Fundamental Statistics for the Behavioral Sciences

David C. Howell

Chapter 3 Displaying Data - all with Video Answers

Educators

Chapter Questions

Problem 1

Have you ever wondered how you would do on the SATs if you didn't even bother to read the passage you were asked about ${ }^{+6}$ Katz, Lautenschlager, Blackburn, and Harris (1990) asked students to answer SAT-type questions without seeing the passage on which the questions were based. This was called the NoPassage group. Data closely resembling what they obtained follow, where the dependent variable was the individual's score on the test.
$$
\begin{aligned}
& 5452515036554446574443523846 \\
& 5534443943365557364649464947
\end{aligned}
$$
(a) Plot a frequency distribution for these data.
(b) What is the general shape of the distribution?

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01:57

Problem 2

Make a histogram for the data in Exercise 3.1 using a reasonable number of intervals.

Jorge Villanueva

Numerade Educator

01:39

Problem 3

What kind of stems would you need for a stem-and-leaf display of the data in Exercise 3.1?

Ashley Volpe

Numerade Educator

01:00

Problem 4

If students had just guessed in the Katz et al. study, they would have been expected to earn a score of approximately 20. Do these students appear to do better than chance even when they haven't read the passage?

Maxime Rossetti

Numerade Educator

07:58

Problem 5

As part of the study described in Exercise 3.1, the experimenters obtained the same kind of data from a smaller group who had read the passage before answering the questions (called the Passage group). Their data follow.
$$
6675727155567293737272739166715659
$$
(a) What can you tell just by looking at these numbers? Do students do better when they have read the passage?
(b) Plot these data on one side of a stem-and-leaf display and the NoPassage data on the other side of the same stem-and-leaf display.
(c) What can you see by looking at this stem-and-leaf display?
(d) A further discussion of this example can be found at
http://www.uvm.edu/ dhowell/fundamentals7/Katzfolder/katz.html
although it also covers material that we will discuss later in this book.

James Kiss

Numerade Educator

Problem 6

In Chapter 2, Exercise 2.4, I asked those with access to SPSS to go to the book's Web site, find the short SPSS manual, and download the apgar.sav file. If you did not do that exercise, go back and read the question to see how to download the file and then open it in SPSS. The introduction to that Web page describes the data. Read the first three chapters (they are very short) and then read Chapter 4 on describing and graphing data. (That chapter is a bit longer, but most of that is taken up with graphics.) Recreate the frequency distributions and graphs that are shown there, varying the courseness of the display.

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Problem 7

Use SPSS to load and plot the data on mental rotation reaction times that were presented (in part) in Table 3.1. These data can be found in the data files of this book's Web site as Tab3-1.dat, and you will probably have to read the material in Chapter 3 of the Web page on how to import text data.

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06:41

Problem 8

Using SPSS with the data imported in Exercise 3.7, determine the percentage of times when the observer (myself) gave the wrong response by looking at the Accuracy variable. Plot and describe the distribution of reaction time data.
The next two exercises refer to a large data set in Appendix D. The data can also be downloaded from the Web at These data come from a research study by Howell and Huessy (1985), which is described at the beginning of the appendix. We will refer to them throughout the book

Gaurav Kalra

Numerade Educator

07:59

Problem 9

Create a histogram for the data for GPA in Appendix D, using reasonable intervals.

Jerelyn Nevil

Numerade Educator

01:06

Problem 10

Create a stem-and-leaf display for the ADDSC score in Add.dat.

Sarah Wallace

Numerade Educator

12:47

Problem 11

What three interesting facts about the populations of Mexico and Spain can be seen in Figure 3.10?

Kadry Samuels

Numerade Educator

01:09

Problem 12

In some stem-and-leaf displays with one or two low values, the last stem is often written as LOW, with the complete values in the leaf section. Why and when might we do this?

Dominador Tan

Numerade Educator

02:48

Problem 13

How would you describe the distributions of the grades of students who did, and did not, attend class in Figure 3.4? Why would you have expected this kind of distribution even before you saw the data?

Akhil Choudhary

Numerade Educator

Problem 14

In Table 3.1 the reaction time data are broken down by the degrees of rotation separating the objects. (You may want to sort the data by this variable.) Use SPSS or another computer program to plot separate histograms of these data as a function of the Angle of rotation. These data are available at
http://www.uvm.edu/ dhowell/fundamentals7/DataFiles/MentalRotation.dat

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05:23

Problem 15

When Krantz devised the experiment that produced the data in Table 3.1, he was interested in seeing whether the required degree of mental rotation influenced reaction time. From the answer to Exercise 3.14, what would you conclude about this question?

Lucas Finney

Numerade Educator

06:41

Problem 16

In addition to comparing the reaction times as a function of rotation, how else might you use these data to draw conclusions about how people process information?

