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

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406 CHAPTER 12 | Introduction to Analysis of VarianceFOCUS ON PROBLEM SOLVING1. It can be helpful to compute all three SS values separately, and then check to verifythat the two components (between and within) add up to the total. However, you cangreatly simplify the calculations if you simply find SS totaland SS within treatments, then obtainSS between treatmentsby subtraction.2. Remember that an F-ratio has two separate values for df: a value for the numerator andone for the denominator. Properly reported, the df betweenvalue is stated first. You will needboth df values when consulting the F distribution table for the critical F value. You shouldrecognize immediately that an error has been made if you see an F-ratio reported with asingle value for df.3. When you encounter an F-ratio and its df values reported in the literature, you should beable to reconstruct much of the original experiment. For example, if you see “F(2, 36) =4.80,” you should realize that the experiment compared k = 3 treatment groups (becausedf between= k – 1 = 2), with a total of N = 39 subjects participating in the experiment(because df within= N – k = 36).DEMONSTRATION 12.1ANALYSIS OF VARIANCEA human factors psychologist studied three computer keyboard designs. Three samples ofindividuals were given material to type on a particular keyboard, and the number of errorscommitted by each participant was recorded. The data are as follows:Keyboard A Keyboard B Keyboard C0 6 6 N = 154 8 5 G = 600 5 9 ΣX 2 = 3561 4 40 2 6T = 5 T = 25 T = 30SS = 12 SS = 20 SS = 14Are these data sufficient to conclude that there are significant differences in typing performanceamong the three keyboard designs?STEP 1State the hypotheses, and specify the alpha level The null hypothesis states that there isno difference among the keyboards in terms of number of errors committed. In symbols, wewould stateH 0: μ 1= μ 2= μ 3(type of keyboard used has no effect.)As noted previously in this chapter, there are a number of possible statements for the alternativehypothesis. Here we state the general alternative hypothesis:H 1:At least one of the treatment means is different.We will set alpha at α = .05.
DEMONSTRATION 12.1 407STEP 2Locate the critical region To locate the critical region, we must obtain the values fordf betweenand df within.df between= k – 1 = 3 – 1 = 2df within= N – k = 15 – 3 = 12The F-ratio for this problem has df = 2, 12. Consult the F-distribution table for df = 2 in thenumerator and df = 12 in the denominator. The critical F value for α = .05 is F = 3.88. Theobtained F-ratio must exceed this value to reject H 0.STEP 3Perform the analysis The analysis involves the following steps:1. Perform the analysis of SS.2. Perform the analysis of df.3. Calculate mean squares.4. Calculate the F-ratio.Perform the Analysis of SS We will compute SS totalfollowed by its two components.SS total5SX 2 2 G2 602 36005 356 2 5 356 2N 15 15= 356 – 240 = 116SS within= ΣSS inside each treatment= 12 + 20 + 14= 46SS between5S T2n 2 G2N5 525 1 2525 1 3025 2 602155 25 5 1 6255 1 9005 2 3600155 5 1 125 1 180 2 2405 70Analyze Degrees of Freedom We will compute df total. Its components, df betweenanddf within, were previously calculated (step 2).df total= N – 1 = 15 – 1 = 14df between= 2df within= 12Calculate the MS Values The values for MS betweenand MS withinare determined.MS between5 SS betweendf between5 70 2 5 35MS within5 SS withindf within5 4612 5 3.83
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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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Probability and Samples: TheDistrib
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SECTION 7.1 | Samples, Populations,
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SECTION 7.1 | Samples, Populations,
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SECTION 7.2 | The Distribution of S
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SECTION 7.3 | Probability and the D
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SECTION 7.3 | Probability and the D
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SECTION 7.4 | More about Standard E
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SECTION 7.4 | More about Standard E
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FOCUS ON PROBLEM SOLVING 219SUMMARY
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PROBLEMS 221STEP 2Compute the z-sco
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Introduction toHypothesis TestingCH
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SECTION 8.1 | The Logic of Hypothes
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SECTION 8.2 | Uncertainty and Error
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SECTION 8.2 | Uncertainty and Error
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SECTION 8.3 | More about Hypothesis
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SECTION 8.3 | More about Hypothesis
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SECTION 8.4 | Directional (One-Tail
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SECTION 8.5 | Concerns about Hypoth
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SECTION 8.5 | Concerns about Hypoth
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SECTION 8.6 | Statistical Power 255
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FOCUS ON PROBLEM SOLVING 2618. The
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PROBLEMS 263In this distribution, o
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PROBLEMS 26513. A random sample is
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Introduction to the t StatisticCHAP
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SECTION 9.1 | The t Statistic: An A
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SECTION 9.2 | Hypothesis Tests with
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SECTION 9.2 | Hypothesis Tests with
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SECTION 9.3 | Measuring Effect Size
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SECTION 9.4 | Directional Hypothese
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SUMMARY 2913. A researcher rejects
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DEMONSTRATION 9.1 293One-Sample Sta
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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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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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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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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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