Chapter 7Chapter 7Experimental Design:Experimental Design:

Independent Groups Independent Groups DesignDesign

Independent groups designsIndependent groups designs We can confidently conclude a cause We can confidently conclude a cause

and effect relationship between and effect relationship between variables if (and only if) the appropriate variables if (and only if) the appropriate study has been conducted.study has been conducted.

GoalGoal in conducting experiments in conducting experiments to show to show that an IV causes a change in the DV.that an IV causes a change in the DV.

True experimentTrue experiment – the independent variable – the independent variable must be under the control of the researcher.must be under the control of the researcher.

Quasi-experimental designQuasi-experimental design – the IV is not – the IV is not manipulated and/or is a characteristicmanipulated and/or is a characteristic

Steps in conducting an Steps in conducting an experimentexperiment

Step 1. Formulate a hypothesisStep 1. Formulate a hypothesis

– Hypothesis – a statement about the Hypothesis – a statement about the expected relationships between expected relationships between variables.variables.

Step 2. Select appropriate Step 2. Select appropriate independent and dependent independent and dependent variablesvariables

– Operationalize, or make measurable, the Operationalize, or make measurable, the IV and DV. IV and DV.

Steps in conducting an Steps in conducting an experimentexperiment

Step 3. Limit alternative explanations Step 3. Limit alternative explanations for variationfor variation

– Consider what other variables might be Consider what other variables might be involved and find ways to control them. involved and find ways to control them.

Step 4. Manipulate the IVs and Step 4. Manipulate the IVs and measure the DVsmeasure the DVs

– Carry out the experiment and collect the Carry out the experiment and collect the data.data.

Steps in conducting an Steps in conducting an experimentexperiment

Step 5. Analyze the variation in the DVsStep 5. Analyze the variation in the DVs

– Choose the appropriate statistical Choose the appropriate statistical technique to analyze the variance in the technique to analyze the variance in the DV.DV.

Step 6. Draw inferences about Step 6. Draw inferences about relationship between IVs and DVsrelationship between IVs and DVs

– Use inferential statistical procedures to Use inferential statistical procedures to make statements about populations based make statements about populations based on your sample findings.on your sample findings.

Where we do experimentsWhere we do experiments

Controlled experiments in the Controlled experiments in the laboratorylaboratory

– Advantages:Advantages: Better control over the independent variableBetter control over the independent variable

Superior control over secondary or Superior control over secondary or extraneous sources of variationextraneous sources of variation

Can more precisely measure the DVCan more precisely measure the DV

Improved internal validityImproved internal validity

Where we do experimentsWhere we do experiments

Controlled experiments in the Controlled experiments in the laboratorylaboratory

– Disadvantages:Disadvantages: Some phenomena can’t be studied in the labSome phenomena can’t be studied in the lab

Some research topics present ethical Some research topics present ethical problemsproblems

Practical disadvantages (e.g.. costly, time Practical disadvantages (e.g.. costly, time consuming)consuming)

Outcomes may not be applicable to the real Outcomes may not be applicable to the real world (lack external validity)world (lack external validity)

Where we do experimentsWhere we do experiments

Experiments in the fieldExperiments in the field

– Improved external validityImproved external validity

– May lack internal validity (because of May lack internal validity (because of lack of control)lack of control)

How we do experiments: How we do experiments: Independent groups designsIndependent groups designs Important assumption in experimental Important assumption in experimental

design design initial equivalence of groups initial equivalence of groups

Independent groups designIndependent groups design

– Participants are randomly and Participants are randomly and independently assigned to each level of independently assigned to each level of the independent variable.the independent variable.

– Also known as between participants Also known as between participants design.design.

Independent groups designsIndependent groups designs Completely randomized groups Completely randomized groups

designs: One IVdesigns: One IV

– Research participants are randomly Research participants are randomly assigned to different levels of assigned to different levels of oneone IV. IV.

– Simplest completely randomized design: Simplest completely randomized design: two group design where participants are two group design where participants are randomly assigned and independently randomly assigned and independently assigned to either an experimental group assigned to either an experimental group or a control group (i.e.. IV has two or a control group (i.e.. IV has two levels).levels).

Independent Groups Design Independent Groups Design - Stats- Stats

With one IV having two levelsWith one IV having two levels– t-test for independent groupst-test for independent groups– One-way ANOVAOne-way ANOVA

Total variance is partitioned into between groups Total variance is partitioned into between groups variance and within group variance.variance and within group variance.

