values. I would like to know how to turn these z scores to p values using normcdf function?

How to obtain p values both for one-tailed and two-tailed p values using normcdf?

Many thanks in advance!

Answer 1

[Star Strider]

If I remember correctly, the probability of a one-tailed test is twice the probability of a two-tailed test, so:

p_one = 2*normcdf(z_vector);
p_two = normcdf(z_vector);

[lou]

Are these p_one & p_two the p values or they need to be subtracted from 1?

for example

p_one = 2*normcdf(z_vector);

p_value=1-p_one

[Star Strider]

If you want the complementary values, use the 'upper' option:

p_one = 2*normcdf(z_vector, 'upper');
p_two = normcdf(z_vector, 'upper');

[lou]

Unfortunately this does not work - I get this error after command

p_one = 2*normcdf(z_values, 'upper');

Error using normcdf (line 56)

Non-scalar arguments must match in size.

[Star Strider]

I cannot reproduce that error, given the information you have supplied. There may be version differences. I’m using R2016b.

Try one of these to see if it works for you:

N = 5;
z_vector = randn(1,N);                                  % Create Data

p_one = 2*normcdf(-abs(z_vector));
p_two = normcdf(-abs(z_vector));
p_one_c = 1-2*normcdf(-abs(z_vector));
p_two_c = 1-normcdf(-abs(z_vector));

The last two are complementary to the first two.

[lou]

This works! thank you!

[Star Strider]

My pleasure!

[Jos (10584)]

Be aware that can have a left-tail one-sided z-test and a right-tail one-sided test, so simply taking the absolute value is inappropriate:

p_left = normcdf(zval)
p_right = normcdf(-zval)

[Star Strider]

I agree, but that wasn’t the Question here.

[lou]

why for right-sided p-values I need to take "-zval"? I mean why do I need to insert the negative z values?

[Star Strider]

It depends upon the hypothesis you are testing.

[Noah]

Note that the accepted answer is backwards, unless you mean something strange by your hypothesis. The probability of one-tailed test is HALF the probability of a two-tailed test. The area under a bell curve on one side is half the area on both sides.

p_oneTailed = normcdf(z_vector);
p_twoTailed = 2*normcdf(z_vector);

Answer 2

[Ziwei Liu]

Two-tailed p value should actually be 2 * (1 - normcdf(z)).

normcdf(z) gives the area under curve on the left side of z. This is not p value. One-tailed p value should be the area on the right side, which is (1 - normcdf(z)).Two-tailed p value should be the double of that.

You can use the arrayfun function to compute p value for each entry in your z score matrix. i.e. p = arrayfun(@(x) 2*(1-normcdf(x)), ZScoreMatrix).

[Germano Gallicchio]

For this to work with negative z scores, you also need to take the absolute value of z:

z = [-2.58 -1.96 -1.65 0 1.65 1.96 2.58]; % vector of z scores
p = 2 * (1 - normcdf(abs(z))); % vector of associated pvalues
disp([z' p'])

   -2.5800    0.0099
   -1.9600    0.0500
   -1.6500    0.0989
         0    1.0000
    1.6500    0.0989
    1.9600    0.0500
    2.5800    0.0099