Statistics for the Behavioral Sciences by Frederick J. Gravetter, Larry B. Wallnau ISBN 10: 1305504917 ISBN 13: 9781305504912

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244 CHAPTER 8 | Introduction to Hypothesis Testinghypothesis test, however, the sample comes from an unknown population (see Figure 8.3).If the population is really unknown, it would suggest that we do not know the standard deviationand, therefore, we cannot calculate the standard error. To solve this dilemma, we havemade an assumption. Specifically, we assume that the standard deviation for the unknownpopulation (after treatment) is the same as it was for the population before treatment.Actually, this assumption is the consequence of a more general assumption that is partof many statistical procedures. This general assumption states that the effect of the treatmentis to add a constant amount to (or subtract a constant amount from) every score inthe population. You should recall that adding (or subtracting) a constant changes the meanbut has no effect on the standard deviation. You also should note that this assumption is atheoretical ideal. In actual experiments, a treatment generally does not show a perfect andconsistent additive effect.Normal Sampling Distribution To evaluate hypotheses with z-scores, we have usedthe unit normal table to identify the critical region. This table can be used only if the distributionof sample means is normal.BOX 8.1 Independent ObservationsIndependent observations are a basic requirementfor nearly all hypothesis tests. The critical concernis that each observation or measurement is not influencedby any other observation or measurement. Anexample of independent observations is the set ofoutcomes obtained in a series of coin tosses. Assumingthat the coin is balanced, each toss has a 50–50chance of coming up either heads or tails. Moreimportant, each toss is independent of the tosses thatcame before. On the fifth toss, for example, there isa 50% chance of heads no matter what happened onthe previous four tosses; the coin does not rememberwhat happened earlier and is not influenced bythe past. (Note: Many people fail to believe in theindependence of events. For example, after a seriesof four tails in a row, it is tempting to think thatthe probability of heads must increase because thecoin is overdue to come up heads. This is a mistake,called the “gambler’s fallacy.” Remember that thecoin does not know what happened on the precedingtosses and cannot be influenced by previousoutcomes.)In most research situations, the requirement forindependent observations is typically satisfied byusing a random sample of separate, unrelated individuals.Thus, the measurement obtained for eachindividual is not influenced by other participants inthe study. The following two situations demonstratecircumstances in which the observations are notindependent.1. A researcher is interested in examiningtelevision preferences for children. To obtaina sample of n = 20 children, the researcherselects 4 children from family A, 3 childrenfrom family B, 5 children from family C, 2children from family D, and 6 children fromfamily E.It should be obvious that the researcher doesnot have 20 independent observations. Withineach family, the children probably share televisionpreference (at least, they watch the sameshows). Thus, the response, for each child islikely to be related to the responses of his orher siblings.2. The principle of independent observationsis violated if the sample is obtained usingsampling without replacement. For example, ifyou are selecting from a group of 20 potentialparticipants, each individual has a 1 in 20chance of being selected first. After the firstperson is selected, however, there are only19 people remaining and the probability ofbeing selected changes to 1 in 19. Because theprobability of the second selection depends onthe first, the two selections are not independent.
SECTION 8.4 | Directional (One-Tailed) Hypothesis Tests 245LEARNING CHECK1. A research report summarizes the results of the hypothesis test by stating, “z = 2.13,p < .05.” Which of the following is a correct interpretation of this report?a. The null hypothesis was rejected and the probability of a Type I error is lessthan .05.b. The null hypothesis was rejected and the probability of a Type II error is lessthan .05.c. The null hypothesis was not rejected and the probability of a Type I error is lessthan .05.d. The null hypothesis was not rejected and the probability of a Type II error is lessthan .05.2. Which of the following is not an assumption for the z-score hypothesis test?a. The observations must be independent.b. The value for μ must be the same after treatment as it was before treatment.c. The value for σ must be the same after treatment as it was before treatment.d. The sample must be obtained by random sampling.3. A sample of n = 16 individuals is selected from a population with µ = 80 and σ = 5,and a treatment is administered to the sample. If the treatment really does have aneffect, then what would be the effect of increasing the standard deviation to σ = 25?a. Increase the chances that the sample will produce an extreme z-score andincrease the likelihood that you will conclude that a treatment effect exists.b. Increase the chances that the sample will produce an extreme z-score andincrease the likelihood that you will conclude that a treatment effect doesnot exist.c. Increase the chances that the sample will produce a z-score near zero andincrease the likelihood that you will conclude that a treatment effect exists.d. Increase the chances that the sample will produce a z-score near zero and increasethe likelihood that you will conclude that a treatment effect does not exist.ANSWERS1. A, 2. B, 3. D8.4 Directional (One-Tailed) Hypothesis TestsLEARNING OBJECTIVE9. Describe the hypotheses and the critical region for a directional (one-tailed)hypothesis test.The hypothesis-testing procedure presented in Sections 8.2 and 8.3 is the standard, ortwo-tailed, test format. The term two-tailed comes from the fact that the critical regionis divided between the two tails of the distribution. This format is by far the most widelyaccepted procedure for hypothesis testing. Nonetheless, there is an alternative that isdiscussed in this section.
