Reasoning With Data An Introduction To Traditional And Bayesian Statistics Using R 1st Edition Jeffrey M. Stanton - Solutions

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14. For the following scores, find the (a) mean, (b) median, (c) sum of squared deviations, (d) variance, and (e) standard deviation:1,112; 1,245; 1,361; 1,372; 1,472.
13. For the following scores, find the (a) mean, (b) median, (c) sum of squared deviations, (d) variance, and (e) standard deviation:2, 2, 0, 5, 1, 4, 1, 3, 0, 0, 1, 4, 4, 0, 1, 4, 3, 4, 2, 1, 0.
12. (a) Describe the variance and standard deviation. (b) Explain why the standard deviation is more often used as a descriptive statistic than the variance.
11. (a) Describe and explain the difference between the mean, median, and mode. (b) Make up an example (not in the course or in your lectures) in which the median would be the preferred measure of the representative value of a group of scores.
10. In a study by Gonzaga, Keltner, Londahl, and Smith (2001), romantic couples answered questions about how much they loved their partner and also were videotaped while revealing something about themselves to their partner. The videotapes were later rated by trained judges for various signs of
9. A researcher studied the number of nights students reported having too little sleep over a 4-week period. In an article describing the results of the study, the researcher reports: “The mean number of nights of too little sleep was 6.84 (SD=3.18).” Explain these results to a person who has
8. Six months after a divorce, the former wife and husband each take a test that measures divorce adjustment. The wife’s score is 63, and the husband’s score is 59. Overall, the mean score for divorced women on this test is 60 (SD=6); the mean score for divorced men is 55 (SD=4).Which of the
7. If the mean of a measure is 145 and the standard deviation is 19, what are the raw scores for each of the following Z scores? (a) 0, (b) 1.43, (c)−2.54.
6. If the mean of a measure is −11.46 and the standard deviation is 2.28, what are the Z scores for each of the following raw scores? (a) −13.12,(b) −7.26, and (c) −11.23.
5. On a measure of concern for the environment, the mean is 79 and the standard deviation is 12 (scores on the measure can vary from 0 to 150).What are the Z scores for each of the following raw scores? (a) 91, (b)68, and (c) 103.
4. A researcher is studying the amygdala (a part of the brain involved in emotion). Six participants in a particular fMRI (brain scan) study are measured for the increase in activation of their amygdala while they are viewing pictures of violent scenes. The activation increases are .43, .32,.64,
3. Here are the noon temperatures (in degrees Celsius) in a particular Canadian city on Thanksgiving Day for the 10 years from 2008 through 2017: 0, 3, 6, 8, 2, 9, 7, 6, 4, 5. Describe the representative (typical)temperature and the amount of variation to a person who has never had a course in
2. For the following scores, find the (a) mean, (b) median, (c) sum of squared deviations, (d) variance, and (e) standard deviation:6, 1, 4, 2, 3, 4, 6, 6.
1. For the following scores, find the (a) mean, (b) median, (c) sum of squared deviations, (d) variance, and (e) standard deviation:32, 28, 24, 28, 28, 31, 35, 29, 26.
4. Roughly speaking, the standard deviation is the average amount that scores differ from the mean. Explain that the standard deviation is directly related to the variance and is figured by taking the square root of the variance.
3. The variance is the average of each score’s squared difference from the mean. Describe the steps for figuring the variance.
2. Explain that the variance and standard deviation both measure the amount of variability (or spread) among a group of scores.
1. Explain that the mean is a type of representative value of a group of scores. Mention that the mean is the ordinary average, the sum of the scores divided by the number of scores.
6. Suppose a person has a Z score for overall health of +2 and a Z score for overall sense of humor of +1. What does it mean to say that this person is healthier than she is funny?
5. For a particular group of scores, M=10 and SD=2. Give the raw score for a Z score of (a) +2, (b) +.5, (c) 0, and (d) −3.
4. Write the formula for changing a Z score to a raw score and define each of the symbols.
3. For a particular group of scores, M=20 and SD=5. Give the Z score for(a) 30, (b) 15, (c) 20, and (d) 22.5.
2. Write the formula for changing a raw score to a Z score and define each of the symbols.
1. How is a Z score related to a raw score?
6. What is the difference between the formula for the variance you learned in this chapter and the formula that is typically used to figure the variance in research articles?
