DASC 120 Week 9 Lecture 7.2/3 Paired T-Testing and T-Test for two means

Quantitative Data / Numeric Data Inference

Scenarios:

We have one variable and we compare the mean of this data to an expected, previously reported, or theoretical mean

We have two variables and we compare the two means to see if they are different from each other 

• Samples are paired

• Samples are independent

Paired Samples

Paired samples are treated as the same sample with two measurements assigned to each

sample

We analyse the DIFFERENCE for each set, creating a single variable

• Shininess factor in cats fur before and after a 30 day diet change

• Prices of a single book title at two different book stores

Creating the sample:

Take the difference of each pair consistently:

Re active index measured at Treatment D30 - D0

A price - Bookstore B price

(Could also use the |absolute value|)

Conditions to use the T-Test

In effect, we have now created ONE variable that we can evaluate using the T-Test

Independence. D must be independent. Usually met when randomly sampled OR the

process is a random process

Normality. When sample size is small, must be normally distributed. Larger sized

samples may be less normally distributed.

EXAMPLE

In an earlier edition of the textbook, the authors found that Amazon prices were, on average, lower than those of the UCLA Bookstore for UCLA courses in 2010. It’s been several years, and many stores have adapted to the online market, so the authors wondered how the UCLA Bookstore is doing today?

They sampled 201 UCLA courses. Of those, 68 required books could be found on Amazon. These 68 are the basis of the analysis.