Gaurav Kalra

Numerade Educator

00:14

Problem 17

One frequent assumption in statistical analyses is that observations are independent of one another (knowing one response tells you nothing about the magnitude of another response). How would you characterize the reaction time data in Table 3.1, just based on what you know about how it was collected? (A lack of independence would not invalidate anything we have done with these data in this chapter, though it might have an effect on more complex analyses.)

Trent Speier

Numerade Educator

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Problem 18

Figure 3.12 is adapted from a paper by Cohen, Kaplan, Cunnick, Manuck, and Rabin (1992), which examined the immune response of nonhuman primates raised in stable and unstable social groups. In each group animals were classed as high or low in affiliation, measured in terms of the amount of time they spent in close physical proximity to other animals. Higher scores on the immunity measure represent greater immunity to disease. Write two or three sentences describing what these results would seem to suggest.

Victor Salazar

Numerade Educator

03:17

Problem 19

Rogers and Prentice-Dunn (1981) had 96 white male undergraduates deliver shocks to their fellow subjects as part of a biofeedback study. They recorded the amount of shock that the subjects delivered to white participants and black participants when the subjects had and had not been insulted by the experimenter. Their results are shown in Figure 3.13. Interpret these results. (One of my earlier guidelines said to start each axis at zero or break the axis. Why does that not make sense here?)

Sheryl Ezze

Numerade Educator

01:41

Problem 20

The following data represent U.S. college enrollments by census categories as measured in 1982, 1991, and 2005. (The 2005 data are approximate.) Plot the data in a form that represents the changing ethnic distribution of college students in the United States. (The data entries are in $1,000 \mathrm{~s}$. )
Figure 3.12
From Cohen, Kaplan, et al. (1992)
(FIGURE CAN'T COPY)
Figure 3.13
From Rogers and Prentice-Dunn (1981)
(FIGURE CAN'T COPY)
$$
\begin{array}{lrrr}
\hline \text { Ethnic Group } & 1982 & 1991 & 2005 \\
\hline \text { White } & 9,997 & 10,990 & 11,774 \\
\text { Black } & 1,101 & 1,335 & 2,276 \\
\text { Native American } & 88 & 114 & 179 \\
\text { Hispanic } & 519 & 867 & 1935 \\
\text { Asian } & 351 & 637 & 1,164 \\
\text { Foreign } & 331 & 416 & 591 \\
\hline
\end{array}
$$
You can find additional data at
http://professionals.collegeboard.com/data-reports-research/trends

Breanna Ollech

Numerade Educator

01:59

Problem 21

The New York Times (March 16, 2009) reported that approximately $3 \%$ of the population of Washington, D.C., was living with HIV/AIDS. Search the Web for world-wide statistics that would put that number in context.

Sheryl Ezze

Numerade Educator

00:57

Problem 22

The following data represent the total number of U.S. households, the number of households headed by women, and family size from 1960 to 1990 . Present these data in a way that reveals any changes in U.S. demographics. What do the data suggest about how a social scientist might look at the problems facing the United States? (Households are given in 1,000 s.)$$
\begin{array}{cccc}
\hline & \begin{array}{c}
\text { Total } \\
\text { Year } \\
\text { Households }
\end{array} & \begin{array}{c}
\text { Households } \\
\text { Headed by } \\
\text { Women }
\end{array} & \text { Family Size } \\
\hline 1960 & 52,799 & 4,507 & 3.33 \\
1970 & 63,401 & 5,591 & 3.14 \\
1975 & 71,120 & 7,242 & 2.94 \\
1980 & 80,776 & 8,705 & 2.76 \\
1985 & 86,789 & 10,129 & 2.69 \\
1987 & 89,479 & 10,445 & 2.66 \\
1988 & 91,066 & 10,608 & 2.64 \\
1989 & 92,830 & 10,890 & 2.62 \\
1990 & 92,347 & 10,890 & 2.63 \\
\hline
\end{array}
$$

Joseph Palsic

Numerade Educator

07:07

Problem 23

Moran (1974) presented data on the relationship, for Australian births, between maternal age and Down's syndrome (a serious handicapping condition on which psychologists have done a lot of work). The data follow, though in a form that may require some minor calculations on your part to be meaningful. What can you conclude from these results?$$
\begin{array}{lrc}
\hline \text { Age of Mother } & \begin{array}{c}
\text { Total Number } \\
\text { of Births }
\end{array} & \begin{array}{c}
\text { Number of Births } \\
\text { With Down's Syndrome }
\end{array} \\
\hline 20 \text { or less } & 35,555 & 15 \\
20-24 & 207,931 & 128 \\
25-29 & 253,450 & 208 \\
30-34 & 170,970 & 194 \\
35-39 & 86,046 & 197 \\
40-44 & 24,498 & 240 \\
45 \text { or more } & 1,707 & 37 \\
\hline
\end{array}
$$
Further information on Down's Syndrome and maternal age can be found at
http://www.aafp.org/afp/20000815/825.html

