Review of T-Tests

Flashcards for reviewing the concepts of Student's T-test, One-Sample test and Paired t-test. Focus on understanding the origins, calculations, and application of each test.

Student’s t-test

A statistical test used to determine if a sample mean is similar to a null expectation.

Student

The pen name under which William Sealy Gosset published his work on the t-distribution.

Student’s t-distribution

A distribution developed to help determine if a sample mean was similar to a null expectation.

One-Sample t-Test

A t-test comparing the mean values of a small sample taken from a large population.

Two-Sample t-Test

A t-test comparing sales generated by two independent campaigns.

Paired Sample t-Test

A t-test comparing the mean values of one sample at two different times (e.g., pre-training and post-training).

𝑥̅

Sample mean

𝜃

Null hypothesised value

𝑆𝐸𝑥

Standard Error of x

𝑡 = 𝑥̅ − 𝜃 / 𝑆𝐸𝑥

The formula for Student's t-test.

H0 : Mean Barley length = Factory average (6.2)

Denotes that the mean barley length is equal to the factory average (6.2).

HA : Mean Barley length ≠ Factory average (6.2)

Denotes that the mean barley length is not equal to the factory average (6.2).

H0 : The mean of the treatment group = mean of the control group

The hypothesis that the mean of the treatment group equals the mean of the control group.

HA : The mean of the treatment group ≠ mean of the control group

The hypothesis that the mean of the treatment group does not equal the mean of the control group.

H0 : The mean difference = 0

The hypothesis that the mean difference between pre-treatment and post-treatment is 0.

HA : The mean difference ≠ 0

The hypothesis that the mean difference between pre-treatment and post-treatment is not 0.