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statistics principles and methods
Fundamental Statistics For The Behavioral Sciences 7th Edition David C Howell - Solutions
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?
In Table
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
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?
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
Figure
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
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 1,000s.)
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
Make a histogram for the data in Exercise
using a reasonable number of intervals.
What kind of stems would you need for a stem-and-leaf display of the data in Exercise 3.1?
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.66 75 72 71 55 56 72 93 73 72 72 73 91 66 71 56 59(a) What can you tell just by
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
Create a histogram for the data for GPA in Appendix D, using reasonable intervals.
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?
In Table
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
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?
Figure
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
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 1,000s.)Ethnic
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
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
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
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
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
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 athttp://www.elderweb.com/home/node/2838
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
As part of the Katz et al. (1990) study previously described, the experimenters obtained the same kind of data from a smaller group of students who had read the passage (called the Passage group). Their data follow.66 75 72 71 55 56 72 93 73 72 72 73 91 66 71 56 59 Calculate the mode, median, and
Plot the data for each of the three conditions in Figure 4.2 and describe the results.
A group of 15 rats running a straight-alley maze required the following number of trials to perform to a predetermined criterion. The frequency distribution follows.Trials to reach criterion 18 19 20 21 22 23 24 Number of rats (frequency) 1 0 4 3 3 3 1 Calculate the mean and median number of trials
Given the following set of data, demonstrate that subtracting a constant (e.g., 5) from every score reduces all measures of central tendency by that amount.8 7 12 14 3 7
Given the following data, show that multiplying each score by a constant multiplies all measures of central tendency by that constant.8 3 5 5 6 2
Why would it not make any sense to calculate the mean for SEX or ENGL in Appendix D?If we did go ahead and compute the mean for SEX, what would the value of ( ) really represent?
With reference to Exercise 4.13, if people take longer to process an image that has been both reversed and rotated, then the mean reaction time should depend on whether or not the comparison stimulus has been reversed. If reversal does not alter the difficulty of processing information, then the
suggest about how we process information?
In Chapter 3 (Figure 3.5) we saw data on grades of students who did and did not attend class regularly. What are the mean and median scores of those two groups of students?(The data are reproduced here for convenience.) What do they suggest about the value of attending class?Attended class 241 243
Why do you think that I did not ask you to calculate the mode? (Hint: If you calculate the mode for those who skipped class frequently, you should see the problem.)
The Internet is a great resource when you don’t know how to do something. Search the Internet to find out how to use SPSS (or whatever software you have access to) to calculate the mode of a set of data. You can just go to Google and enter “How do I calculate the mode in SPSS?”
Seligman, Nolen-Hecksema, Thornton, and Thornton (1990) classified participants in their study (who were members of a university swim team) as Optimists or Pessimists. They then asked them to swim their best event, and in each case they reported times that were longer than the swimmer actually
I have suggested that if you don’t understand something I write, go to Google and find something better. In Chapter 2 I admitted that it was pretty easy to define a dependent variable, but the definition of an independent variable is a bit more complicated. Go to Google and type in “What is an
Calculate the range, the variance, and the standard deviation for data that Katz et al. collected on SAT performance without reading the passage. The data follow.54 52 51 50 36 55 44 46 57 44 43 52 38 46 55 34 44 39 43 36 55 57 36 46 49 46 49 47
Calculate the range, the variance, and the standard deviation for the Katz et al. data on SAT performance after reading the passage.66 75 72 71 55 56 72 93 73 72 72 73 91 66 71 56 59
Compare the answers to Exercises
and 5.2. Is the standard deviation for performance when people do not read the passage different from the standard deviation when people do read the passage?
Using what you have learned from Exercises 5.6 and 5.7, transform the following set of data to a new set with a standard deviation of 1.00.5 8 3 8 6 9 9 7
Use the answers to Exercises 5.6 and 5.7 to modify the answer to Exercise 5.8 to have a mean of 0 and a standard deviation of 1.00. (Note: The solution to Exercises 5.8 and 5.9 will be important in Chapter 6.)
Create a boxplot for the data in Exercise 5.1.
Create a boxplot for the data in Exercise 5.2.
Create a boxplot for the variable ADDSC in Appendix D. These data are available athttp://www.uvm.edu/~dhowell/fundamentals7/DataFiles/Add.dat
Using the data for ENGG in Appendix D:(a) Calculate the variance and the standard deviation for ENGG.(b) These measures should be greater than the corresponding measures on GPA. Can you explain why this should be? (We will come back to this later in Chapter 12, but see if you can figure it out.)
Use SPSS, or other software, to draw a set of boxplots (similar to Figure 5.4b) to illustrate the effect of increase the angle of rotation in the Mental Rotation data set. The data can be found at http://www.uvm.edu/~dhowell/fundamentals7/DataFiles/MentalRotation.dat(A file with the “sav”
Given the following data:1 3 3 5 8 8 9 12 13 16 17 17 18 20 21 30(a) Draw a boxplot.(b) Calculate the standard deviation of these data and divide every score by the standard deviation.(c) Draw a boxplot for the data in (b).(d) Compare the two boxplots.
The following graph came from the JMP statistical package applied to the data in Table 5.2 on length of hospitalization. Notice the boxplot on the top of the figure. How does that boxplot compare with the ones we have been using? (Hint: The mean is 4.66.)
Everitt, as reported in Hand et al. (1994), presented data on the amount of weight gained by 72 anorexic girls under one of three treatment conditions. The conditions were Cognitive Behavior Therapy, Family Therapy, and a Control group who received no treatment. The data follow:Cog. 1.7 0.7 0.1 0.7
Compare the mean, standard deviation, and variance for the data in Exercise 5.1 with their trimmed and Winsorized counterparts.
