I. General kinds of descriptive data:

A. Count data

B. Data about the relationship between two or more variables.
Ex: Correlation coefficients or comparing means of one group with the means of another group. Note that it's not how data are analyzed that make data correlational, it's how data are collected. Can analyze experiments using correlations, still make causal conclusions; use ANOVA on descriptive data, still correlational.

II. Why we can't make causal inferences from correlational data

A. A may cause B

B. B may cause A

C. Any number of "C" s may cause both A and B

III. The language of correlations

A. Correlations can range from -1.00 to +1.00

B. The sign of the relationship indicates the kind of relationship

1. Positive correlations

a. the more ___, the more ___

b. the less ___, the less ____

2. Zero correlations: no relationship.

3. Negative relationships: reverse relationship.

a. the more ___, the less ___

b. the less ___, the more ___

C. The further away from zero, the larger the relationship (-.8 as strong as +.8). To get a more precise idea of relationship strength, square r to get coefficient of determination

IV. Common statistical tests used with correlational data

A.  t test: for two groups

B. F test: for more than two groups or for detecting nonlinear relationships and/or interactions

C. Test of the significance of the correlation coefficient: Usually, the most powerful test of significance because you are using each individual's score.

V. The meaning of statistical significance (when the data are from a descriptive study)

A. Significant result indicates that the kind of relationship (positive or negative) observed in the sample holds in the population. It is not due to random sampling error, but to the fact that the variables are related.
However, to make that conclusion, be sure that:

1. Your data constitute a random sample of some population

2. You aren't doing many significance tests--or if you are that you statistically correct for number of analyses and/or cross validate. Otherwise, your risk of making a Type 1 error may be very high.

B. Null results: Failure to establish that variables are related in the population. Possible causes:

1. Not enough observations

2. Insensitive measures

3. Nonlinear relationship among variables

4. Restriction of range

5. Using a t test based on median split rather than testing significance of correlation coefficient

VI. Conclusions: Similarities between correlational and nonexperimental research. For both, you:

A. Should have hypotheses and rationale for those hypotheses

B. Need measures that have construct validity

C. Should look at the effects of combinations of variables and their interactions rather than just the relationship between a single predictor and a single criterion variable.

D. Should look for nonlinear functional relationships.

E. Should be extremely cautious about interpreting null results.

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