5. Explain the difference between a definitional formula and a computational formula.
4. Figure the (a) variance and (b) standard deviation for the following scores: 2, 4, 3, and 7(M=4).
3. Give the full formula for the variance and indicate what each of the symbols mean.
2. (a) Define the standard deviation, (b) describe its relation to the variance, and (c) explain what it tells you approximately about a group of scores.
1. (a) Define the variance. (b) Describe what it tells you about a distribution and how this is different from what the mean tells you.
4. For the following scores, find (a) the mean; (b) the mode; (c) the median: 5, 3, 2, 13, 2. (d) Why is the mean different from the median?
3. Figure the mean of the following scores: 2, 3, 3, 6, and 6.
2. Write the formula for the mean and define each of the symbols.
1. Name and define three measures of the representative value of a group of scores.
24. Give an example of something having these distribution shapes: (a)bimodal, (b) approximately rectangular, and (c) positively skewed. Do not use an example given in this book or in class.
23. Make up and draw an example of each of the following distributions: (a)symmetrical, (b) rectangular, and (c) skewed to the right.
21. Kärnä and colleagues (2013) tested the effects of a new antibullying program, called KiVa, among students in grades 1–3 and grades 7–9 in 147 schools in Finland. The schools were randomly assigned to receive the new antibullying program or no program. At the beginning, middle, and end of
20. Explain to a person who has never taken a course in statistics the meaning of a grouped frequency table.
19. Here are the number of holiday gifts purchased by 25 families randomly interviewed at a local mall at the end of the holiday season:22, 18, 22, 26, 19, 14, 23, 27, 2, 18, 28, 28, 11, 16, 34, 28, 13, 21, 32, 17, 6, 29, 23, 22, 19 Make (a) a frequency table and (b) a grouped frequency table using
18. A researcher asked 15 university students how many times they “fell in love” before they were 11 years old. The numbers of times were as follows:2, 0, 6, 0, 3, 1, 0, 4, 9, 0, 5, 6, 1, 0, 2 Make (a) a frequency table and (b) a histogram. Then (c) describe the general shape of the
17. An organizational researcher asks 20 employees in a company to rate their job satisfaction on a 5-point scale from 1 = very unsatisfied to 5 =very satisfied. The ratings were as follows:3, 2, 3, 4, 1, 3, 3, 4, 5, 2, 3, 5, 2, 3, 3, 4, 1, 3, 2, 4 Make (a) a frequency table and (b) a histogram.
16. Pick a book and page number of your choice (select a page with at least 30 lines; do not pick a textbook or any book with tables or illustrations).Make a list of the number of words on each line; use that list as your group of scores. Make (a) a frequency table and (b) a histogram. Then(c)
15. Here are the number of children in each of 30 classrooms in an elementary school:24, 20, 35, 25, 25, 22, 26, 28, 38, 15, 25, 21, 24, 25, 25, 24, 25, 20, 32, 25, 22, 26, 26, 28, 24, 22, 26, 21, 25, 24 Make (a) a frequency table and (b) a histogram. Then (c) describe the general shape of the
14. Explain and give an example for each of the following types of variables: (a) equal-interval, (b) rank-order, and (c) categorical.
13. A participant in a research study is given 50 words to remember and later asked to recall as many of the words as she can. She recalls 17 words. What is the (a) variable, (b) possible values, and (c) score?
12. Raskauskas and Stoltz (2007) asked a group of 84 adolescents about their involvement in traditional and electronic bullying. The researchers defined electronic bullying as “a means of bullying in which peers use electronics [such as text messages, emails, and defaming Web sites] to taunt,
11. What is a ceiling effect?
10. Explain to a person who has never had a course in statistics what is meant by (a) a symmetrical unimodal distribution and (b) a negatively skewed unimodal distribution. (Be sure to include in your first answer an explanation of what “distribution” means.)