– Between groups variance is due to the treatment Between groups variance is due to the treatment and to other factors (chance, individual differences, and to other factors (chance, individual differences, etc).etc).

– Within group variance is due to only the other Within group variance is due to only the other factors (not to the treatment).factors (not to the treatment).

F test compares BGV and WGV while correcting for F test compares BGV and WGV while correcting for sample size –- F= MSB/MSWsample size –- F= MSB/MSW

The greater the effect of the treatment, the greater The greater the effect of the treatment, the greater will be the numerator and the greater will be the numerator and the greater FF will be. will be.

One-Factor Between Groups One-Factor Between Groups DesignsDesigns

Some experiments require more Some experiments require more than two levels of the independent than two levels of the independent variable to test the hypothesis.variable to test the hypothesis.

This is especially true when the This is especially true when the relationship between the variables relationship between the variables is believed to be complex.is believed to be complex.– More that two levels allows More that two levels allows

researchers a finer grained analysisresearchers a finer grained analysis

One Factor BG Design StatsOne Factor BG Design Stats

One-way ANOVA is the correct testOne-way ANOVA is the correct test– Need to conduct follow-up tests to Need to conduct follow-up tests to

compare groups meanscompare groups means In a three group design you would have In a three group design you would have

– 1 vs 2, 1 vs 3 and 2 vs 31 vs 2, 1 vs 3 and 2 vs 3

Tukey’s HSD is used to make these Tukey’s HSD is used to make these comparisonscomparisons

Our THC and STM StudyOur THC and STM Study Problem – The effects of THC Intoxication on the Problem – The effects of THC Intoxication on the

ability to do occupational tasks requiring STMability to do occupational tasks requiring STM Research Hypothesis – THC intoxication will Research Hypothesis – THC intoxication will

impair STMimpair STM IV – Three smoked THC dosesIV – Three smoked THC doses

– 0%, 5%, 10%0%, 5%, 10% DV – Span test for words at different time DV – Span test for words at different time

intervalsintervals– 15min, 1hr and 3hrs15min, 1hr and 3hrs– The average of these three timesThe average of these three times

SPSS AnalysisSPSS Analysis

Using our file from the previous Using our file from the previous assignmentassignment– Analyze ---- Compare Means ---- One-Analyze ---- Compare Means ---- One-

way ANOVAway ANOVA SpanT1, SpanT2, SpanT3 and SpanAvg SpanT1, SpanT2, SpanT3 and SpanAvg

entered into the “Dependent Varaibles” boxentered into the “Dependent Varaibles” box THC entered into the “Fixed Factor” boxTHC entered into the “Fixed Factor” box

– Options ---- click “Descriptives”Options ---- click “Descriptives”– Post –Hoc ---- click “Tukey’s” Post –Hoc ---- click “Tukey’s”

DescriptivesDescriptives

ANOVA TableANOVA Table

Post-Hocs ---Tukey’s HSDPost-Hocs ---Tukey’s HSD

Statistical ConclusionsStatistical Conclusions

What do the post-hoc patterns tell What do the post-hoc patterns tell us?us?– T1T1– T2T2– T3T3– AvgAvg

When There is More Than One Cause – When There is More Than One Cause – Studies with Multiple IVsStudies with Multiple IVs

Various causes can be investigated Various causes can be investigated individually, via a series of simple individually, via a series of simple experiments, each manipulating only experiments, each manipulating only one independent variable, ORone independent variable, OR

They can be manipulated together in They can be manipulated together in a single, more complex experiment.a single, more complex experiment.

These designs are called FACTORIAL These designs are called FACTORIAL DESIGNSDESIGNS

Factorial ExperimentsFactorial Experiments

A A factorialfactorial experiment is one in experiment is one in which there are two or more causes which there are two or more causes (independent variables) that are (independent variables) that are believed to affect the dependent believed to affect the dependent variable.variable.

Factorial experiments are more like Factorial experiments are more like real life, in that there can be multiple real life, in that there can be multiple causes for the same behavior.causes for the same behavior.

We can test for these multiple causesWe can test for these multiple causes

Factorial ExperimentsFactorial Experiments

Allow researchers to determine Allow researchers to determine whether the causes whether the causes interactinteract with with each othereach other

An interaction occurs when the effect An interaction occurs when the effect of one cause depends on the level of of one cause depends on the level of the other cause that is present.the other cause that is present.

Single-factor experiments do not Single-factor experiments do not allow experimenters to detect allow experimenters to detect interactions.interactions.