Tawana Stiff

Numerade Educator

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Problem 24

Does the month in which you were born relate to your later mental health? Fombonne (1989) took all children referred to a psychiatric clinic in Paris with a diagnosis of psychosis and sorted them by birth month. (There were 208 such children.) He had a control group of 1,040 children referred with other problems. The data are given below, along with the percentage in the general population born in that month.$$
\begin{array}{lccccccccccccr}
\hline & \text { Jan } & \text { Feb } & \text { Mar } & \text { Apr } & \text { May } & \text { Jun } & \text { Jul } & \text { Aug } & \text { Sep } & \text { Oct } & \text { Nov } & \text { Dec } & \text { Total } \\
\hline \text { Psychosis } & 13 & 12 & 16 & 18 & 21 & 18 & 15 & 14 & 13 & 19 & 21 & 28 & 208 \\
\text { Control } & 83 & 71 & 88 & 114 & 86 & 93 & 87 & 70 & 83 & 80 & 97 & 88 & 1040 \\
\text { \% General } & & & & & & & & & & & & & \\
\text { Population } & 8.4 & 7.8 & 8.7 & 8.6 & 9.1 & 8.5 & 8.7 & 8.3 & 8.1 & 8.1 & 7.6 & 8.0 & \\
\hline
\end{array}
$$
(a) How will you adjust (transform) the Psychosis and Control groups' data so that all three data sets can fit on the same graph?
(b) How will you plot the data?
(c) Plot the data.
(d) Do those diagnosed with psychosis appear to differ from the general population?
(e) What purpose does the Control group play?
(f) What do you conclude?

Rashmi Sinha

Numerade Educator

02:44

Problem 25

Psychologists concerned about self-injurious behaviors (smoking, eating fatty diets, drug abuse, etc.) worry about the effects of maternal smoking on the incidence of low birthweight babies, who are known to be at risk for developmental problems. The Centers for Disease Control and Prevention has published statistics relating maternal smoking to low birthweight. The data follow in terms of the percentage of birthweights $<2,500$ grams. Find a way to present these data that illustrates this relationship clearly. Why is this relationship not likely to be a statistical fluke?
$$
\begin{array}{lcrrrr}
\hline & 1989 & 1990 & 1991 & 1992 & 1993 \\
\hline \text { Smokers } & 11.36 \% & 11.25 & 11.41 & 11.49 & 11.84 \\
\text { Nonsmokers } & 6.02 & 6.14 & 6.36 & 6.35 & 6.56 \\
\hline
\end{array}
$$
Additional (and more recent) data on smoking and low birthweight can be found at
http://www.smw.ch/docs/pdf200x/2005/35/smw-11122.pdf

Brandon Cleary

Numerade Educator

01:55

Problem 26

The Journal of Statistics Education maintains a fairly extensive collection of data on a wide variety of topics. Each data set is accompanied by a description of the data and how they might be used. These data are available at
http://www.amstat.org/publications/jse/jse_data_archive.html
Go to this Internet link, find a set of data that interests you, and display those data in a way that makes their meaning clear. For most of these data sets you will want to use some sort of computer software, although that is not a requirement. There are many things that could be done with the data that we have not yet covered, but displaying the data will reveal much that is of interest.

Sheryl Ezze

Numerade Educator

05:57

Problem 27

The following graph plots the data on life expectancy of white and black females. What conclusions would you draw from this graph? (Comparable data for men can be found at
http://www.elderweb.com/home/node/2838

Derrick Hanson

Numerade Educator

01:29

Problem 28

In 1970, at the height of the Vietnam War, the U.S. government held a lottery to determine which individuals would be drafted. Balls representing the 366 possible birthdays were drawn from an urn, and the order in which the days were drawn represented the order in which young males would be drafted. (If your birthday was one of those selected early, you would have a low selection number and a very high probability of being drafted, and if it was one of those with a high selection number, you probably would not be called.) That particular lottery received considerable criticism because people born late in the year appeared much more likely to receive a low number. (The average selection number for those born in December was 121.5, while the average selection number for those born in January was 201.2.)

The results appear below. Graph these data and draw appropriate conclusions. There is every reason to believe that those that carried out the lottery did their best to be fair, but if you were one of those eligible to be drafted, would you be satisfied with the result? How might you explain these results? More complete data are available at
http://www.amstat.org/publications/jse/v5n2/datasets.starr.htm|
(FIGURE CAN'T COPY)
$$
\begin{array}{cccccccccccc}
\hline \text { Jan } & \text { Feb } & \text { Mar } & \text { Apr } & \text { May } & \text { June } & \text { July } & \text { Aug } & \text { Sept } & \text { Oct } & \text { Nov } & \text { Dec } \\
\hline 201.2 & 203.0 & 225.8 & 203.7 & 208.0 & 195.7 & 181.5 & 173.5 & 157.3 & 182.5 & 148.7 & 121.5 \\
\hline
\end{array}
$$

Dominador Tan

Numerade Educator