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Table 1.

Professor Ginsburgs 3302 Review of Statistical Tests.

Knowing which analyses to use depends upon (1) the kind of numerical measurement

scale (2) number of samples (whether the research design has 2 or >2 treatment conditions)

and (3) whether samples are related (when all participants are measured under alltreatment conditions) or independent (different participants are each measured under only

one treatment condition).

STATISTICAL TESTS

Test Cause-Effect Test RelationInference for two or Inference for

> two samples two samples

Non-Interactive Types of Statistical Analyses

SAMPLE

NUMBER 1 Sample 2 Samples >2 samples

/ \ / \SAMPLE

TYPE Independent Related Independent Related Independent

MEASUREMENT

SCALE

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1 NOMINAL McNemar Chi square Cochran Q Chi square Contingency Coefficient

Binomial test (test for 50/50 odds)

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2 ORDINAL Wilcoxen Mann-Whitney Friedman Kruskal-WallisU

Spearman r

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3 INTERVAL/ t-test t-test One-way One-way Pearson r

4 RATIO repeated samples independent samples(within-subjects) (between-subjects)

ANOVA ANOVA

VariousPost-hoc Analyses (see SPSS options )

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*Interactive Types of Analyses listed below all require interval/ratio numbers)

1. Factorial ANOVA test for Interaction Effects (2x2, 3x2. 4x3, ect.)

2. Covariant ANOVA (equates any pre-existing differences)3. Linear Multiple Discriminant Regression Analysis or Path Analysis

What Do Interactive Types of Analysis Show?

Why Are Interactive Analyses Typically Preferred?

I. Factorial ANOVA Designs and Interaction Effects

A. What is an Interaction Effect? - An interaction occurs when the effect produced by one

manipulated, independent variable is different at each level of a second independent variable.

1. When may Interaction Effects occur? When there are two or > two treatments (independent

variables); When either a repeated (within-subjects) or independent (between subjects) samples

research design is used; and, when an interval/raio scale of measuring the dependent variable is

used.

2. This is called a FACTORIAL DESIGN.

a. Cells The factorial design and ANOVA statistical test are characterized by the number of levels

for each independent variable (treatment), described as cells. A factorial design with 2

treatments and 2 levels for each treatment is called a 2x2 factorial (2 x 2 = 4 cells). A design with 3

treatments having 4 levels for each would be a 3x4 factorial design (3x4 = 12 cells).

b. What are the advantages of performing research using factorial designs?

(1) INTERACTIONS - The investigator wants to know whether a significant interaction effect

occurs. Sometimes treatment A and treatment B will not have an effect when presented alone, but

will have an effect when combined with each other

(2) EFFICIENCY it is more time and cost effective to examine several variables at once instead

of performing multiple studies on single independent variables.

(3) CONTROL there is greater control over transient influences like room temperature,different times of day when a unified factorial design research is conducted (3x4), rather than

conducting 12 separate studies.

(4) GENERALITY in nature, 2 or more variables may often occur simultaneously, thus creating

a more natural effect than when single factors are studied sequentially.

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c. How are Interaction Effects identified? The results of a factorial design are analyzed by

Analysis of Variance, ANOVA. ANOVA describes MAIN EFFECTS for each separate treatment

and INTERACTION EFFECTS when the treatments are combined with each other.

d. Examples: The Marilyn Monroe Effect - When taken alone, it takes relatively high amounts ofalcohol or barbiturates to cause sudden cardiac arrest. When combined with sleeping pills

much less alcohol is required to produce death.

e. How can interaction effects be readily identified in tables or figures? In tables, interaction

effects can be recognized when the mean recorded in one cell appears very different than the

means shown in the other cells. In figures, interaction effects are recognized when the lines

depicting dependent measures of the different levels of treatments appear to intersect. When the

lines appear by-and-large parallel, there are no interaction effects.

f. Post-hoc Analyses - Post hocanalyses (meaning after data has been collected) are performed

when the overall ANOVA shows some significant main effect(s) and/ or any interaction effect. Theinvestigator may perform appropriate post-hoc tests to localize the specific cells in the factorial

design producing the statistically significant main effects, and those combined cells responsible for

interaction effects. For example in a 3x3 ANOVA, 3 (levels of a drug, 1,2,3) x 3 (levels of

environmental stress, low, moderate, high), when the ANOVA shows significant and interaction

effects, which specific level of the drug produced main effects on the outcome measure? Which

specific level of stress? Which level of drug interacted with which level of stress to produce an

interaction? Sometimes these specific effects are apparent from examining a table or figure. Often

they are not readily apparent, which is when post-hoc analyses are very useful for understanding

what happened in a research investigation. The choice of post-hoc analysis depends upon the type

of primary design.

II. Analysis of Co-variance- Another common statistical technique is called the analysis of co-

variance. COANOVA should be used to equate different treatment conditions when some factor

makes the two or more groups unequal before any treatment was introduced. You can only use

COANOVA when a measurement is made (often a pre-test) has been administered and you know

that the participants in the different conditions had preexisting differences in some salient

measured variable. You may want to covary to hold a variable constant and equate that variable

for all the participants. Suppose that you were studying how a particular therapy improved

stroke patients recovery of motor skills. You create groups assigned to control or therapy a or

Therapy B conditions, but in your pretest measures you discover that participants in the control

group already had a 5-point IQ score advantage compared to the ones in therapy groups. You feel

that a persons pre-IQ may influence the outcome. So, after data is collected, your initial ANOVA

may show that there were no differences between the therapy & control group. A Covariate

ANOVA will factor the pre-IQ difference to allow fair and equal comparisons when the groups

are initially unequal in some relevant dimension. With IQ covaried, there may be a significant

effect of one or both of the therapies with a COANOVA.

III. Linear Multiple Dicriminant ANOVAand other Path Analysesmay be used with advanced

research designs with multiple predictor variables*. You may wish to determine which cluster of

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factors has the greatest predictive values for example, suppose you have identified 4 clusters of

measured factors that may predict a childhood injury (e.g., style of parenting, childs perceptual-

motor skills, childs temperament, home safety index, etc). With a path analysis, one can

determine how predictor variables may interact and which predictor variable carries the greatest

weight (e.g., home safety accounts for the greatest variance of the dependent variable (measured

injury rates, followed by childs temperament, motor coordination, & parenting styles).

IV. Eta 2 - is a post-hoc measure showing how much total variance between conditions accrues

from the treatment, apart from any random error variance. Eta 2 is a another post-hoc test

(meaning after initial analysis is performed) used to determine the extent to which the

independent (or predictor) variables studied account for the amount of variance between the

treatment (or predictor) conditions. A high * Eta 2 score means that most of the effects were due

to the actual variables used to predict the outcome differences. Low * Eta 2 means that the

variables didnt account for much of the total variability between the treatment conditions. A

researcher could obtain a statistically significant ANOVA effect, but a low Eta 2 means that the

treatment (or predictor) variables themselves did not account for very much of the variation of

outcome scores. Low Eta

2

means that some other factors that were not considered and measuredaccounted for more of the between condition differences (variance) than the actual treatment or

predictor variables. High Eta 2 means that the specific variables under study did account for most

of the variance in the study.