Interpreting and Statistically Evaluating a Correlation

r2 = .64

A correlation of r = 0.80 would mean that # (or 64%) of the differences in grade point average can be predicted by difference in IQ. A correlation of r = .30 would mean that only 0.09 (9%) of the differences are predictable.

r2

Because a correlation is typically identified by the letter r, the coefficient of determination is #.

statistical significance of a correlation

In a correlational study, the correlation in the sample is large enough that it is very unlikely to have been produced by random variation, but rather represents a real relationship in the population.

significant

In the context of a correlation, the term # means that a correlation found in the sample data is very unlikely to have been produced by random variation. Instead, whenever a sample correlation is found to be #, you can reasonably conclude that it represents a real relationship that exists in the population.

pairs of variables should produce a negative relationship

Number of hours studying and number of errors on a math exam

25% .25

large

9% .09

medium

1% .01

small

perfectly, lack

For both numerical and non-numerical data, the value of a correlation, which ranges from 0.00 to 1.00, describes the consistency of the relationship with 1.00 (or −1.00) indicating a # consistent relationship and 0.00 indicating a complete # of consistency.

determination, correlation

However, there are two additional factors that must be considered when interpreting the strength of a relationship. One is the coefficient of #, which is obtained by squaring the correlation, and the other is the significance of the #

Spearman correlation

If there is a consistent relationship between two variables so that Y tends to increase each time X increases, but not a linear relationship, then which correlation is designed to measure the consistency of the relationship?

coefficient of determination

The most common technique for measuring the strength of the relationship between two variables is to compute the #, which is obtained by squaring the numerical value of the correlation.

coefficient of determination

The squared value of a correlation that measures the percentage of variability in one variable, which is determined or predicted by its relationship with the other variable.

the numerical value of the correlation.

The strength or consistency of a relationship between variables is indicated by

measure the reliability of measurement, researchers usually look for large values, typically much greater than

There are some situations, however, in which a correlation of 0.50 would not be considered to be large. For example, when using correlations to #

no relationship between the two variables being examined.

With a small sample, it is possible to obtain what appears to be a very strong correlation when, in fact, there is absolutely #

substantial relationship

a research study that finds a theoretically important relationship between two variables might view a "small" correlation of r = .10 as a #