What is the Z-test for Proportions in Statistics? Easy Explanation for Data Science Interviews

The z-test is a great asset to use when exploring proportions. In this video, I go over conducting both one-proportion and two-proportion tests, using loads of step-by-step examples. I’ll also share some of my top tips on when to use “pooled” vs. “unpooled” variance.

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Contents of this video:
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00:00 Introduction
00:53 Why Use Z-Test for Proportions?
02:24 One-Proportion Z-Test
07:37 Two-Proportion Z-Test
13:00 Confidence interval example
13:35 Conclusion

[emma_ding]

Thanks to Yue Cao for pointing out my mistakes at 10:50! It should be 0.5 instead of 0.05. Sorry guys, I will triple check my code before publishing it next time.

[baizunshan]

Thanks Emma. I was thinking about testing the CTR last night and today all of my questions are answers in this video! A great demonstration of presenting using Notion as well.

[vegetableball]

I think the most mathematical part of the procedure is the Central Limit Theorem which asserts that the sample proportion has a distribution approximately Gaussian given some statistical assumptions. The note mentions Slutsky's theorem but not Central Limit Theorem...

[zioncheng]

Great video as always!

A question: Why do we use Z-test instead of T-test? My understanding is that T-test should be used when the standard deviation of the underlying population is unknown, which is true here since we can't run the experiment for the whole population. Could you please tell me what I am missing here? Thanks!

[DavidLee-ws]

Hi Emma, Thanks for your sharing, and I have a question, how do you make sure ad impressions are independent Bernoulli trials, since it can be one user behind tons of ad impressions and clicks, how do you measure this impact is acceptable or not, and still keep the assumption of the data points are independent ? many thanks.

[cococnk]

Emma thanks for the awesome video ..

For the pooled variance or un Pooled variance

I think it comes from the fact that .. if the two samples have equal or un equal variance .. so we will kind of do the F ratio first ..

Then for equal variance we use a pooled variance

For an un equal variance between the two samples we use unpooled variance for the standard error in the test statistic formula.

😅 hope i am not mixing things !

Thanks.

[junqichen]

I liked the presentation material you put together. May I ask what tool you used to create it? Thanks!

[yuecao]

10:50 the square root calculation seems wrong - should be 0.5 instead of 0.05

[TohaBgood]

Great video! But some of the Python math is wrong. You applied the square root only to the last terms in two places for pooled and unpooled std. You’re just missing a set of parentheses in those two places.

Otherwise, great video! Keep it up!