Matched-Pairs Data and One-Sample t Tests of Mean Differences

All flashcards

What is a matched-pairs study?

A study in which measurements are linked by person, object, or a deliberate pairing process.

What values are analyzed in a paired-samples test?

One calculated difference for each matched pair, treated as a single sample.

Why must the subtraction order be stated?

It determines the signs and interpretation of the differences; after minus before makes positive values indicate increases.

What statistic and degrees of freedom are used in a paired-samples t test?

A one-sample t statistic calculated from the differences, with $n-1$ degrees of freedom.

What distribution condition matters when there are few pairs?

The population distribution of differences should be approximately normal, and unusual differences should be checked.

Quiz questions

1. For paired differences with sample mean $\bar{x}_d$, sample standard deviation $s_d$, and $n$ pairs, which expression gives the test statistic for hypothesized mean difference $\mu_{d,0}$?Answer: $t=\frac{\bar{x}_d-\mu_{d,0}}{s_d/\sqrt{n}}$
2. A paired-samples t test uses 9 matched pairs. How many degrees of freedom does the test have?Answer: 8
3. Differences are defined as after minus before. Which alternative hypothesis tests whether the population mean increased after treatment?Answer: $H_a: \mu_d>0$
4. A paired-samples test has p-value 0.03 and significance level $\alpha=0.05$. What decision should be made?Answer: Reject the null hypothesis because the p-value is below $\alpha$.
5. A paired-samples test has a large p-value. What is the appropriate interpretation?Answer: The data do not provide sufficient evidence against the null hypothesis.