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Copyright © Allyn & Bacon (2010)Copyright © Allyn & Bacon (2010)

Correlated-Groups Correlated-Groups and Single-Subject and Single-Subject DesignsDesignsGraziano and RaulinGraziano and RaulinResearch Methods: Chapter 11Research Methods: Chapter 11This multimedia product and its contents are protected under copyright law. The following are This multimedia product and its contents are protected under copyright law. The following are prohibited by law: (1) Any public performance or display, including transmission of any image prohibited by law: (1) Any public performance or display, including transmission of any image over a network; (2) Preparation of any derivative work, including the extraction, in whole or in over a network; (2) Preparation of any derivative work, including the extraction, in whole or in part, of any images; (3) Any rental, lease, or lending of the program.part, of any images; (3) Any rental, lease, or lending of the program.


Correlated-Groups Correlated-Groups DesignsDesigns Introduces a correlation between Introduces a correlation between

groups in the way groups are groups in the way groups are formedformed– Within-subjects design:Within-subjects design:

Same participants in each groupSame participants in each group

– Matched-groups designMatched-groups design Uses matched random assignmentUses matched random assignment

More sensitive than independent-More sensitive than independent-groups designsgroups designs


Within-Subjects Within-Subjects DesignsDesigns All participants are exposed to all All participants are exposed to all

experimental conditionsexperimental conditions Need to control for sequence Need to control for sequence

effectseffects– The experience with one condition The experience with one condition

affecting performance in subsequent affecting performance in subsequent conditionsconditions

– Controlled by varying the order of Controlled by varying the order of presentation (counterbalancing)presentation (counterbalancing)

Sequence EffectsSequence Effects

SOURCESSOURCES– Positive Practice Positive Practice

Effects (PPE)Effects (PPE)– Negative Practice Negative Practice

Effects (NPE)Effects (NPE)– Carryover EffectsCarryover Effects

CONTROLSCONTROLS– Control PPE with Control PPE with

prior trainingprior training– Control NPE with Control NPE with

rest intervalsrest intervals– Control carryover Control carryover

effects by varying effects by varying the order of the order of conditionsconditions



Target Search StudyTarget Search Study

Hypothetical StudyHypothetical Study– Within-subjects designWithin-subjects design– Six participants; order counterbalancedSix participants; order counterbalanced– Three conditionsThree conditions

10 distracters10 distracters 15 distracters15 distracters 20 distracters20 distracters

Design on next slideDesign on next slide Data on the following slideData on the following slide


Within-SubjectsWithin-SubjectsDesign ExampleDesign Example


Target Search StudyTarget Search Study

ConditionsConditions

AA(10)(10)

BB(15)(15)

CC(20)(20)ParticipaParticipa

ntntOrderOrder

11 ABCABC 18.3318.33 22.3922.39 24.9724.97

22 ACBACB 15.9615.96 20.7220.72 21.7921.79

33 BACBAC 19.0219.02 22.7822.78 25.4625.46

44 BCABCA 25.3625.36 27.4827.48 27.9127.91

55 CABCAB 19.5219.52 24.6424.64 26.7526.75

66 CBACBA 23.2723.27 24.9624.96 25.4925.49

Mean ScoresMean Scores 20.2420.24 23.8323.83 25.4025.40


Graph of ResultsGraph of Results

The graph shows The graph shows how the mean how the mean search time search time increases as the increases as the number of number of distracter items distracter items increasesincreases 0

5

10

15

20

25

30

Search

Time

10 15 20

Number of Distracters


Statistical AnalysisStatistical Analysis

Appropriate Statistical AnalysesAppropriate Statistical Analyses– Correlated Correlated tt-test (for 2 groups only)-test (for 2 groups only)

– Repeated measures ANOVARepeated measures ANOVA Order data so that each line Order data so that each line

represents one participant and represents one participant and each column represents one each column represents one conditioncondition– Note that the columns represent conditions, Note that the columns represent conditions,

NOT the order of testingNOT the order of testing


ANOVA Summary TableANOVA Summary Table

SourceSource dfdf SSSS MSMS FF pp

BetweenBetween 22 83.6983.69 41.8541.85 32.2532.25 <0.01<0.01

SubjectsSubjects 55 95.8595.85 19.1719.17

ErrorError 1010 12.9712.97 1.301.30


Within-Subjects Within-Subjects StrengthsStrengths More sensitive to small group More sensitive to small group

differencesdifferences – The variability due to individual The variability due to individual

differences is statistically eliminateddifferences is statistically eliminated Fewer participants are neededFewer participants are needed

