Exploring Statistics: Tales of Distributions (12th edition) by Chris Spatz

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for Exploring Statistics: Tales of Distributions (12th edition)

Chapter 1
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Multiple Choice   Short Answer   Problems

Introduction

Summary

The overall purpose of the first chapter of the textbook is to introduce

  1. some of the history of the field of statistics and the changing nature of the field,
  2. broad categories and important terms used in statistics (such as descriptive and inferential statistics, parameter, independent variable), and
  3. the organization of the book.

There are two main types of statistics: descriptive statistics and inferential statistics. The notion of descriptive statistics is pretty straightforward: a single number or graph is used to capture a particular characteristic of a set of data. Examples include the average of a set of scores or how spread out scores are from each other. Inferential statistics is a set of procedures that allow you to draw conclusions about a population even though all your information comes from a sample. An assumption of inferential statistics is that results are influenced by chance (random factors) not under your control. With inferential statistics, you can make predictions that are likely to be true, but cannot be proven absolutely.

The idea of using a sample (a subset of the population of interest) as a substitute for a larger, unmeasurable population is found in every chapter of the textbook. The characteristics of samples, called statistics, and the characteristics of populations, called parameters, are easy to keep straight. The two p's go together and the two s's go together.

Quantitative and categorical variables find their way into the text in several chapters after this first one. Continuous quantitative variablesare expressed in amounts and have lower and upper limits that show the range of values a particular score actually represents. For example, you may write down your height as 5'8", even if you're really 5'8.125" tall. Discrete quantitative variables are also expressed in amounts, but there are no intermediate values. For example, a household cannot have 2.3 children. Because intermediate values are not possible upper and lower limits are not meaningful. Categorical variables (also called qualitative variables) get their name because scores indicate members of a category. There are no intermediate values between categories, and categories may or may not convey order.

S. S. Stevens' categorization of variables focused on the kind of information conveyed in a variable (category, order, equal intervals, a true zero point). Nominal scales have the least information of all. On a nominal scale, numbers name a category to which a score belongs. Different numbers mean only that the things measured are different. Numbers that are the same mean the things measured are the same. On an ordinal scale, the numbers convey categories, like nominal scales, but also convey that one category is more or less than another. On ordinal scales, equal distances between numbers do not mean equal amounts of the variable. A larger number means more, but it does not tell you how much more. For example, the difference between 5 and 10 on an ordinal scale is not necessarily the same size difference as the difference between 10 and 15. For both interval scales and ratio scales, numbers convey category and order, but now equal distances between numbers do mean equal amounts of the variable. Additionally, for ratio scales, zero means a complete absence of the thing measured. Statements such as "twice as much" and "reduced by one-third" are meaningful on ratio scales but not for the other three scales.

The topic of experimental design covers the procedures necessary to gather data. Statistics covers the task of analyzing data. A good researcher should be able to do both well.

Variables within an experiment can be categorized as independent, dependent, or extraneous. The independent variable in an experiment is the variable manipulated by the researcher. Changes in the independent variable may cause differences in the dependent variable. The dependent variable in an experiment is the thing being measured and is thought to "depend" on the level of the independent variable.  Extraneous variables are variables that, if not controlled, can influence the relation between the independent and dependent variables. The distinctions between independent, dependent, and extraneous variables, which can be troublesome, will appear again and again, both in the text and in your academic career.

Epistemology is the study of how we come to have knowledge. Some knowledge is created by using reason, one example is a technique called statistics.  The textbook briefly reviews some of the history of statistics and some of the major changes that have occurred in the past 200 years illustrating statistics is a dynamic, changing field.

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Multiple-Choice Questions

1. ______ is the statistician who developed X2 as a way of helping scientists to determine whether or not data fit a theory.

  1. Pearson
  2. Fisher
  3. Neyman
  4. Cohen
Answer

2. This statistician advocated for using effect size statistics along with NHST to show the size of differences observed not just that there were differences.

  1. Pearson
  2. Fisher
  3. Neyman
  4. Cohen
Answer

3. _______ suggested abandoning NHST entirely and replacing it with what he called "new statistics".

  1. Cumming
  2. Fisher
  3. S.S. Stevens
  4. Zeigarnik.
Answer

4. Statistics is a stable, unchanging discipline. There is no controversy about procedures to follow within the discipline.

