<aside> 💡 I’m spending so much time on t-test and z-test. It’s confusing to me because I’m a visual learner who does great with tables, charts and graphs, and does terrible with paragraphs of words. Unfortunately most materials are in paragraphs.

I have synthesized what I read into tables for easy memorization.

This page is in progress and gets frequent updates as I try to synthesize the topic a bit more.

Apparently, in A/B testing , t-test is the one that’s used.

</aside>

At-A-Glance

the null hypothesis

		One-Sample
t-test	for means	H0: sample mean is equal to the population mean
H0: mean of population 1 is equal to mean of population 2
H0: the mean difference between the paired observations is zero

z-test	for means

(i.e. before & after treatment on the same subjects) |

when to use what

https://towardsdatascience.com/non-parametric-tests-in-hypothesis-testing-138d585c3

the assumption

		One-Sample	Two-Sample	Paired-Sample
Sample Size	t-test	arbitrary	arbitrary	arbitrary
	z-test	≥ 30	≥ 30	≥ 30
Normally Distributed Population	t-test	yes	yes	yes
	z-test	no need to assume because CLT implies normality	no need to assume because CLT implies normality	no need to assume because CLT implies normality
Population Variance	t-test	unknown	unknown	unknown
	z-test	known (rare in application, use CLT to assume sample variance = population variance)	known (rare in application, use CLT to assume sample variance = population variance)	known (rare in application, use CLT to assume sample variance = population variance)
Independent Population AND
Independent Sample	t-test	not applicable	yes	not applicable
	z-test	not applicable	yes	not applicable

standard deviation and variance are interchangeable, since std dev = sqrt variance

CLT —> Central Limit Theorem

terminologies

Created by Soph Zhang

data distribution = sample data distribution

CLT does not necessarily apply

sampling distribution = sample statistic distribution