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EDITION10Statistics for theBehavior
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Statistics for the Behavioral Scien
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CONTENTSCHAPTER 1 Introduction to S
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CONTENTSvii5.4 Using z-Scores to St
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CONTENTSixCHAPTER 10 The t Test for
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CONTENTSxiCHAPTER 15 Correlation 48
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PREFACEMany students in the behavio
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PREFACExv3. The former Chapter 19,
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PREFACExviiTo the StudentA primary
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ABOUT THE AUTHORSFREDERICK J GRAVET
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PREVIEWBefore we begin our discussi
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4 CHAPTER 1 | Introduction to Stati
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10 CHAPTER 1 | Introduction to Stat
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PREVIEWThere is some evidence that
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36 CHAPTER 2 | Frequency Distributi
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Central TendencyCHAPTER3Tools You W
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SECTION 3.1 | Overview 69DEFINITION
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SECTION 3.2 | The Mean 71research r
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SECTION 3.2 | The Mean 73the distri
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SECTION 3.2 | The Mean 75TABLE 3.1S
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SECTION 3.2 | The Mean 77Table 3.2
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SECTION 3.3 | The Median 793.3 The
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SECTION 3.3 | The Median 81To find
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SECTION 3.4 | The Mode 832. What is
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SECTION 3.4 | The Mode 85FIGURE 3.7
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SECTION 3.5 | Selecting a Measure o
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SECTION 3.6 | Central Tendency and
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FOCUS ON PROBLEM SOLVING 95of centr
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PROBLEMS 976. A population of N = 1
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VariabilityCHAPTER4Tools You Will N
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SECTION 4.1 | Introduction to Varia
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SECTION 4.2 | Defining Standard Dev
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SECTION 4.3 | Measuring Variance an
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SECTION 4.4 | Measuring Standard De
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SECTION 4.5 | Sample Variance as an
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SECTION 4.6 | More about Variance a
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SUMMARY 1252. A population has a me
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FOCUS ON PROBLEM SOLVING 127VAR0000
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PROBLEMS 1299. For the following se
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z-Scores: Location of Scoresand Sta
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SECTION 5.1 | Introduction to z-Sco
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SECTION 5.2 | z-Scores and Location
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SECTION 5.2 | z-Scores and Location
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SECTION 5.3 | Other Relationships B
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SECTION 5.4 | Using z-Scores to Sta
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SECTION 5.4 | Using z-Scores to Sta
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SECTION 5.5 | Other Standardized Di
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SECTION 5.5 | Other Standardized Di
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SECTION 5.6 | Computing z-Scores fo
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SECTION 5.7 | Looking Ahead to Infe
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SUMMARY 153LEARNING CHECK1. In N =
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DEMONSTRATION 5.2 155sure that your
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PROBLEMS 15716. A distribution of e
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PREVIEWHow likely is it that you wi
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162 CHAPTER 6 | Probabilitythe prob
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164 CHAPTER 6 | Probability(Note: W
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166 CHAPTER 6 | ProbabilityFIGURE 6
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168 CHAPTER 6 | Probability■ The
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170 CHAPTER 6 | ProbabilityFinding
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172 CHAPTER 6 | Probabilityand exac
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174 CHAPTER 6 | ProbabilityFinally,
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176 CHAPTER 6 | ProbabilityXz-score
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178 CHAPTER 6 | ProbabilityBOX 6.1
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180 CHAPTER 6 | ProbabilityEXAMPLE
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182 CHAPTER 6 | ProbabilityFIGURE 6
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184 CHAPTER 6 | Probability6.5 Look
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186 CHAPTER 6 | Probability2. For a
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188 CHAPTER 6 | ProbabilityDEMONSTR
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190 CHAPTER 6 | Probability6. Draw
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Page 241 and 242: FOCUS ON PROBLEM SOLVING 219SUMMARY
Page 243 and 244: PROBLEMS 221STEP 2Compute the z-sco
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Page 247 and 248: SECTION 8.1 | The Logic of Hypothes
Page 259 and 260: SECTION 8.2 | Uncertainty and Error
Page 261 and 262: SECTION 8.2 | Uncertainty and Error
Page 263 and 264: SECTION 8.3 | More about Hypothesis
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PROBLEMS 295PROBLEMS1. Under what c
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PROBLEMS 297b. Construct the 90% co
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The t Test for TwoIndependent Sampl
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SECTION 10.1 | Introduction to the
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SECTION 10.2 | The Null Hypothesis
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SECTION 10.3 | Hypothesis Tests wit
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SECTION 10.4 | Effect Size and Conf
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SECTION 10.5 | The Role of Sample V
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KEY TERMS 325SUMMARY1. The independ
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FOCUS ON PROBLEM SOLVING 327Group S
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PROBLEMS 329The t Statistic Finally
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PROBLEMS 331c. Write a sentence dem
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PROBLEMS 33319. If other factors ar
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PREVIEWIt’s the night before an e