  1. true
  2. false, it is stable, but there is much controversy
  3. false, it is dynamic rather than stable, but no controversy
  4. false, it is both dynamic and has a good deal of controversy

Answer

5. Which of these disciplines do not use statistics?

  1. anthropology
  2. psychology
  3. biology
  4. none of the above alternatives are correct; all three disciplines use statistics

Answer

Explanation

6. Inferential statistics allow a researcher to ______.

  1. select representative samples
  2. make decisions about populations
  3. characterize a set of data with one number or name
  4. all of the above

Answer

7. ______ are used as estimates of parameters.

  1. Statistics
  2. Constants
  3. Populations
  4. Upper limits

Answer

8. Five means more than three on a(n) ______ scale.

  1. ordinal
  2. interval
  3. ratio
  4. all of the above

Answer

Explanation

9. Many schools rank their graduates each year from highest to lowest. Graduates wind up with scores such as 21 and 111. Such a scale is one example of a(n) ______ scale.

  1. nominal
  2. ordinal
  3. interval
  4. ratio

Answer

10. On the ________ scale, zero means a complete absence of the thing measured.

  1. ordinal
  2. interval
  3. ratio
  4. all of the above

Answer

11. Epistemology deals with the nature of ________.

  1. reason
  2. experience
  3. mathematics
  4. knowledge

Answer

12. In a study of the effect of handedness on athletic ability, participants were divided into three groups: right-handed, left-handed, and ambidextrous. Athletic ability was measured on a 12-point scale. The independent variable is ________; the number of levels of the independent variable is ________.

  1. athletic ability; three
  2. athletic ability; twelve
  3. handedness; three
  4. handedness; twelve

Answer

13. In the study of handedness and athletic ability, the dependent variable is ________.

  1. handedness
  2. athletic ability
  3. not described
  4. both a. and b.

Answer

Explanation

14. When numbers are used as substitutes for names, the numbers constitute a ________ variable.

  1. categorical
  2. quantitative
  3. sample
  4. population

Answer

15. If an experiment has two groups of participants and if the researcher made sure that both groups experience chronic symptoms of schizophrenia, then chronic symptoms of schizophrenia is most likely a(n) ________.

  1. independent variable
  2. dependent variable
  3. controlled extraneous variable
  4. any of the above are likely

Answer

Explanation

16. In an experiment to determine the effect of a stimulant on amount of time spent studying, an extraneous variable is ________.

  1. the stimulant
  2. the time spent studying
  3. both a. and b.
  4. neither a. nor b.

Answer

Explanation

17. A statistics student is interested in determining if studying in the room where class is held improves scores on a statistics exam. To conduct this experiment, she has half the class study in the room where class is held and the other half study in the library. In this experiment, an example of an extraneous variable is _______.

  1. room temperature
  2. where the students studied
  3. both a. and b.
  4. neither a. nor b.

Answer

Explanation

18. In an experiment on the effect of sleep on memory, the independent variable might be ________.

  1. number of hours of sleep
  2. recall score on a test
  3. gender of the participants
  4. gender of the experimenter

Answer

Explanation

19. When rats are startled or fearful, they often hold completely still (freeze). For this reason, the length of time a rat freezes is sometimes used as a measure of fear. A researcher gives 36 rats a new drug thought to reduce fear. He puts the rats in a novel environment that has the scent of a cat. The researcher measures how long the rat freezes during the first minute of time in the environment. The researcher compares this time to the time that 36 other rats freeze in the same environment after being given a placebo. What is the independent variable in this experiment?

  1. time freezing
  2. treatment group (drug or placebo)
  3. scent of cat
  4. novel environment

Answer

Explanation

20. According to your text, the reason for doing an experiment using samples is to ________.

  1. find out about the sample
  2. find out about the population
  3. obtain numbers so that statistics may be calculated
  4. obtain numbers so that parameters may be calculated

Answer

21. If you were interested in what state people are from for an entire college, but collected only the data from the people in one class of students at that college, you have collected data from a _______.

  1. statistic
  2. population
  3. sample
  4. parameter

Answer

22. After a study finds a difference between two samples, inferential statistics tells you ________.

  1. whether or not the descriptive statistics showing a difference were correct
  2. the probability that the descriptive statistics were correct
  3. the probability of the difference, if there is actually no difference between the two populations the samples were drawn from
  4. the probability that chance caused the results

Answer

23. The experimenter has no direct control on the values of the ________.

  1. independent variable
  2. dependent variable
  3. extraneous variables
  4. all of these choices

Answer

Explanation

24. In a typical experiment, a dependent variable is the ________ and the independent variable is the ________.

  1. cause; effect
  2. effect; cause
  3. sample; population
  4. population; sample

Answer

Explanation

25. An extraneous variable is one that ________.

  1. can foul up the interpretation of an experiment
  2. is important but not part of the present experiment
  3. is important in a theory that is not part of the present experiment
  4. is more similar to the dependent variable than to the independent variable

Answer

26. According to your text, the simplest way to control an extraneous variable is to ________.

  1. eliminate it before gathering data by making sure all of the participants are equal on that variable
  2. eliminate it from the gathered data by using statistical techniques
  3. both of these are simple ways mentioned by the text
  4. neither of these are simple ways mentioned by the text

Answer

 

Short-Answer Questions

1. Distinguish between descriptive and inferential statistics.

Answer

2. Distinguish between populations and samples.

Answer

3. Distinguish between interval and ordinal scales of measurement.

4. Distinguish between categorical and quantitative variables.

Answer

5. Distinguish between continuous and discrete variables.

 

Problems

1. Marigold covered the walls of three small rooms with red, blue, or white paper. Participants in her study entered a room, worked on three difficult logic problems for 10 minutes, and then filled out a mood survey. For the 36 participants, the mood survey scores ranged from 10 (calm) to 40 (agitated). The mean mood scores for the three rooms were red-24; blue-16; white-18.
Identify:

  1. the independent variable
  2. the number of levels of the independent variable and their names
  3. the dependent variable
  4. a controlled extraneous variable
  5. a variable measured with a nominal scale
  6. another variable and the scale used to measure it
  7. the question the study is asking

2. Khiela interviewed 60 students who were 20 years old. She used a questionnaire that allowed her to classify the parenting style of the parents of those she interviewed. The parenting style classifications were authoritarian, authoritative, and permissive. After filling out the questionnaire, the students indicated their grade point average (GPA). An inferential statistical test did not reveal any statistically significant differences in GPA among the three groups of students.
Identify:

  1. the independent variable
  2. the number of levels of the independent variable and their names
  3. the dependent variable
  4. a controlled extraneous variable
  5. a variable measured with a nominal scale
  6. another variable and the scale used to measure it
  7. the question the study is asking

3. Social loafing occurs when people do not work as hard in a group as they work alone. For example, three people pulling on a rope together exert less force than the sum of the three when each is pulling individually. Jay wondered if social loafing occurs when the task is mental rather than physical. All participants worked at small tables in groups of three. Each individual worked on a word square (a 15 x 15 array of letters) for six minutes searching for 20 words hidden in the word square. Half of the 30 participants were told that the words they found would be averaged with the other two people at their table; the other half were told that their words were scored individually. The number of words circled was recorded for each participant; the mean was 7.6 words for participants working in groups and 9.6 words for participants working alone.
Identify:

  1. the independent variable
  2. the number of levels of the independent variable and their names 
  3. the dependent variable
  4. a controlled extraneous variable
  5. a variable measured with a nominal scale
  6. another variable and the scale used to measure it
  7. the question the study is asking

4. Blaine was interested in the relationship between food spiciness and personality characteristics. The participants in Blaine's study were women who had not eaten for at least three hours. They first tasted three dips (with chips). One was mild, another medium, and one was hot. After indicating their favorite dip, the participants filled out a risk survey that indicated their desire to engage in activities such as skydiving, bungee jumping, and driving fast. The three spice preference groups averaged about the same score on the risk survey.

Identify:

  1. the independent variable
  2. the number of levels of the independent variable and their names
  3. the dependent variable
  4. a controlled extraneous variable
  5. a variable measured with a nominal scale
  6. another variable and the scale used to measure it
  7. the question the study is asking

5. What are the lower and upper limits of the following numbers?

  1. 3 minutes
  2. 8 errors
  3. 23°F
  4. 10 grams

6. Identify the scale of measurement that each set of values comes from (nominal, ordinal, interval, or ratio).

  1. Lieutenant, Captain, Major
  2. anxiety disorder, phobic disorder, adjustment disorder
  3. 0°C, 20°C, 40°C
  4. hat, shirt, shoes, pants
  5. 1st place, 2nd place, 3rd place
  6. 5 meters, 10 meters, 150 meters

7. Identify the scale of measurement that each set of values comes from (nominal, ordinal, interval, or ratio).

  1. achievement-test scores
  2. numbers assigned to identify individuals taking one of three different drugs (an opioid, an amphetamine, an antipsychotic)
  3. numbers given to different sections of the same college course
  4. win, place, and show in a horse race
  5. dollar amounts in a bank statement
  6. rank order of teams in a sport
  7. amount of liquid measured in fluid ounces

8. Identify each measurement below as being based on a continuous quantitative, discrete quantitative, or categorical variable. For continuous quantitative variables, identify the lower and upper limits of the measurement.

  1. 16, cubic yards of dirt
  2. 8, identification for Druid College among private schools in Transylvania
  3. 101, km/hr registered on a radar machine used by the state police
  4. 23, the time in seconds required for Sam to swim 50 yards
  5. 4, the time in minutes to run a mile
  6. 2, visits to a doctor's office in a year 
  7. 1, percentage of material recalled from a text
  8. 2, identification number of an individual registered as a Democrat

9. Identify each measurement below as being based on a continuous quantitative, discrete quantitative, or categorical variable. For continuous quantitative variables, identify the lower and upper limits of the measurement.

  1. 2, styles of sonnets
  2. 3, feet of paper
  3. 4, species of protozoa
  4. 5, seconds of time
  5. 6, decibels of noise
  6. 100, points on an IQ test 
  7. 118, wins in a season by a baseball team

10. A classic experiment by Warden (1931) measured the motivation of rats for food, water, or sex. After deprivation, a rat had to cross an electrified grid to get to the goal object (the whole apparatus was called the Columbia Obstruction Box). In each condition of deprivation (food, water, or sex), the amount of electrical shock a rat would tolerate and still cross to the goal object was measured. Name the dependent and independent variable. Identify an extraneous variable that should have been controlled.

11. Lu and colleagues (2018) wanted to know whether exposure to air pollution influenced unethical behavior. Half of their participants viewed a scene with polluted air and the other half viewed a scene with clean air. They asked participants to imagine that the picture was taken where they lived and what it would feel like and be like walking around and breathing the air. Next, participants were given the opportunity to solve five difficult problems and promised $0.50 for each correct solution. In addition, they were told there was a way to peek at the problem answers (i.e., to cheat) but that they should not do so. The researchers recorded the number of times the participants engaged in the unethical act of cheating. Name the independent and dependent variable and at least one extraneous variable that should have been controlled.

12. A researcher investigates whether cognitions (things you are thinking about) influence the experience of pain. Thirty women were divided into three equal groups and exposed to a painful stimulus, which was to put their hand into a bucket of ice water for 60 seconds. The three groups were all given different information about what to think about while they experienced the painful stimulus. One group was told to concentrate on their breathing, one was told to imagine that the day was very hot and that they would be allowed to place their hand in cool water, and the third group was told nothing. At the end of 60 seconds, they rated the pain they experienced on a scale of one to seven.

  1. The type of instructions the females received was the _________ variable.
  2. The rating of pain was the ________ variable.
  3. How many levels did the independent variable have? 

13. Four groups of men were monitored during their sleep for the number of minutes of REM sleep they obtained in one night. During the seven hours before going to sleep, one group watched six hours of TV, one group watched four hours, and one group watched no TV.

  1. The number of minutes of REM sleep was the ________ variable.
  2. The hours of viewing TV was the __________ variable.
  3. How many levels did the independent variable have?

References

Lu, J. G., Lee, J. J., Gino, G., & Galinsky, A. D. (2018). Polluted morality: Air pollution predicts criminal activity and unethical behavior. Psychological Science, 29(3), 340–355. doi: 10.1177/0956797617735807

Warden, C. J. (1931). Animal motivation studies:  The albino rat. New York:  Columbia University Press.

 

We hope you enjoyed checking out Chapter 1 of our study guide. One of the best things you can do as a student of statistics is to practice applying what you know to new questions.

This online (mobile-friendly) study guide is meant to provide you with that extra practice, helping you to conveniently strengthen your knowledge, assess what you've learned so far, and work out any remaining troubles before a homework assignment, quiz, or test. We'll be there with you in the explanations if you find yourself struggling to understand a concept. Good luck!

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Exploring Statistics: Tales of Distributions (12th ed.) Online Study Guide

 

Exploring Statistics: Tales of Distributions

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