– Each participant appears in each conditionEach participant appears in each condition Instructions may take less timeInstructions may take less time

– Participants were already instructed on the Participants were already instructed on the task in previous conditionstask in previous conditions


Within-Subjects Within-Subjects WeaknessesWeaknesses Because participants experience all Because participants experience all

conditions, they may figure out the conditions, they may figure out the hypothesis (potential subject effects)hypothesis (potential subject effects)

Major issue is sequence effectsMajor issue is sequence effects– Practice and carry-over effectsPractice and carry-over effects– Controlled by varying the order of Controlled by varying the order of

presentationpresentation CounterbalancingCounterbalancing Random order of presentationRandom order of presentation Latin square designLatin square design


Matched-Subjects Matched-Subjects DesignsDesigns Introduces correlation through Introduces correlation through

matched random assignmentmatched random assignment Should match on “relevant” Should match on “relevant”

variablesvariables– Variables that affect the dependent Variables that affect the dependent

variablevariable– Variables that show considerable Variables that show considerable

natural variation in the population natural variation in the population sampledsampled


Matching ParticipantsMatching Participants

Match participants in setsMatch participants in sets– Set size is equal to the number of conditionsSet size is equal to the number of conditions

Matching gets more difficult as:Matching gets more difficult as:– The number of matching variables increasesThe number of matching variables increases– Matching is done on continuous variablesMatching is done on continuous variables– The number of conditions increaseThe number of conditions increase

Once sets are matched, randomly assign Once sets are matched, randomly assign participants in the set to the conditionsparticipants in the set to the conditions


Statistical AnalysisStatistical Analysis

Analyze as if it were a within-subjects Analyze as if it were a within-subjects studystudy– Data from matched participants are organized Data from matched participants are organized

as if the data came from a single participantas if the data came from a single participant Act as if the number of participants was Act as if the number of participants was

equal to the actual number of participants equal to the actual number of participants divided by the number of conditionsdivided by the number of conditions(e.g., for 40 participants and 4 conditions, tell the program (e.g., for 40 participants and 4 conditions, tell the program that you had 10 participants and 4 conditions in a within-that you had 10 participants and 4 conditions in a within-subjects design)subjects design)


Strengths and Strengths and WeaknessesWeaknesses StrengthsStrengths

– Increased sensitivity to group Increased sensitivity to group differencesdifferences

– No sequence effects No sequence effects WeaknessesWeaknesses

– Extra work of matching participantsExtra work of matching participants– Participants without appropriate Participants without appropriate

matches cannot be used in the studymatches cannot be used in the study


Single-Subject DesignsSingle-Subject Designs

Extensions of within-subjects designsExtensions of within-subjects designs Single participant tested under all Single participant tested under all

conditions, with the researcher conditions, with the researcher actively manipulating the actively manipulating the independent variableindependent variable

Variation on time-series designs, with Variation on time-series designs, with repeated measurement of the repeated measurement of the dependent variabledependent variable


History of these History of these DesignsDesigns Intensive studies of individuals Intensive studies of individuals

was common before R. A. Fisherwas common before R. A. Fisher Fisher’s development of ANOVA Fisher’s development of ANOVA

changed the focus of psychology changed the focus of psychology to comparing groups of to comparing groups of individualsindividuals

Skinner was one of the few Skinner was one of the few psychologists who advocated the psychologists who advocated the intensive study of individualsintensive study of individuals


Logic of these DesignsLogic of these Designs

Includes independent variable Includes independent variable manipulationmanipulation

Expect dependent variable responseExpect dependent variable response– Note that the response must occur shortly Note that the response must occur shortly

after the manipulation unless there is a after the manipulation unless there is a theoretical reason to expect a delaytheoretical reason to expect a delay

Multiple measures before and after the Multiple measures before and after the manipulation to identify normal variation manipulation to identify normal variation and rule out regression to the meanand rule out regression to the mean


Single-Subject DesignsSingle-Subject Designs

Basic Single-Subject design includesBasic Single-Subject design includes– Baseline periodBaseline period– A treatment phaseA treatment phase– A post-treatment evaluation periodA post-treatment evaluation period


Types of DesignsTypes of Designs

ABA Reversal DesignABA Reversal Design Multiple Baseline DesignMultiple Baseline Design Single-Subject, Randomized, Single-Subject, Randomized,

