Matched Group, Natural Group, Repeated Measures

Matched Groups Design

• Different subjects serve at the different levels of the IV however the subjects are matched on the basis of some “important” secondary variable

• An attempt to create equivalent groups when you cannot gather a large number of participants and/or your population is very heterogeneous (with respect to your DV).

Steps to forming “Matched Groups”

1) Rank-order subjects by performance on the selected “matching task”. Often the task used is the same as your DV but could be some other similar variable relevant to the outcome of the study.

2) Form sets of similar (“matched”) subjects and randomly assign one member from each set to each level of your IV.

• Will help to take important secondary variables and form groups that are equivalent with respect to that variable.

Example: New drug to control high blood pressure

• Measure participants’ blood pressure WITHOUT medication.

• Form pairs of people with similar pre-study BP.

• Randomly assign one member of each pair to the new medication group and the other to the old medication group.

Natural Groups Design

• There is no true IV• The variable of interest is an “individual

differences” variable• Very common in Psychological Research• Example: Relationship between divorce and

subsequent emotional disorders• Even if you find a “statistically significant”

result, you cannot claim causality.

Repeated Measures Designs:Incomplete and Complete

Definition of Repeated Measures Design

• Researcher’s point of view: the same set of subjects serves at all levels of the IV. Each subject is measured at each level of the IV.

• Subject’s point of view: each subject experiences all levels of the IV.

• The ultimate “Matched Groups” Design.• Example: Mirror tracing task with two forms:

triangle/square

Suppose we had all participants trace first the square and then the triangle and we found more errors on the square than the triangle, as we predicted.

What other “plausible explanations” might exist?

How can we “fix” this issue in this study?

• Repeated measures designs are very powerful. Perfectly matched subjects at each level of IV.

• Because subjects are measured repeatedly, there are potential issues of co-varying time-related secondary variables (threats to internal validity), commonly called “order effects” or “carry-over effects”

• The most common order effects are: practice, boredom, and fatigue.

• You cannot eliminate these order effects but you can “balance” them across levels of your IV (counterbalancing)

• This can be done in several different ways and how you do this is tied to the type (name) of repeated measures design you use (Incomplete versus Complete)

Incomplete Repeated Measures Design

• The same set of subjects is measured at all levels of the IV but each subject experiences and is measured at each level of the IV only once (only one trial at each level of the IV).

• Example: The Mirror drawing study we just discussed. Each person traced a square once and a triangle once

• DV= # errors. • Each subject contributed two scores, one for

square and one for triangle.• How can we deal with time-related secondary

variables such as boredom, practice, fatigue?

Counterbalancing for Incomplete Repeated Measures Designs

• Controlling time-related variables that are potential threats to internal validity in incomplete repeated measures designs is easy for a two-level IV.

• There are only two possible orders for your IV: AB and BA (square/triangle and triangle/square)

• ½ subjects do one order and ½ do the other• Does not eliminate order effects but does

“balance” them over the two levels of the IV.

• With a 3-level IV there are six possible orders (3! Or 3 factorial=3 X 2 X 1=6)

• ABC• ACB• BAC• BCA• CAB• CBA• 1/6 of subjects for each order!

• Four level IV= 4! Orders=4X3X2X1=24 orders! Divide subjects into 1/24th!

• For an IV with >3 levels, can use a “Latin Square”

• Latin Square: an arrangement of symbols in rows and columns such that each symbol occurs only once in each row and each column

Latin Square Example for a 4-level IV

Each letter occurs once and only once in each column and each row. ¼ of subjects assigned to each “order” (row)

ACBD

DACB

BDAC

CBDA

NOT a Latin Square!!!!

ACBD

DBAC

CDBA

BADC

How to use a Latin Square• Three level IV: Levels= A, B, C• Equal # of subjects for each order (row).• ACB (1/3 of subjects)

BAC (1/3 of subjects)CBA (1/3 of subjects)

• Each letter occurs only once in each row=each subject experiences each condition only once.

• Each letter occurs only once in each column= balances order effects across levels of IV.

Example of an Incomplete Repeated Measures Design:

Effect of exercise on mood (Hansen, Stevens, & Coast, 2001, page 236 hardback text)

Four levels of “exercise”, 0 (30 minutes of quiet resting), 10, 20, 30 min exercise on stationary bike. All participants did all levels one time each at one week intervals (over a 4 week period).

Rotation Method of generating a Latin Square

• Quick and “dirty”, not the best method• Better method= “Diagram Balanced Latin

Square”• Use a random arrangement of symbols

for your conditions for your first row.

A= 0 min, B=10 min, C=20 min, D=30 min

First Row:

BCAD• For next row, put B at far right and slide rest of

symbols over one to the left

CADB• Now put C at far right and slide rest of symbols

one to the left

ADBC• For last row, put A at far right and slide rest of

symbols one to the left

DBCA

• A= 0 min, B=10 min, C=20 min, D=30 min

BCAD (1/4 subjects)

CADB (1/4 subjects)

ADBC (1/4 subjects)

DBCA (1/4 subjects)

Complete Repeated Measures Design Definition

• The same set of subjects is measured at all levels of the IV but each subject experiences each level of the IV more than once.

Counterbalancing Complete Repeated Measures Designs: Block Randomization

• In block randomization each block involves one occurrence of each level of the IV. The order of the levels in each block is randomly arranged. (hence, “block randomization”)

Generic example of a Block Randomization (4 level IV)

• Four level IV: level A, level B, level C, level D.• Suppose we want 6 trials at each level• One block= a random order of the 4 levels

(A,B,C,D), for example “BDAC” is one block.• We would need 6 blocks:

BDAC DACB BADC CADB ACBD DBCA

Each subject would be exposed to all 6 blocks.

Each subject would experience each level (A,B,C,D) six times.

Research example of block randomization

• Sackheim, Gur and Saucy (1978) (Page 232-233 of text)

• Does one side of our face express emotion more intensely than the other?

• Set of photos of people expressing emotions• Cut photos in half down middle and created:

– Composite photos of two left sides (L)– Composite photos of two right sides (R)– Original photo (O)– One IV (type of photo) with three levels: O, L, R

Three versions of “disgust”:L,O,R

• One IV (type of photo) with three levels: O, L, R

• Had different people pose expressing several different emotions (disgust, fear, joy etc)

• Each participant viewed 54 photos, 18 O, 18L, and 18 R

• Participants rated each photo on a 7-point scale indicating the intensity of the emotion expressed.

• Photos ordered by “block randomization”

• Each block contains one O, one L, and one R.

• There were 18 blocks altogether with O,L, R randomly ordered in each block.

Which do you think showed most intense emotion? Left side(a), Original (b), or Right side (c)?

• Findings: Most people judged left-side composite (L) as showing more intense emotion. We may display stronger emotion with the left side of our face. (controlled by right hemisphere of brain).

Advantages of Repeated Measures over Independent group Designs

1) Uses fewer subjects. More economical.

2) Controls for all individual differences variables

3) Statistically more powerful. More likely to be able to “correctly reject a false null hypothesis” or more likely to be able to accurately detect a true effect of the IV.

Disadvantages of Repeated Measures Designs

1) Must deal with order effects. Usually use counterbalancing which takes time.

2) You cannot study some variables as repeated measures manipulations. Any variable that causes a permanent or semi-permanent change in the subjects cannot be studied as a repeated measures variable.