Research Analysis Guide   |   Explanation of Research Analysis Guide   |   Experimental Checklist   |   Problems, Hypotheses & Operational Definitions   |   VARIABLE CONTROL   |   Intro to Research Designs   |   Random (Independent)Groups Designs   |   Randomized Blocks Designs   |   Factorial Designs   |   Factorial Designs

We can define an experiment as an observation situation in which one or more IVs are varied and XVs are held constant.
     This is too narrow and incomplete--  better is:

     An experiment is an observation (measurement of DV) situation in which one or more IVs are systematically varied (manipulated) and the effects of XVs are controlled (e.g. held constant).

     Research designs (aka experimental designs) are plans for conducting experiments, and the type of design is primarily determined by the method of assigning participants to experimental conditions (groups).

I. (Mathematical) Models of Experimental Designs.

     A. Simplest case--one IV and one DV:
          Y = a.  

                  i.e. the value of the DV (Y) is a function of the single IV (a).  

     1. Behavior is never a function of a single IV, but the combined effect of the IV and other confounding ("contaminating") or extraneous variables.  egs. effects of individual differences among participants or imprecise measurements.
     2. The effects of these XVs are called experimental error.

          B. Adding experimental error to the model:

          Y = a + e          Where      Y= observed value of DV
                                   a= effect of IV (a) on DV
                                   e= effect of exp. error on DV.
                                   (see pg 91 for egs. of sources of exp. error).

      1. The above equation forms the basic math model for one value of the DV;  it is modified by adding terms to represent other IVs or factors influencing the DV.

II. Randomized Groups Design(s) with Two Experimental Conditions.
     (aka Independent Groups-two levels)
     A. Value of random assignment of Ss to groups:
        1. Reduces probability of confounding of XVs with IV(s).
        2. Increases probability that groups will be equivalent at start of experiment (ie. equal means, SDs, and shape of distribution [homogeneous].  Not guaranteed.
        3. All experiments contain some experimental error, but random assignment allows you to assume that no systematic differences existed between the groups at start of experiment, and observed diffs between groups is due primarily to effects of IV.
        4. maximizes external validity, i.e. allows more confident generalization to the population in question.

     B. Rarely are Ss randomly assigned in psych. experiments;  mostly volunteers and/or college students.  ?How representative of the general population are college students????

     C. Fixed- vs. Random-Effects Experimental Models:
        1. E can choose values of IVs (levels) from all possible values randomly or non-randomly.
           a. choice determines type of analysis applicable &
           b. degree to which effects can be generalized to other (than tested) levels of IV.
           c. In fixed effects model result can only be interpreted for IV values used in the study.
        2. Logic of the Design.
           a. comparison of DV values between the two groups.

     In a study to determine which of two schedules of reinforcement (Rt) result in greater resistance to extinction of bar-pressing behavior in rats:
               Yij = u + aj + eij


     Yij = observed extinction ratio for rat i on Rt schedule j     
             {j = 1 for continuous reinforcement (CRF) and j = 2 for intermittent reinforcement (IRF)}.

     u = effect of underlying bar-pressing ability of the rat population.
     aj = effect of the jth schedule of Rt on the extinction ratio.
     eij = effect of experimental error on the observed value of the extinction ratio for the ith rat on the jth Rt schedule.

     Observed diffs (eg. between the means of the two groups) in the DV should be a function of the DV.

*****You must know the derivation and the meaning of each expression eg. Y-bar sub1 = mu-bar + a-bar sub1 + e-bar sub1..

      1)  Y1 = u + a1 + e1        &     Y2 = u + a2 + e2

      2) u = u, therefore u - u = 0   &
      3) Y1 - Y2 = 0 + (a1 - a2) + (e1 - e2)

     Since rats were randomly assigned to Rt conditions the average experimental error (ej) should be roughly equal.  i.e.

            e1 =~ e2  

     The (traditional) null hypothesis states there is no difference between the groups:
                    a1 = a2 or a1 - a2 = 0  and therefore

                    Y1 - Y2 = (e1 - e2)

That is, that if the null hypothesis (H0) is true, differences observed between the means of the groups should be small and due only to experimental error.

     The research (aka experimental) or alternate hypothesis would hold that the different Rt schedules do have an effect (i.e. a1 /= a2) &
                    Y1 - Y2 = (a1 - a2) + (e1 - e2).

     As the difference between the mean values of the DVs of the two groups increases, the probability the difference is due to experimental error decreases and reduces the likelihood the null hypothesis is true.

     The probability the null hypothesis is true and rejected can be evaluated by use of inferential statistical tests:  e.g. t-test (a parametric test) or the Mann-Whitney U-test (non-parametric test).  The proper test to be used is determined by the measurement scale etc..

     3.  Steps in Implementing the Design

     1. State the problem in the form of a general question.
     2. Formulate the hypothesis. **not in form of if, then*
     3. Define variables (operationally):  IV(s), DV(s), conditions, measures.
     4. Define population of interest.  Nobody cares about samples.
     5. Select Ss (randomly, if possible).
     6. Randomly assign Ss to groups (experimental conditions).
     7. Establish experimental methodology--procedures for application of IVs and data collection.
     8. Administer experimental conditions (IVs)
     9. Observe & record DV measures.
     10. Compare observations between groups.

Show Model Diagram:

II.  Randomized Groups Designs: More Than 2 Experimental Conditions

     The most an experiment utilizing two levels of an IV can indicate is that the IV had and effect on the DV.  It can not indicate how much of an effect.  Also, the design may indicate no effect or only reflect a linear relationship, when in fact the relationship may be curvilinear.  Show example of dominance and resting heart rate in rhesus monkeys.

     The mathmatical model for the DV is the same as for 2 level randomized group designs, as are the steps in implementing the design.      

Design  Model: