How to Perform a One Proportion Z-Test in Python

How to Perform a One Proportion Z-Test in Python

Performing a one-proportion Z-test in Python is a method used to determine if the proportion of a particular outcome in a sample is significantly different from a hypothesized proportion. This test is applicable in scenarios such as testing the success rate of a new product, the proportion of people preferring a certain option, etc.

To perform a one-proportion Z-test, you can use the statsmodels package, which provides a function called proportions_ztest for this purpose. Here's a step-by-step guide:

Step 1: Install statsmodels (if not already installed)

pip install statsmodels

Step 2: Import Required Libraries

import statsmodels.api as sm

Step 3: Define Your Data

  • count: The number of successes in your sample.
  • nobs: The total number of observations in your sample.
  • value: The proportion you want to test against (the null hypothesis value).

Example:

count = 80 # e.g., 80 successes nobs = 100 # e.g., out of 100 observations value = 0.7 # e.g., test against the proportion of 0.7

Step 4: Perform the Z-Test

Use the proportions_ztest function from statsmodels.

z_stat, p_value = sm.stats.proportions_ztest(count, nobs, value)

Step 5: Interpret the Results

  • z_stat: The Z-statistic for the test.
  • p_value: The p-value for the test.

The interpretation typically focuses on the p-value:

  • If the p-value is less than your chosen significance level (commonly 0.05), you reject the null hypothesis, suggesting that the sample proportion is significantly different from the hypothesized proportion.
  • If the p-value is greater than your chosen significance level, you do not reject the null hypothesis.

Full Example Code

import statsmodels.api as sm # Example data count = 80 # number of successes nobs = 100 # number of observations value = 0.7 # null hypothesis proportion # Perform one proportion z-test z_stat, p_value = sm.stats.proportions_ztest(count, nobs, value) # Output the results print(f"Z-Statistic: {z_stat}") print(f"P-value: {p_value}")

In this example, count = 80 and nobs = 100 means you observed 80 successes in 100 trials, and you're testing if this proportion is significantly different from the hypothesized proportion of 0.7. The interpretation of the result will depend on the Z-statistic and the p-value.

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