(9.3B) Paired Samples Objectives: Use computer output Recognize paired data Use a one-sample t-test appropriately for paired data Recognize alternate mechanics formulas

Do we have one sample or two??? Two samples are said to be independent when the elements of one sample have no bearing on the selection of those in the other sample. We can only use two-sample procedures when samples are independent.

What happens when the data from one sample is not independent of the data from another sample? Sometimes it means you have paired data. Turns out that paired data functions as ONE sample, not two. Do we have one sample or two???

How can we tell that we have paired data? We might compare subjects to themselves “before and after.” In an experiment, we might create blocks with just two elements. In an observation, we might match two elements.

Understand the design The design drives the analysis. If you have a matched-pairs design then you do NOT have two independent random samples. Without two independent samples, you cannot run a 2-sample test.

But don’t go on a snipe hunt Just because your samples have the same number of elements doesn’t automatically make it a matched- pairs opportunity. You have to read the stem.

Example A Would a four-day work week save on resources such as gasoline? Lake County, Illinois Department of Health decided to find out.

Example A (from BVD 2e page 574) Name5-day4-dayName5-day4-day Amelia Michael Juliet Meredith Savannah Thomas Jason Katherine Margaret Elizabeth Marianna Evelyn Put 5-day data in List 1. Put 4-day data in List 2

Example A, con’t The 5-day data is in List 1 The 4-day data is in List 2 You want the DIFFERENCES. So you must subtract L1-L2

Example A, con’t  Write hypotheses and identify variables appropriately  Check conditions ‽Random ‽Independent ‽Normal

Example A, con’t About normality―You must graph the appropriate data. Be careful to choose the correct list!

Example A, con’t Be careful when you write your formula to name the test!

Example A, con’t