Assuming that the following data represent a population of XX values with μ=4μ=4 and σ=1.58σ=1.58:X=122334445556667X=122334445556667(a) Plot the distribution as given.(b) Convert the distribution in (a) to a distribution of X−μX−μ.(c) Go the next step and convert the distribution in (b)
Using the distribution in Exercise 6.1, calculate z scores for 6.2, and 9. Interpret these results.
Most of you have had experience with exam scores that were rescaled so that the instructor could “grade on a curve.” Assume that a large Psychology 1 class has just taken an exam with 300 four-choice multiple-choice questions. (That’s the kind of Psych 1 exam I took when I was but a lad, and
We have referred several times to data on reaction times in a mental rotation task. These data can be found on this book’s Web site as Ex6 –14.dat. Using SPSS, read in the data and plot a histogram of reaction times in seconds. Click on the appropriate box to superimpose a normal distribution
The data in Appendix D, also available at http://www.uvm.edu/~dhowell/fundamentals7/DataFiles/Add.dat are actual data on high school students. What is the 75th percentile for GPA in these data?(This is the point below which 75% of the observations are expected to fall.)
In Section 6.4 I said that T scores are designed to have a mean of 50 and a standard deviation of 10 and that the Achenbach Youth Self Report measure produces T scores. The data in Figure 6.3 do not have a mean and standard deviation of exactly 50 and 10. Why do you suppose that this is so?
You can use SPSS to create normally distributed variables (as well as variables having a number of other shapes). Start SPSS, and under Data/Go To Case, tell it to go to case 1000 and then enter any value in that cell. (That just sets the size of the data set to 1000.)Then click on
Give one example each of an analytic, a frequentist, and a subjective view of probability.
Which parts of Exercise
dealt with joint probabilities?
Which parts of Exercise
dealt with conditional probabilities?
In Exercise
assume that both mother and child sleep from 8:00 P.M. to 7:00 A.M. What would be the probability now?
A graduate admissions committee has finally come to realize that it cannot make valid distinctions among the top applicants. This year the committee rated all 500 applicants and randomly chose 10 from those at or above the 80th percentile. (The 80th percentile is the point at or below which 80
How might you use conditional probabilities to determine if an ADDSC cutoff score in Appendix D of 66 is predictive of whether or not a person will drop out of school?
Compare the conditional probability from Exercise
with the unconditional probability of dropping out of school.
In 2000 the U. S. Department of Justice released a study of the death penalty from 1995 to 2000, a period during which U.S. Attorneys were required to submit to the Justice Department for review and approval all cases in which they sought the death sentence.(The report can be found at
What would be a Type I error in Exercise 8.2?
What would be a Type II error in Exercise 8.2?
Imagine that you have just invented a statistical test called the Mode Test to determine whether the mode of a population is some value (e.g., 100). The statistic (M) is calculated as Describe how you could obtain the sampling distribution of M. (Note: This is a purely fictitious statistic.)
In Exercise 8.7, what would we call M in the terminology of this chapter?
For the distribution in Figure
I said that the probability of a Type II error is .64.Show how this probability was obtained.
Rerun the calculations in Exercise
for
In Sub-Saharan Africa, more than half of mothers lose at least one child before the child’s first birthday. Below are data on 36 countries in the region, giving country, infant mortality, per capita income (in U.S. dollars), percentage of births to mothers under 20, percentage of births to
Calculate the correlations among all numeric variables in Exercise 9.1 using SPSS.
Using Table E.2 in Appendix E, how large a correlation would you need for the relationships shown in Exercise 9.2 to be significant?
What are the strongest predictors of infant mortality in Exercise 9.2?
Down’s syndrome is another problem that psychologists deal with. It has been proposed that mothers who give birth at older ages are more likely to have a child with Down’s syndrome.Plot the data below relating age to incidence. The data were taken from Geyer (1991).Age 17.5 18.5 19.5 20.5 21.5
Why would you not feel comfortable computing a Pearson correlation on the data in Exercise 9.10?
The data relevant to Exercise 9.13 are the test scores and SAT-V scores for the 28 people in the group that did not read the passage. These data are Score 58 48 48 41 34 43 38 53 41 60 55 44 43 49 SAT-V 590 590 580 490 550 580 550 700 560 690 800 600 650 580 Score 47 33 47 40 46 53 40 45 39 47 50
Interpret the results from Exercises 9.11 to 9.13.
The correlation in the Katz et al. (1990) study between Score and SAT-V for the 17 subjects in the group that did read the passage was .68. This correlation is not significantly different from the correlation you computed in Exercise 9.13, although it is significantly different from 0.00. What does
Do the results of the Katz et al. (1990) study fit with your expectations, and why?
David Lane at Rice University has an interesting example of a study involving correlation.This can be found at http://www.ruf.rice.edu/~lane/case_studies/physical_strength/index.html.Work through his example and draw your own conclusions from the data. (For now, ignore the material on regression.)
The following data are from 10 health-planning districts in Vermont. Y is the percentage of live births grams. is the fertility rate for women or years of age (is known as the “high-risk fertility rate.”). is the percentage of births to unmarried women. Compute the regression equation for
Calculate the standard error of estimate for the regression equation in Exercise 10.1.
If, as a result of ongoing changes in the role of women in society, we saw a change in the age of childbearing such that the high-risk fertility rate jumped to 70 in Exercise 9.1, what would we predict for the incidence of birthweight grams?
Why should you feel uncomfortable making a prediction in Exercise 10.3 for a rate of 70?
In Exercise 9.1 we saw data on infant mortality and risk factors. Why might you feel more comfortable making a prediction based on Income for Senegal than for Ethiopia or Namibia?
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