# Lesson 10—Matched-Pairs t tests

#### By Olivia Mah

First published on April 20, 2019

### Learning Objectives

Perform a matched-pair hypothesis t test

### Demonstration

Here is the dataset that we are using in this demo from #17.16 in our textbook:

sitting_squatting.csv

Goal: To conduct a two-sided t test of no difference for a matched-pair t test

Here are the null and alternative hypotheses in this example:

$$H_0: \mu_1 = \mu_2$$

$$H_a: \mu_1 \neq \mu_2$$

where

$$\mu_1$$ = population mean angle in squatting

$$\mu_2$$= population mean angle in sitting

Here are the steps:

#### Step 2: Create a column of difference

w = sitting_squatting$Sitting - sitting_squatting$Squatting



DO NOT use name your column of difference as diff  because diff is a built-in function in R.

In this demonstration, we name our column of difference w.

#### Step 3: Draw a stemplot to check data

Draw a stemplot on the column of difference to check if data are roughly symmetric and without too many extreme outliers:

stem(w)


#### Step 3: Run the matched-pair t test via the R function t.test

t.test(sitting_squatting$Sitting, sitting_squatting$Squatting,
mu=0, paired=TRUE,
conf.level = 0.95)

Explanation:

Whenever R runs a hypothesis test, R automatically calculates the corresponding confidence interval —the range of values which the population mean is estimated to lie within.

Given a set of data, the corresponding hypothesis test result and the confidence interval are closely related. Therefore if we want the significance level $$\alpha$$ to be 0.05, then we set the argument conf.level = 0.95  because  conf.level = 1 – $$\alpha$$ .

By default, R automatically sets $$\mu = 0$$ and conf.level = 0.95 even if you don’t explicitly type these arguments. So you can skip typing these arguments into the t.test function if you are testing a two-sided alternative hypothesis with  $$\alpha =0.05$$.

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