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

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356 CHAPTER 11 | The t Test for Two Related Samples2. The repeated-measures t test begins by computing a differencebetween the first and second measurements foreach subject (or the difference for each matched pair).The difference scores, or D scores, are obtained byD = X 2− X 1The sample mean, M D, and sample variance, s 2 , areused to summarize and describe the set of differencescores.3. The formula for the repeated-measures t statistic ist 5 M D 2m DsMDIn the formula, the null hypothesis specifies μ D= 0,and the estimated standard error is computed bysMD5Îs2n4. For a repeated-measures design, effect size can bemeasured using either r 2 (the percentage of varianceaccounted for) or Cohen’s d (the standardized meandifference). The value of r 2 is computed the same forboth independent and repeated-measures designs,t2r 2 5t 2 1 dfCohen’s d is defined as the sample mean differencedivided by standard deviation for both repeated- andindependent-measures designs. For repeated-measuresstudies, Cohen’s d is estimated asestimated d 5 M Ds5. An alternative method for describing the size of thetreatment effect is to construct a confidence intervalfor the population mean difference, μ D. The confidenceinterval uses the repeated-measures t equation,solved for the unknown mean difference: D5 M D6 tsMDFirst, select a level of confidence and then look up thecorresponding t values. For example, for 95% confidence,use the range of t values that determine the middle95% of the distribution. The t values are then used inthe equation along with the values for the sample meandifference and the standard error, which are computedfrom the sample data.6. A repeated-measures design may be preferred toan independent-measures study when one wants toobserve changes in behavior in the same subjects, asin learning or developmental studies. An importantadvantage of the repeated-measures design is that itremoves or reduces individual differences, which inturn lowers sample variability and tends to increasethe chances for obtaining a significant result.KEY TERMSrepeated-measures design (336)within-subjects design (336)matched-subjects design (337)related-samples design (337)difference scores (339)estimated standard error for M D(341)repeated-measures t statistic (342)individual differences (353)Wilcoxon test (346)order effects (354)SPSS ®General instructions for using SPSS are presented in Appendix D. Following are detailedinstructions for using SPSS to perform the Repeated-Measures t Test presented in thischapter.Data Entry1. Enter the data into two columns (VAR0001 and VAR0002) in the data editor with thefirst score for each participant in the first column and the second score in the secondcolumn. The two scores for each participant must be in the same row.
SPSS ® 357Data Analysis1. Click Analyze on the tool bar, select Compare Means, and click on Paired-Samples TTest.2. One at a time, highlight the column labels for the two data columns and click the arrow tomove them into the Paired Variables box.3. In addition to performing the hypothesis test, the program will compute a confidenceinterval for the population mean difference. The confidence level is automatically set at95% but you can select Options and change the percentage.4. Click OK.SPSS OutputWe used the SPSS program to analyze the data from the cursing and pain experiment inExample 11.2 and the program output is shown in Figure 11.5. The output includes a tableof sample statistics with the mean and standard deviation for each treatment. A secondtable shows the correlation between the two sets of scores (correlations are presented inPaired Samples StatisticsMeanNStd. DeviationStd. ErrorMeanPair 1VAR000017.77789.83333.27778VAR000025.777891.71594.57198Paired Samples CorrelationsNCorrelationSig.Pair 1VAR00001 & VAR000029–.126.746Paired Samples TestPaired DifferencesMeanStd. DeviationStd. ErrorMeanPair 1 VAR00001 - VAR00002 2.00000 2.00000 .66667Paired Samples TestPaired Differences95% Confidence Intervalof the DifferenceLower Upper t df Sig. (2-tailed)Pair 1 VAR00001 - VAR00002 .46266 3.53734 3.000 8 .017F I G U R E 11.5The SPSS output for the repeated-measures hypothesis test in Example 11.2.
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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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406 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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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 17.3 | The Chi-Square Test
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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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