Two of More Factors in the Same Two of More Factors in the Same ExperimentExperiment

typical names for factorial designs:typical names for factorial designs:2 X 3 (read: “2 by 3”)2 X 3 (read: “2 by 3”)3 X 63 X 62 X 2 X 32 X 2 X 3

There is one numeral for each There is one numeral for each independent variable.independent variable.2 X 3 has two independent variables 2 X 3 has two independent variables 3 X 6 has two independent variables 3 X 6 has two independent variables 2 X 2 X 3 has three independent 2 X 2 X 3 has three independent variables variables

Understanding Factorial Understanding Factorial DesignsDesigns

The value of each numeral indicates the number of The value of each numeral indicates the number of levels of that variable.levels of that variable.– 2 X 3: has 2 levels in one variable, 3 levels in the 2 X 3: has 2 levels in one variable, 3 levels in the

otherother– 3 X 6: has 3 levels in one variable, 6 levels in the 3 X 6: has 3 levels in one variable, 6 levels in the

otherother– 2 X 2 X 3: has 2 levels in two of the variables, and 3 2 X 2 X 3: has 2 levels in two of the variables, and 3

levels in the third variable levels in the third variable The product indicates the number of separate The product indicates the number of separate

combinations of the two variables present in the combinations of the two variables present in the experiment.experiment.2 X 3 = 62 X 3 = 63 X 6 = 183 X 6 = 182 X 2 X 3 = 122 X 2 X 3 = 12

Cells in Factorial DesignsCells in Factorial Designs

A “cell” is a particular combination of A “cell” is a particular combination of levels of the independent variables.levels of the independent variables.

Each level of every independent variable Each level of every independent variable is systematically combined with each is systematically combined with each level of every other independent level of every other independent variable.variable.

A factorial design can be represented by A factorial design can be represented by a table in which the levels of one factor a table in which the levels of one factor are represented by the rows and the are represented by the rows and the levels of the other factor are represented levels of the other factor are represented by the columns.by the columns.

Combining the FactorsCombining the FactorsFactor A - Alcohol

Factor B

Anxiety

Level 1 - A

Level 1 - No

Level 2 - P

Level 2 - Yes

cell 1, 1

Alc + No Anx

cell 1, 2

Pla + No Anx

cell 2, 1

Alc + Anx

cell 2, 2

Pla + Anx

Assigning Participants to Assigning Participants to GroupsGroups

Participants are assigned randomly Participants are assigned randomly to “groups.”to “groups.”

Participants in each group Participants in each group experience only one combination of experience only one combination of levels of each of the variables.levels of each of the variables.

Partitioning the VariancePartitioning the Variance

For Factor A: Level 1 is compared with For Factor A: Level 1 is compared with Level 2Level 2

For Factor B: Level 1 is compared with For Factor B: Level 1 is compared with Level 2Level 2

For the Interaction between Factor A and For the Interaction between Factor A and Factor B:Factor B:Level 1, 1 compared with Level 1, 2, Level 1, 1 compared with Level 1, 2, compared with Level 2, 1 compared with compared with Level 2, 1 compared with Level 2, 2Level 2, 2(all cells compared with each other)(all cells compared with each other)

ANOVA Summary TableANOVA Summary Table

Source SS df MS F

Factor A X X X X

Factor B X X X X

Factor A X Factor B X X X X

Within Cells X X X

Total X X

Factorial ANOVAFactorial ANOVA

A separate A separate FF ratio is calculated for: ratio is calculated for: each main effecteach main effect

Factor AFactor AFactor BFactor B

the interaction:the interaction:A X BA X B

When there are more than two levels When there are more than two levels to an IV you would then do follow-upsto an IV you would then do follow-ups

Main EffectsMain Effects

For Factor A: For Factor A: Is the mean of Level 1 significantly Is the mean of Level 1 significantly different from the mean of level 2?different from the mean of level 2?

For Factor B: For Factor B: Is the mean of Level 1 significantly Is the mean of Level 1 significantly different from the mean of level 2?different from the mean of level 2?

Possible OutcomesPossible Outcomes

Either main effect can be significant.Either main effect can be significant. Both main effects can be significant.Both main effects can be significant. The interaction can be significant.The interaction can be significant. Any Any combinationcombination of the above of the above

outcomes can occur.outcomes can occur.

InteractionsInteractions

Do the individual cell means differ Do the individual cell means differ significantly from the grand mean? significantly from the grand mean?