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What is the difference between a between- groups research design and a within-groups research design?

Let’s assume the average speed of a serve in men’s tennis is around 135 mph, with a standard deviation of 6.5 mph. Because these statistics are calculated over many years and many players, we will treat them as population parameters. We develop a new training method that will increase arm strength, the force of the tennis swing, and the speed of the serve, we hope. We recruit 9 professional tennis players to use our method. After 6 months, we test the speed of their serves and compute an average of 138 mph.

a. Using a 95% confidence interval, test the hypothesis that our method makes a difference.

b. Compute the effect size and describe its strength.

c. Calculate statistical power using an alpha of 0.05, or 5%, and a one-tailed test.

d. Calculate statistical power using an alpha of 0.10, or 10%, and a one-tailed test.

e. Explain how power is affected by alpha in the calculations in parts (c) and (d). 

In an exercise in Chapter 7, we asked whether college football teams tend to be more likely or less likely to be mismatched in the upper National Collegiate Athletic Association (NCAA) divisions. During one week of a college football season, the population of 53 Football Bowl Subdivision (FBS) games had a mean spread (winning score minus losing score) of 16.189, with a standard deviation of 12.128. We took a sample of 4 games that were played that week in the next-highest league, the Football Championship Subdivision (FCS), to see if the spread were different; one of the many leagues within FCS, the Patriot League, played 4 games that weekend. Their mean was 8.75.

a. Calculate the 95% confidence interval for this sample.

b. State in your own words what we learn from this confidence interval.

c. What information does the confidence interval give us that we also get from a hypothesis test?

d. What additional information does the confidence interval give us that we do not get from a hypothesis test?

Using the football data presented in Exercise 8.49, practice evaluating data using confidence intervals.

a. Compute the 80% confidence interval.

b. How do the conclusion and the confidence interval change as you move from 95% confidence to 80% confidence?

c. Why don’t we talk about having 100% confidence?

In Exercises 8.49 and 8.50, we considered the study of one week of a 2006 college football season, during which the population of 53 FBS games had a mean spread (winning score minus losing score) of 16.189, with a standard deviation of 12.128. The sample of 4 games that were played that week in the next highest league, the FCS, had a mean of 8.75.

a. Calculate the appropriate measure of effect size for this sample.

b. Based on Cohen’s conventions, is this a small, medium, or large effect?

c. Why is it useful to have this information in addition to the results of a hypothesis test? 

In Exercise 8.51, you calculated an effect size for data from one week of a 2006 college football season with 4 games. Imagine that you had a sample of 20 games. How would the effect size change? Explain why it would or would not change.

In Exercise 4.51

we considered the study of one week of a 2006 college football season, during which the population of 53 FBS games had a mean spread (winning score minus losing score) of 16.189, with a standard deviation of 12.128. The sample of 4 games that were played that week in the next highest league, the FCS, had a mean of 8.75.

According to the Nielsen Company, Americans spend $345 million on chocolate during the week of Valentine’s Day. Let’s assume that we know the average married person spends $45, with a population standard deviation of $16. In February 2009, the U.S. economy was in the throes of a recession. Comparing data for Valentine’s Day spending in 2009 with what is generally expected might give us some indication of the attitudes during the recession.

a. Compute the 95% confidence interval for a sample of 18 married people who spent an average of $38.

b. How does the 95% confidence interval change if the sample mean is based on 180 people?

c. If you were testing a hypothesis that things had changed under the financial circumstances of 2009 as compared to previous years, what conclusion would you draw in part (a) versus part (b)?

d. Compute the effect size based on these data and describe the size of the effect.

Let’s assume the average speed of a serve in women’s tennis is around 118 mph, with a standard deviation of 12 mph. We recruit 100 amateur tennis players to use our new training method this time, and after 6 months we calculate a group mean of 123 mph.

a. Using a 95% confidence interval, test the hypothesis that our method makes a difference.

b. Compute the effect size and describe its strength. 

As in the previous exercise, assume the average speed of a serve in women’s tennis is around 118 mph, with a standard deviation of 12 mph. But now we recruit only 26 amateur tennis players to use our method. Again, after 6 months we calculate a group mean of 123 mph.

a. Using a 95% confidence interval, test the hypothesis that our method makes a difference.

b. Compute the effect size and describe its strength.

c. How did changing the sample size from 100 (in Exercise 8.54) to 26 affect the confidence interval and effect size? Explain your answer. 

In several exercises in this chapter, we considered the study of one week of a college football season, during which the population of 53 FBS games had a mean spread (winning score minus losing score) of 16.189, with a standard deviation of 12.128. The sample of 4 games that were played that week in the next-highest league, the FCS, had a mean of 8.75.

a. Calculate statistical power for this study using a one-tailed test and a p level of 0.05.

b What does the statistical power suggest about how we should view the findings of this study?

c. Using G*Power or an online power calculator, calculate statistical power for this study for a one-tailed

test with a p level of 0.05

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