Proportion Test – Example

In the previous post, we explained how to calculate P-value and thus perform hypothesis testing for categorical data.

In this post we will give an example.

A study was performed to see if there is a difference between males and females who use cannabis regularly.

The sample size was 134 , 51 Females and 83 Males.

The data result was as follows:

Our Null Hypothesis would be : There is no difference between the proportion of males using cannabis regularly and the proportion of females using cannabis regularly. Namely : H0: p_F = p_M

The two sided alternative hypothesis would be : There is a difference between the proportion of males using cannabis regularly and the proportion of females using cannabis regularly. Namely : HA: p_F != p_M

If we did the calculations we will find the following:

n_F = 51, p_hat_F = 0.2745
n_M = 83, p_hat_M = 0.7349

(absolute) z = 5.2129
p_value = < 0.0001

The following web app will calculate this example. You can use it to any similar data changing the values to your results:

Proportion Test

Group1

Group2

Two-Tailed
One-Tailed

Z value:

P_Value :

Two-sided p_value is 2 x 10 -7

This is a very small number. So we reject the Null hypothesis and conclude that:

There is a statistically significant difference between the proportion of males using cannabis and the proportion of females using cannabis.

Usually, we set the cutoff p value at 0.05. If the p value is less than 0.05 we reject the null hypothesis but if p value is more than 0.05 we fail to reject the null hypothesis.

Always check the cutoff value, which is also known as the significance level or alpha.