Chapter 7 Experimental Design: Independent Groups Design

Independent groups designs We can confidently conclude a cause and effect relationship between variables if (and only if) the appropriate study has been conducted. We can confidently conclude a cause and effect relationship between variables if (and only if) the appropriate study has been conducted. Goal in conducting experiments  to show that an IV causes a change in the DV. Goal in conducting experiments  to show that an IV causes a change in the DV. True experiment – the independent variable must be under the control of the researcher. True experiment – the independent variable must be under the control of the researcher. Quasi-experimental design – the IV is not manipulated and/or is a characteristic Quasi-experimental design – the IV is not manipulated and/or is a characteristic

Steps in conducting an experiment Step 1. Formulate a hypothesis Step 1. Formulate a hypothesis –Hypothesis – a statement about the expected relationships between variables. Step 2. Select appropriate independent and dependent variables Step 2. Select appropriate independent and dependent variables –Operationalize, or make measurable, the IV and DV.

Steps in conducting an experiment Step 3. Limit alternative explanations for variation Step 3. Limit alternative explanations for variation –Consider what other variables might be involved and find ways to control them. Step 4. Manipulate the IVs and measure the DVs Step 4. Manipulate the IVs and measure the DVs –Carry out the experiment and collect the data.

Steps in conducting an experiment Step 5. Analyze the variation in the DVs Step 5. Analyze the variation in the DVs –Choose the appropriate statistical technique to analyze the variance in the DV. Step 6. Draw inferences about relationship between IVs and DVs Step 6. Draw inferences about relationship between IVs and DVs –Use inferential statistical procedures to make statements about populations based on your sample findings.

Where we do experiments Controlled experiments in the laboratory Controlled experiments in the laboratory –Advantages:  Better control over the independent variable  Superior control over secondary or extraneous sources of variation  Can more precisely measure the DV  Improved internal validity

Where we do experiments Controlled experiments in the laboratory Controlled experiments in the laboratory –Disadvantages:  Some phenomena can’t be studied in the lab  Some research topics present ethical problems  Practical disadvantages (e.g.. costly, time consuming)  Outcomes may not be applicable to the real world (lack external validity)

Where we do experiments Experiments in the field Experiments in the field –Improved external validity –May lack internal validity (because of lack of control)

How we do experiments: Independent groups designs Important assumption in experimental design  initial equivalence of groups Important assumption in experimental design  initial equivalence of groups Independent groups design Independent groups design –Participants are randomly and independently assigned to each level of the independent variable. –Also known as between participants design.

Independent groups designs Completely randomized groups designs: One IV Completely randomized groups designs: One IV –Research participants are randomly assigned to different levels of one IV. –Simplest completely randomized design: two group design where participants are randomly assigned and independently assigned to either an experimental group or a control group (i.e.. IV has two levels).

Independent Groups Design - Stats With one IV having two levels With one IV having two levels –t-test for independent groups –One-way ANOVA  Total variance is partitioned into between groups variance and within group variance. –Between groups variance is due to the treatment and to other factors (chance, individual differences, etc). –Within group variance is due to only the other factors (not to the treatment).  F test compares BGV and WGV while correcting for sample size –- F= MSB/MSW  The greater the effect of the treatment, the greater will be the numerator and the greater F will be.

One-Factor Between Groups Designs Some experiments require more than two levels of the independent variable to test the hypothesis. Some experiments require more than two levels of the independent variable to test the hypothesis. This is especially true when the relationship between the variables is believed to be complex. This is especially true when the relationship between the variables is believed to be complex. –More that two levels allows researchers a finer grained analysis

One Factor BG Design Stats One-way ANOVA is the correct test One-way ANOVA is the correct test –Need to conduct follow-up tests to compare groups means  In a three group design you would have –1 vs 2, 1 vs 3 and 2 vs 3  Tukey’s HSD is used to make these comparisons

Our THC and STM Study Problem – The effects of THC Intoxication on the ability to do occupational tasks requiring STM Problem – The effects of THC Intoxication on the ability to do occupational tasks requiring STM Research Hypothesis – THC intoxication will impair STM Research Hypothesis – THC intoxication will impair STM IV – Three smoked THC doses IV – Three smoked THC doses –0%, 5%, 10% DV – Span test for words at different time intervals DV – Span test for words at different time intervals –15min, 1hr and 3hrs –The average of these three times

