# STATS 13 Lecture Notes - Lecture 21: Repeated Measures Design, Random Assignment, Statistical Power

by OC2550403

Department

StatisticsCourse Code

STATS 13Professor

Tsiang, MikeLecture

21This

**preview**shows page 1. to view the full**4 pages of the document.**Chapter 7: Paired Data: One Quantitative Variable!

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Section 7.1: Paired Designs !

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Independent and Dependent Samples!

We have two types of scenarios when comparing two populations:!•

we have two independent samples from two populations; the observations in each group do not aﬀect the ◦

observations in the other!

we have paired (dependent) samples, where the data is actually related pairs of observations from one ◦

sample!

In chapters 5 and 6, we looked at independent samples. !•

This chapter: pair samples!•

the way we analyze paired data is diﬀerent from the way we analyze data from independent samples so it is •

important to recognized what kind of data we have!

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Independent or Dependent samples?!

examples!•

people chosen in random sample were asked how many minutes they spend the day before watching TV. ◦

Researchers want to known how diﬀerent the mean amounts of time are for these two activities!

paired (sample people measured twice)!‣

researchers randomly assigned overweight people to one of two diets. researchers want to know whether ◦

the mean weight loss of one was diﬀerent from the other !

independent samples!‣

the number of hours of sleep husbands and wives get are compared to see whether the means are diﬀerent!◦

paired samples (each husband is paired with one wife)!‣

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Introduction!

the paired data sets in this chapter have one pair of quantitative response values for each observational unit!•

allows for a built in comparison!•

studies with paired data remove individual variability by looking at the diﬀerence score for each individual!•

reducing variability in data improves inference:!•

narrower conﬁdence intervals!◦

better ability to detect a false null hypothesis (higher statistical power)!◦

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Example 7.1: Can you study with music blaring!

many students study while listening to music!•

does listening to music hurt ability to focus!•

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experimental designs!

1 -- random assignment assigned to one of two groups!•

one group listens to music with lyrics!◦

one group listens to music without lyrics !◦

students play a memorization game while listening to the particular music that they were assigned!•

2 -- paired design using repeated measures!•

all students play the memorization game twice!◦

once while listening to music with lyrics!‣

once while listening to music without lyrics!‣

3 -- paired design using matching!•

sometimes repeating something is impossible (testing a surgical procedure) but we can still pair!◦

test each student on memorization!‣

match students with similar scores and assign randomly!‣

have one play the game while listening to music with lyrics and the other while listening to music ‣

without lyrics!

Studying with Music: Repeated Measures!

Paired Design using repeated measures!•

there could be a lot of overlap between ◦

the two sets of scores and it would be

diﬃcult to detect a diﬀerence as shown

here!

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