PSY-520 Graduate Statistics

Topic 1 – Descriptive Statistics Project

__Directions:__ Use the following information to complete the questions below. While APA format is not required for the body of this assignment, solid academic writing is expected, and documentation of sources should be presented using APA formatting guidelines, which can be found in the APA Style Guide, located in the Student Success Center.

A researcher was interested in the anxiety present in students just prior to the midterm exam. The research used an anxiety self-quiz to gage the student’s anxiety. The score for 30 students are given here.

69 | 99 | 91 | 66 | 70 | 98 | 70 | 53 | 40 | 58 |

61 | 66 | 94 | 77 | 70 | 56 | 88 | 85 | 86 | 40 |

84 | 86 | 54 | 48 | 86 | 43 | 78 | 53 | 79 | 89 |

- Construct a frequency table with class, frequency, relative percent, and cumulative percent that has 6 classes to describe the distribution of the data in SPSS.
- Use the frequency table created in problem to construct a histogram in SPSS.
- Use SPSS to calculate the numerical descriptive statistics mean, median, standard deviation, and variance of the anxiety scores.

Topic 1 Exercises

**Due Date:** **Max Points: **20

**Details:**

Complete the following exercises from “Review Questions” located at the end of each chapter and put them into a Word document to be submitted as directed by the instructor.

- Chapter 1, numbers 1.8 and 1.9
- Chapter 2, numbers 2.14, 2.17, and 2.18
- Chapter 3, numbers 3.13, 3.14, 3.18, and 3.19
- Chapter 4, numbers 4.9, 4.14, 4.17, and 4.19

Show all relevant work; use the equation editor in Microsoft Word when necessary

1.8 Indicate whether each of the following studies is an experiment or an observational study. If it is an experiment, identify the independent variable and note any possible confounding variables.

(a) A psychologist uses chimpanzees to test the notion that more crowded living con-ditions trigger aggressive behavior. Chimps are placed, according to an impartial assignment rule, in cages with either one, several, or many other chimps. Subse-quently, during a standard observation period, each chimp is assigned a score based on its aggressive behavior toward a chimplike stuffed doll.

(b) An investigator wishes to test whether, when compared with recognized scientists, recognized artists tend to be born under different astrological signs.

(c) To determine whether there is a relationship between the sexual codes of primitive tribes and their behavior toward neighboring tribes, an anthropologist consults avail-able records, classifying each tribe on the basis of its sexual codes (permissive or repressive) and its behavior toward neighboring tribes (friendly or hostile).

(d) In a study of group problem solving, an investigator assigns college students to groups of two, three, or four students and measures the amount of time required by each group to solve a complex puzzle.

(e) A school psychologist wishes to determine whether reading comprehension scores are related to the number of months of formal education, as reported on school transcripts, for a group of 12-year-old migrant children.

(f) To determine whether Graduate Record Exam (GRE) scores can be increased by cramming, an investigator allows college students to choose to participate in either a GRE test-taking workshop or a control (non-test-taking) workshop and then com-pares the GRE scores earned subsequently by the two groups of students.

(g) A social scientist wishes to determine whether there is a relationship between the attractiveness scores (on a 100-point scale) assigned to college students by a panel of peers and their scores on a paper-and-pencil test of anxiety.

(h) A political scientist wishes to determine whether males and females differ with respect to their attitudes toward defense spending by the federal government. She asks each person if he or she thinks that the current level of defense spending should be increased, remain the same, or be decreased.

(i) Investigators found that four year-old children who delayed eating one marshmal-low in order to eat two marshmallows later, scored higher than non-delayers on the Scholastic Aptitude Test (SAT) taken over a decade later.

REVIEW QUESTIONS 19

1.9

Recent studies, as summarized, for example, in E. Mortensen et al. (2002). The association between duration of breastfeeding and adult intelligence. Journal of the American Medical Association, 287, 2365–2371, suggest that breastfeeding of infants may increase their subsequent cognitive (IQ) development. Both experiments and observational studies are cited.

(a) What determines whether some of these studies are experiments?

(b) Name at least two potential confounding variables controlled by breastfeeding experiments.

2.14

(a) Construct a frequency distribution for the number of different residences occu-pied by graduating seniors during their college career, namely1, 4, 2, 3, 3, 1, 6, 7, 4, 3, 3, 9, 2, 4, 2, 2, 3, 2, 3, 4, 4, 2, 3, 3, 5

(b) What is the shape of this distribution?

2.18

The following table shows distributions of bachelor’s degrees earned in 2011–2012 for selected fields of study by all male graduates and by all female graduates

(a) How many female psychology majors graduated in 2011–2012?

(b) Since the total numbers of male and female graduates are fairly different—600.0 thousand and 803.6 thousand—it is helpful to convert first to relative frequencies before making comparisons between male and female graduates. Then, inspect these relative frequencies and note what appear to be the most conspicuous differences between male and female graduates.