Time-Series DesignTime-Series Design


Reversal DesignReversal Design

LOGICLOGIC– Apply, then Apply, then

remove, remove, independent independent variable variable manipulationmanipulation

– If change occurs at If change occurs at both application both application and removal, it and removal, it suggests a causal suggests a causal connectionconnection

PROCEDURESPROCEDURES– Baseline measures Baseline measures

(Condition A)(Condition A)– Treatment Treatment

application application (Condition B)(Condition B)

– Return to baseline Return to baseline (Condition A again)(Condition A again)

– Additional Additional reversals can be reversals can be includedincluded


Reversal Design Reversal Design Example Example Reversal conditionsReversal conditions

– Condition A: attending to self-Condition A: attending to self-stimulation stimulation

– Condition B: withdrawing attention Condition B: withdrawing attention when self-stimulation occurswhen self-stimulation occurs

Hypothetical results (next slide) Hypothetical results (next slide) suggests that attention does suggests that attention does influence self-stimulationinfluence self-stimulation

Ethics requires return to Condition BEthics requires return to Condition B


Published Example Published Example DeLeon et al. (1997)DeLeon et al. (1997)


Multiple Baseline Multiple Baseline DesignDesign LOGICLOGIC

– Show the effect of Show the effect of the independent the independent variable on several variable on several dependent dependent variablesvariables

– Use when Use when Reversals are Reversals are

undesirableundesirable Behavioral changes Behavioral changes

would not reversewould not reverse

PROCEDURESPROCEDURES– BaselineBaseline– Manipulation Manipulation

focused on first focused on first dependent variabledependent variable

– Manipulation Manipulation focused on second focused on second dependent variabledependent variable

– ……and so onand so on


Multiple Baseline Multiple Baseline DesignDesign


Variations onVariations onMultiple Baseline Multiple Baseline DesignDesign Across BehaviorsAcross Behaviors

– Testing effects on different Testing effects on different behaviorsbehaviors

Across IndividualsAcross Individuals– Testing effects on different peopleTesting effects on different people

Across Settings and TimeAcross Settings and Time– Testing effects in different settings Testing effects in different settings

or at different timesor at different times


Single-Subject, Single-Subject, Randomized Time-Series Randomized Time-Series DesignDesign LOGICLOGIC

– Repeated Repeated measures of the measures of the dependent variable dependent variable interrupted by a interrupted by a randomly placed randomly placed interventionintervention

– If change occurs at If change occurs at the point of the point of intervention, it intervention, it suggests a causal suggests a causal connectionconnection

PROCEDURESPROCEDURES– Select minimum Select minimum

baseline and baseline and follow-up periodsfollow-up periods

– Randomly select Randomly select the point of the point of interventionintervention

– Compare pattern Compare pattern of scores before of scores before and after the and after the interventionintervention


Single-Subject, Single-Subject, Randomized Time-Series Randomized Time-Series DesignDesign


Replicating Single-Replicating Single-Subject ExperimentsSubject Experiments Direct replicationDirect replication

– Repeating study on the same target Repeating study on the same target behavior behavior

Systematic replicationSystematic replication– Evaluate procedures across subjects, Evaluate procedures across subjects,

settings, and/or target behaviorssettings, and/or target behaviors Clinical replicationClinical replication

– Combining procedures into a treatment Combining procedures into a treatment “package”“package”

Ethical PrinciplesEthical Principles

Ethics in treatment studiesEthics in treatment studies– First, do no harmFirst, do no harm– Second, try to do some goodSecond, try to do some good

ThereforeTherefore– Researcher is ethically bound to leave Researcher is ethically bound to leave

participants in the best situation, participants in the best situation, which often means returning to which often means returning to treatment in the reversal designtreatment in the reversal design



SummarySummary

Can introduce a correlation in two waysCan introduce a correlation in two ways– Within-subjects and matched-subjects Within-subjects and matched-subjects

designsdesigns These designs are more sensitive to small These designs are more sensitive to small

differences between groupsdifferences between groups The costs for the greater sensitivity are:The costs for the greater sensitivity are:

– Sequence effects (within-subjects design) Sequence effects (within-subjects design) – Matching difficulties (matched-subjects Matching difficulties (matched-subjects

design)design) Single-subject designs allow the Single-subject designs allow the

experimental manipulation of variablesexperimental manipulation of variables

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