Student Learning Outcomes

At the completion of this instructional unit students will be able to:

1. Understand and explain the practical implications of positive and negative, and high and low correlations coefficients (Be sure you can provide practical examples to illustrate your understanding)
2. Explain the purpose of regression and important considerations when selecting variables to be included in correlations/regressions. (How many variables do we strive to select, which ones, how do we enter them in the regression equation, etc.)
3. Illustrate an understanding of a typical use of correlation and regression by designing a sample research study (How are correlation studies different from true experimental studies?)

Hint

I am less interested in you learning the specifics of the statistical stuff described in this chapter, and more interested in you getting a general understanding of important considerations when examining relationships between sets of data.

Review

What is a correlation?

What is the coefficient of correlation?

What is the difference between a positive and a negative correlation?

What is a "Pearson Product Moment Correlation?"

Q. You'll remember two critical questions we have about the results of our statistics. What were they?

A. Significance and meaningfulness

Q. How can we assess the significance of an r?

A. Compare against a table, e.g. p. 431. Text gave you an r = -.54 between body weight and pull ups. df N - 2 = 8. Can check at .05 and .01 levels and will see it is not significant. Notice as the df increase you need a smaller sample to get a significant r - implications? Get lots of subjects.

Q. How to assess meaningfulness?

A. Coefficient of determination - r2 - which represents variance.

Q. What is variance?

A. Measure of the relationship that two variables have in common. Consider r of .8, squared = 64%. What does this mean?

Note that many standardized tests used to predict success have low correlation to actual success.

Prediction Equation

Q. Prediction is common use of discovering correlations. What is it called when we use correlations for this purpose?

A. Regression. We are interested in the regression of Y scores (DV) on X scores (IV). In other words how the Y scores "go back to" or "depend on" X scores. Predictor variables are IVs because you can manipulate them in the sense of selecting or not selecting certain variables. Score on criterion variable is the measurement you are actually interested in.

Q. Correlations can be made between two variable or more than two variables. What terms do we use to describe whether there are two or more variables?

A. Simple correlation versus multiple correlation

Q. What's the value of a MC over a SC?

A. Addition of variables can increase the accuracy of the prediction. Give me an example?

Q. What's the ideal number of variables we'd like in a correlation?

A. Minimum number that collectively produce a high correlation. If we can predict performance based on 3 predictor variables (IVs) instead of 20 there's no reason to include the other variables.

Text tells us there are various ways in which the order of variables can be combined. How this occurs is less important than you knowing that if an article mentions the Wherry Doolittle method, or forward - backward - or Maximum R-squared method - they are discussing how the variables have been combined.

Also notes that in prediction studies you should seek large sample in order to be able to generalize and because a small sample may give you an erroneous, high correlation. Suggest that subject to variable ratio or 10 to 1 is ideal.

Practice

To check your understanding, I encourage you to use a research review form to briefly outline a plausible correlational study. Bring questions and let's discuss in class.

(Revised 2/3/99)