46 DESCRIBING DATA WITH TABLES AND GRAPHS

(c) Would it be meaningful to cumulate the frequencies in either of these frequency distributions?

(d) Using just one graph, construct bar graphs for all male graduates and for all female graduates. Hint: Alternate shaded and unshaded bars for males and females, respectively.

BACHELOR’S DEGREES EARNED IN 2011–2012 BY SELECTED FIELD OF STUDY AND GENDER (IN THOUSANDS)MAJOR FIELD OF STUDY

MALES

FEMALES

Business 190.0176.7

Social sciences 90.6 87.9

Education 21.8 84.0

Health sciences 24.9138.6

Psychology 25.4 83.6

Engineering 81.3 17.3

Life sciences 39.5 56.3

Fine arts 37.2 58.6

Communications 33.5 55.2

Computer sciences 38.8 8.6

English 17.0 36.8

Total 600.0803.6

Source: 2013 Digest of Educational Statistics at http://nces.ed.gov.

3.13

Garrison Keillor, host of the radio program A Prairie Home Companion, concludes each story about his mythical hometown with “That’s the news from Lake Wobegon, where all the women are strong, all the men are good-looking, and all the children are above average.” In what type of distribution, if any, would

(a) more than half of the children be above average?

(b) more than half of the children be below average?

(c) about equal numbers of children be above and below average?

(d) all the children be above average?

3.14

The mean serves as the balance point for any distribution because the sum of all scores, expressed as positive and negative distances from the mean, always equals zero.

(a) Show that the mean possesses this property for the following set of scores: 3, 6, 2, 0, 4.

(b) Satisfy yourself that the mean identifies the only point that possesses this property. More specifically, select some other number, preferably a whole number(for convenience), and then find the sum of all scores in part (a), expressed as positive or negative distances from the newly selected number. This sum should not equal zero.

3.15

If possible, find the median for the film ratings listed in Question 2.8 on page 3

3.18

Given that the mean equals 5, what must be the value of the one missing observation from each of the following sets of observations? (a) 1, 2, 10 (b) 2, 4, 1, 5, 7, 7 (c) 6, 9, 2, 7, 1, 2

3.19

Indicate whether the following terms or symbols are associated with the population mean, the sample mean, or both means. (a) N (b) varies (c) ∑ (c) n (d) constant (e) subset.

*4. 9 For each of the following pairs of distributions, first decide whether their standard

deviations are about the same or different. If their standard deviations are different, indicate which distribution should have the larger standard deviation. Hint: The distribution with the more dissimilar set of scores or individuals should produce the larger standard deviation regardless of whether, on average, scores or individuals in one distribution differ from those in the other distribution. (a) SAT scores for all graduating high school seniors (a1) or all college freshmen (a2) (b) Ages of patients in a community hospital (b1) or a children’s hospital

80 DESCRIBING VARIABILITY

(c) Motor skill reaction times of professional baseball players (c1) or college students (c2) (d) GPAs of students at some university as revealed by a random sample (d1) or a census of the entire student body (d2) (e) Anxiety scores (on a scale from 0 to 50) of a random sample of college students taken from the senior class (e1) or those who plan to attend an anxiety-reduction clinic (e2) (f) Annual incomes of recent college graduates (f1) or of 20-year alumni (f2)

Key Equations

STANDARD DEVIATION FOR SAMPLE

REVIEW QUESTIONS *

4.9

For each of the following pairs of distributions, first decide whether their standard deviations are about the same or different. If their standard deviations are different, indicate which distribution should have the larger standard deviation. Hint: The distribution with the more dissimilar set of scores or individuals should produce the larger standard deviation regardless of whether, on average, scores or individuals in one distribution differ from those in the other distribution.

(a) SAT scores for all graduating high school seniors (a1) or all college freshmen (a2)

(b) Ages of patients in a community hospital (b1) or a children’s hospital (b2)

DESCRIBING VARIABILITY

(c) Motor skill reaction times of professional baseball players (c1) or college students (c2)

(d) GPAs of students at some university as revealed by a random sample (d1) or a census of the entire student body (d2)

(e) Anxiety scores (on a scale from 0 to 50) of a random sample of college students taken from the senior class (e1) or those who plan to attend an anxiety-reduction clinic (e2)

(f) Annual incomes of recent college graduates (f1) or of 20-year alumni (f2) Answers on page 425.

4.14

(a) Using the computation formula for the sample sum of squares, verify that the sample standard deviation, s, equals 23.33 lbs for the distribution of 53 weights in Table 1.1.

REVIEW QUESTIONS

(b) Verify that a majority of all weights fall within one standard deviation of the mean (169.51) and that a small minority of all weights deviate more than two standard deviations from the mean.

- 17 Why can’t the value of the standard deviation ever be negative? *
- 19 Referring to Review Question 2.18 on page 46, would you describe the distribution of majors for all male graduates as having maximum, intermediate, or minimum variability?