9. Describe the shapes of the three distributions shown below.
8. The following data are the number of minutes it took each of 34 10-year-olds to do a series of abstract puzzles:24, 83, 36, 22, 81, 39, 60, 62, 38, 66, 38, 36, 45, 20, 20, 67, 41, 87, 41, 82, 35, 82, 28, 80, 80, 68, 40, 27, 43, 80, 31, 89, 83, 24 Make (a) a frequency table and (b) a grouped
7. These are the scores on a measure of sensitivity to smell taken by 25 chefs attending a national conference:96, 83, 59, 64, 73, 74, 80, 68, 87, 67, 64, 92, 76, 71, 68, 50, 85, 75, 81, 70, 76, 91, 69, 83, 75 Make (a) a frequency table and (b) a histogram. (c) Make a grouped frequency table using
6. Following are the speeds of 40 cars clocked by radar on a particular road in a 35-mph zone on a Sunday afternoon:30, 36, 42, 36, 30, 52, 36, 34, 36, 33, 30, 32, 35, 32, 37, 34, 36, 31, 35, 20, 24, 46, 23, 31, 32, 45, 34, 37, 28, 40, 34, 38, 40, 52, 31, 33, 15, 27, 36, 40 Make (a) a frequency
5. Fifty students were asked how many hours they had studied this weekend. Here are their answers:11, 2, 0, 13, 5, 7, 1, 8, 12, 11, 7, 8, 9, 10, 7, 4, 6, 10, 4, 7, 8, 6, 7, 10, 7, 3, 11, 18, 2, 9, 7, 3, 8, 7, 3, 13, 9, 8, 7, 7, 10, 4, 15, 3, 5, 6, 9, 7, 10, 6 Make (a) a frequency table and (b) a
4. A particular block in a suburban neighborhood has 20 households. The number of children in these households is as follows:2, 4, 2, 1, 0, 3, 6, 0, 1, 1, 2, 3, 2, 0, 1, 2, 1, 0, 2, 2 Make (a) a frequency table and (b) a histogram. Then (c) describe the general shape of the distribution.
3. Name the kind of variable for each of the following: (a) ethnic group to which a person belongs, (b) number of times a rat makes a wrong turn in a laboratory maze, and (c) position a runner finishes in a race.
2. You fill out a survey question that asks you to give the likelihood that you will vote in an upcoming election. The question uses a 5-point response scale from 1 = not at all likely to 5 = very likely and you answer “5.” What are the (a) variable, (b) possible values, and (c) score?
1. A client rates her satisfaction with her vocational counselor as a “3” on a 4-point scale from 1 = not at all satisfied to 4 = very satisfied. What are the (a) variable, (b) possible values, and (c) score?
4. When a distribution is described as heavy-tailed or light-tailed, what is it being compared to?
3. What kind of skew is created by (a) a floor effect and (b) a ceiling effect?
2. What does it mean to say that a distribution is skewed to the left?
1. Describe the difference between a unimodal and multimodal distribution in terms of (a) a frequency polygon and (b) a frequency table.
4. How is a histogram based on a categorical variable different from one based on a number equal-interval variable?
3. Make a histogram based on the frequency table below.Value Frequency 1 3 2 4 3 8 4 5 5 2 1.5-8 Full Alternative Text
2. When making a histogram from a frequency table, (a) what goes along the bottom, (b) what goes along the left edge, and (c) what goes above each value?
1. Why do researchers make histograms?
4. What values are grouped in a frequency table group?
3. Make a frequency table for the following scores: 5, 7, 4, 5, 6, 5, 4.
2. Why would a researcher want to make a frequency table?
1. What is a frequency table?
3. Name the kind of variable for each of the following variables: (a) a person’s nationality (Mexican, French, Japanese, etc.), (b) a person’s score on a standardized IQ test, and (c) a person’s place on a waiting list(first in line, second in line, etc.).
2. What is the difference between a numeric and a categorical variable?
1. A father rates his daughter as a 2 on a 7-point scale (from 1 to 7) of crankiness. In this example, (a) what is the variable, (b) what is the score, and (c) what is the range of possible values?
Use the USjudgeRatings data set to create a single composite variable representing the favorability ratings of U.S. judges. Report the steps you took and the decisions you made and in particular make sure to justify your choice of items to include and exclude from your composite scale.
As you probably remember from earlier in the book, the mtcars builtin data set con‑tains 11 measurements of 32 different cars from the 1970s. Conduct a principal com‑ponents analysis of mtcars with an eye toward creating one or more composite scales.Report the steps you took and the decisions
Run plot() on the output of the two models from Exercise 4.Explain the results in your own words.
Using the results of Exercise 5, report and interpret the confidence interval around the reported alpha value.
Conduct an alpha() analysis on the first four items in the swiss data set. Hint: you can use swiss[,1:4] to access the first four columns of the data set. Report the alpha value.Is the alpha value acceptable? Explain why or why not in your own words.
Run twocomponent and threecomponent analyses on the swiss data set. Which anal‑ysis shows a better goodness of fit? Interpret the resulting coefficients and describe one group of three or four items that are likely to fit together well.