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338 CHAPTER 11 | The t Test for Two
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PREVIEWYour job interview is tomorr
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368 CHAPTER 12 | Introduction to An
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Repeated-MeasuresAnalysis of Varian
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SECTION 13.1 | Overview of the Repe
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SECTION 13.2 | Hypothesis Testing a
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SECTION 13.3 | More about the Repea
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SPSS ® 4375. When the obtained F-r
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DEMONSTRATION 13.1 439you must also
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PROBLEMS 441PROBLEMS1. How does the
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PROBLEMS 44313. The following summa
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PROBLEMS 44523. The following data
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Two-FactorAnalysis of Variance(Inde
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SECTION 14.1 | An Overview of the T
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SECTION 14.2 | An Example of the Tw
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SECTION 14.3 | More about the Two-F
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SUMMARY 473SUMMARY1. A research stu
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FOCUS ON PROBLEM SOLVING 475Descrip
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DEMONSTRATION 14.1 477STEP 2STAGE 1
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PROBLEMS 479PROBLEMS1. Define each
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PROBLEMS 48115. Research results in
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PROBLEMS 483EasyFactorA TaskDifficu
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PREVIEWA recent report describing t
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488 CHAPTER 15 | CorrelationDEFINIT
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492 CHAPTER 15 | CorrelationSubstit
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494 CHAPTER 15 | Correlationeither
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496 CHAPTER 15 | Correlationreliabl
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498 CHAPTER 15 | Correlation60Numbe
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500 CHAPTER 15 | CorrelationOne of
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502 CHAPTER 15 | CorrelationBOX 15.
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504 CHAPTER 15 | Correlation171615Z
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506 CHAPTER 15 | Correlation3. What
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508 CHAPTER 15 | Correlationon the
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510 CHAPTER 15 | CorrelationLEARNIN
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512 CHAPTER 15 | CorrelationScoresR
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514 CHAPTER 15 | CorrelationThe pro
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516 CHAPTER 15 | Correlationthat a
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518 CHAPTER 15 | Correlationmeasure
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520 CHAPTER 15 | CorrelationSUMMARY
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522 CHAPTER 15 | CorrelationTo comp
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524 CHAPTER 15 | CorrelationSTEP 2C
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526 CHAPTER 15 | Correlation14. Ide
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Introduction to RegressionCHAPTER16
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SECTION 16.1 | Introduction to Line
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SECTION 16.2 | The Standard Error o
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SECTION 16.3 | Introduction to Mult
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KEY TERMS 553a predicted portion an
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DEMONSTRATION 16.1 555DEMONSTRATION
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PROBLEMS 557Alzheimer’s disease.
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The Chi-Square Statistic:Tests for
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SECTION 17.1 | Introduction to Chi-
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SECTION 17.2 | An Example of the Ch
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SECTION 17.4 | Effect Size and Assu
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SECTION 17.4 | Effect Size and Assu
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SECTION 17.5 | Special Applications
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SECTION 17.5 | Special Applications
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SUMMARY 591With df = 2 and α = .05
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SPSS ® SPSS ® 593General instruct
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DEMONSTRATION 17.1 595FOCUS ON PROB
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PROBLEMS 597Finally, we can add the
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PROBLEMS 599response, a sample of 1
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PROBLEMS 601a researcher obtains a
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PREVIEWIn 1960, Gibson and Walk des
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606 CHAPTER 18 | The Binomial Testp
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608 CHAPTER 18 | The Binomial Test2
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610 CHAPTER 18 | The Binomial Test
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612 CHAPTER 18 | The Binomial Test
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614 CHAPTER 18 | The Binomial TestT
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616 CHAPTER 18 | The Binomial Testt
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618 CHAPTER 18 | The Binomial TestB
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Basic Mathematics ReviewAPPENDIXAPR
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APPENDIX A | Basic Mathematics Revi
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648 APPENDIX B | Statistical Tables
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664 APPENDIX C | Solutions for Odd-
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684 APPENDIX D | General Instructio
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Hypothesis Tests for OrdinalData: M
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APPENDIX E | Hypothesis Tests for O
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702 Statistics Organizer: Finding t
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ReferencesAckerman, R. (2011). Meta
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REFERENCES 719Alzheimer’s disease
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REFERENCES 721of aging and estrogen
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724 NAME INDEXKaell, A., 622Kahn, K
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726 SUBJECT INDEXConfidence interva
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728 SUBJECT INDEXIndependent random
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730 SUBJECT INDEXResearch studies,
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732 SUBJECT INDEXTwo-factor ANOVA (
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Statistics for the Behavioral Sciences by Frederick J. Gravetter, Larry B. Wallnau ISBN 10: 1305504917 ISBN 13: 9781305504912

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