SPSS Analysis Using our file from the previous assignment Using our file from the previous assignment –Analyze ---- Compare Means ---- One-way ANOVA  SpanT1, SpanT2, SpanT3 and SpanAvg entered into the “Dependent Varaibles” box  THC entered into the “Fixed Factor” box –Options ---- click “Descriptives” –Post –Hoc ---- click “Tukey’s”

Descriptives

ANOVA Table

Post-Hocs ---Tukey’s HSD

Statistical Conclusions What do the post-hoc patterns tell us? What do the post-hoc patterns tell us? –T1 –T2 –T3 –Avg

When There is More Than One Cause – Studies with Multiple IVs Various causes can be investigated individually, via a series of simple experiments, each manipulating only one independent variable, OR Various causes can be investigated individually, via a series of simple experiments, each manipulating only one independent variable, OR They can be manipulated together in a single, more complex experiment. They can be manipulated together in a single, more complex experiment. These designs are called FACTORIAL DESIGNS These designs are called FACTORIAL DESIGNS

Factorial Experiments A factorial experiment is one in which there are two or more causes (independent variables) that are believed to affect the dependent variable. A factorial experiment is one in which there are two or more causes (independent variables) that are believed to affect the dependent variable. Factorial experiments are more like real life, in that there can be multiple causes for the same behavior. Factorial experiments are more like real life, in that there can be multiple causes for the same behavior. We can test for these multiple causes We can test for these multiple causes

Factorial Experiments Allow researchers to determine whether the causes interact with each other Allow researchers to determine whether the causes interact with each other An interaction occurs when the effect of one cause depends on the level of the other cause that is present. An interaction occurs when the effect of one cause depends on the level of the other cause that is present. Single-factor experiments do not allow experimenters to detect interactions. Single-factor experiments do not allow experimenters to detect interactions.

Two of More Factors in the Same Experiment typical names for factorial designs: 2 X 3 (read: “2 by 3”) 3 X 6 2 X 2 X 3 typical names for factorial designs: 2 X 3 (read: “2 by 3”) 3 X 6 2 X 2 X 3 There is one numeral for each independent variable. 2 X 3 has two independent variables 3 X 6 has two independent variables 2 X 2 X 3 has three independent variables There is one numeral for each independent variable. 2 X 3 has two independent variables 3 X 6 has two independent variables 2 X 2 X 3 has three independent variables

Understanding Factorial Designs The value of each numeral indicates the number of levels of that variable. The value of each numeral indicates the number of levels of that variable. –2 X 3: has 2 levels in one variable, 3 levels in the other –3 X 6: has 3 levels in one variable, 6 levels in the other –2 X 2 X 3: has 2 levels in two of the variables, and 3 levels in the third variable The product indicates the number of separate combinations of the two variables present in the experiment. 2 X 3 = 6 3 X 6 = 18 2 X 2 X 3 = 12 The product indicates the number of separate combinations of the two variables present in the experiment. 2 X 3 = 6 3 X 6 = 18 2 X 2 X 3 = 12

Cells in Factorial Designs A “cell” is a particular combination of levels of the independent variables. A “cell” is a particular combination of levels of the independent variables. Each level of every independent variable is systematically combined with each level of every other independent variable. Each level of every independent variable is systematically combined with each level of every other independent variable. A factorial design can be represented by a table in which the levels of one factor are represented by the rows and the levels of the other factor are represented by the columns. A factorial design can be represented by a table in which the levels of one factor are represented by the rows and the levels of the other factor are represented by the columns.

Combining the Factors Factor 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 Groups Participants are assigned randomly to “groups.” Participants are assigned randomly to “groups.” Participants in each group experience only one combination of levels of each of the variables. Participants in each group experience only one combination of levels of each of the variables.

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

ANOVA Summary Table SourceSSdfMSF Factor AXXXX Factor BXXXX Factor A X Factor BXXXX Within CellsXXX TotalXX

Factorial ANOVA A separate F ratio is calculated for: A separate F ratio is calculated for: each main effect Factor A Factor B each main effect Factor A Factor B the interaction: A X B the interaction: A X B When there are more than two levels to an IV you would then do follow-ups When there are more than two levels to an IV you would then do follow-ups

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

Possible 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 combination of the above outcomes can occur. Any combination of the above outcomes can occur.

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