# Two proportion test¶

This function determines if there is a statistically significant difference in the results from two different tests. Similar to the One_sample_proportion, we are interested in using results from a success/failure test, but we are now interested in whether the difference in results is significant when comparing results between two tests.

Inputs:

• sample_1_trials - number of trials in the first sample
• sample_1_successes - number of successes in the first sample
• sample_2_trials - number of trials in the second sample
• sample_2_successes - number of successes in the second sample
• CI - desired confidence interval. Defaults to 0.95 for 95% CI.
• print_results - True/False. If True the results will be printed to the console. Default is True.

Outputs:

• lower,upper,result - lower and upper are bounds on the difference. If the bounds include 0 then it is a statistically non-significant difference.

In this example, consider that sample 1 and sample 2 are batches of items that two suppliers sent you as part of their contract bidding process. You test everything each supplier sent you and need to know whether the reliability difference between suppliers is significant. At first glance, the reliability for sample 1 is 490/500 = 98%, and for sample 2 is 770/800 = 96.25%. Without considering the confidence intervals, we might be inclined to think that sample 1 is almost 2% better than sample 2. Lets run the two proportion test with the 95% confidence interval.

from reliability.Reliability_testing import two_proportion_test
two_proportion_test(sample_1_trials=500,sample_1_successes=490,sample_2_trials=800,sample_2_successes=770)

'''
Results from two_proportion_test:
Sample 1 test results (successes/tests): 490/500
Sample 2 test results (successes/tests): 770/800
The 95% confidence bounds on the difference in these results is: -0.0004972498915250083 to 0.03549724989152493
Since the confidence bounds contain 0 the result is statistically non-significant.
'''


Because the lower and upper bounds on the confidence interval includes 0, we can say with 95% confidence that there is no statistically significant difference between the suppliers based on the results from the batches supplied.