Use the principal() command to analyze the swiss data set. Report the loadings of the six items on the first principal component. Which item has the “best” loading and which has the “worst” on the first principal component.
Use the cor() command to examine the correlations among items in the swiss data set. Describe in your own words which pairs of items connect most strongly with one another.
Use the “?swiss” command to show the help file for the builtin “swiss” data set. Describe in your own words what this data set contains. Speculate, based on the descriptions of the six variables, how a principal components analysis might break down these vari‑ables into different groups.
Analyze the sunspot.month built-in data set and create a mini-article (similarly to Exercise 7) with scientific background information, appropriate plots, and statistical results.
Use bcp() on the AirPassengers time series. Plot and interpret the results. Make sure to contrast these results with those from Exercise 6.
Find historical information about air travel on the Internet and/or in reference materials that sheds light on the results from Exercises 5 and 6.Write a mini-article (less than 250 words) that interprets your statistical findings from Exercises 5 and 6 in the context of the historical information
Use cpt.mean() on the AirPassengers time series. Plot and interpret the results. Compare the change point of the mean that you uncovered in this case to the change point in the variance that you uncovered in Exercise 5.What do these change points suggest about the history of air travel?
Given that the AirPassengers data set has a substantial growth trend, use diff() to create a differenced data set. Use plot() to examine and interpret the results of differencing. Use cpt.var() to find the change point in the variability of the differenced time series.Plot the result and describe
The AirPassengers built-in data set tracks the number of international air travelers between 1949 and 1960. Use decompose() and plot() to provide a view of the trend, cyclical, and random (irregular) components of this time series. Describe in your own words what each of the four panes contains and
Starting with the EuStockMarket data, use differencing to remove the trend from each of the four time series. Plot the results as shown in this chapter. Then use cpt.var() from the changepoint package to detect the one point in each series where there is a substantial change in the variance of the
Download and library the nlme package and use data (“Blackmore”) to activate the Blackmore data set. Inspect the data and create a box plot showing the exercise level at different ages. Run a repeated measures ANOVA to compare exercise levels at ages 8, 10, and 12 using aov(). You can use a
The following two lines of code produce two samples of n = 100 points each:grp1
Bonus R code question: Develop your own custom function that will take the posterior distribution of a coefficient from the output object from an MCMClogit() analysis and automatically create a histogram of the posterior distributions of the coefficient in terms of regular odds (instead of
Continue the analysis of the Chile data set described in this chapter. The data set is in the “car” package, so you will have to install.packages() and library() that package first, and then use the data(Chile) command to get access to the data set. Pay close attention to the transformations
As noted in the chapter, the BaylorEdPsych addin package contains a procedure for generating pseudoRsquared values from the output of the glm() procedure. Use the results of Exercise 1 to generate, report, and interpret a Nagelkerke pseudoRsquared value.
Plot the output from the MCMClogit() analysis in Exercise 3.Interpret the results of plots in your own words.
Conduct the same analysis as in Exercise 1 using the MCMClogit() function provided in the MCMCpack package. Don’t forget to use install.packages() and library() if this is the first time you have used MCMCpack. Report the point estimates (means) and 95% HDIs for the intercept and each predictor.
Using the output from Exercise 1, convert the logodds coefficients into regular odds and interpret them. Only interpret coefficients on predictors that were significant. Gen‑erate and interpret confidence intervals around the coefficients of the significant pre‑dictors. Would it make sense to
The builtin data sets of R include one called “mtcars,” which stands for Motor Trend cars. Motor Trend was the name of an automotive magazine and this data set contains information on cars from the 1970s. Use “?mtcars” to display help about the data set.The data set includes a dichotomous
Graphical bonus question: Redo Exercise 8 without centering the variables. Use the results, in combination with the modelPredictions() function, to create prediction lines for PREP versus RTEN, with FAMI held constant at two different values—one stan‑dard deviation above the mean and one
Bayesian bonus question: Obtain posterior distributions for the regression coeffi‑cients from Exercise 9.Also use appropriate calculations to obtain a posterior distri‑bution for Rsquared. Report and interpret your results.
Repeat Exercise 8 using lmBF() to conduct one regression analysis that includes the interaction term and one that does not. Interpret the results. Make sure you report an odds ratio for the comparison of a model with linear effects versus a model with linear and interaction effects. Interpret the

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Reasoning With Data An Introduction To Traditional And Bayesian Statistics Using R 1st Edition Jeffrey M. Stanton - Solutions

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