PSY 290 A: Chapter 12

linear relationship

in which the data points in the scatter plot tend to cluster around a straight line.

correlation, or correlation coefficient

numerical values that measure and describe the relationship between two variables. a numerical value that measures and describes the relationship between two variables. The sign of the correlation (1/-) indicates the direction of the relationship. The numerical value of the cor- relation (0.0 to 1.0) indicates the strength or consistency of the relationship. The type of correlation (Pearson or Spearman) indicates the form of the relationship.

predictor variable

the first variable

statistical significance of a correlation

the second important factor for inter- preting the strength of a correlation. In the context of a correlation, the term signifi- cant 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 significant, you can reasonably conclude that it represents a real relationship that exists in the population.

criterion variable

the second variable (the one being explained or predicted)

negative relationship

there is a tendency for two variables to change in opposite directions; increases in one variable tend to be accompanied by decreases in the other.

positive relationship

there is a tendency for two variables to change in the same direction; as one variable increases, the other also tends to increase.

correlational research strategy

two or more variables are measured to obtain a set of scores (usually two scores) for each individual. The measurements are then examined to identify any patterns of relationship that exist between the variables and to measure the strength of the relationship.

Pearson correlation

used to describe and measure linear relationships when both variables are numerical scores from interval or ratio scales

Spearman correlation

used to measure and describe monotonic relationships when both variables are ranks from an ordinal score or have been transformed to ranks

Three characteristics described by a correlation coefficient

1.) The direction of the relationship: (+/-). 2.) The form of the relationship: A pattern in the data that suggests a consistent and predictable relationship between the two variables. 3.) The consistency or strength of the relationship:You may have noticed that the data points presented in Figure 12.2 do not form perfectly linear or perfectly monotonic relationships. In Figure 12.2a, the points are not perfectly on a straight line and in Figure 12.2b, the relationship is not perfectly one directional (there are reversals in the positive trend). In fact, perfectly consistent relationships are essentially never found in real behavioral sciences data. Instead, real data show a degree of consistency. In correlational studies, the consistency of a relationship is typically measured and described by the numerical value obtained for a correlation coefficient. A correlation of +1.00 (or -1.00) indicates a perfectly consistent relationship, and a value of zero indicates no consistency whatsoever. Intermediate values indicate different degrees of consistency.

directionality problem

A correlational study can establish that two variables are related; that is, changes in one variable tend to be accompanied by changes in the other variable. However, a correlational study does not determine which variable is the cause and which is the effect.

monotonic relationship

A relationship that is consistently one-directional, either consistently positive or consistently negative

multiple regression

A statistical procedure, that is a commonly used technique for studying multivariate relationships

third-variable problem

Although a correlational study may establish that two variables are related, it does not mean that there must be a direct relationship between the two variables. It is always possible that a third (unidentified) variable is con- trolling the two variables and is responsible for producing the observed relation.

coefficient of determination

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

regression

The statistical process for using one variable to predict another. Typically, the goal is to find the equation that produces the most accurate predictions of Y (the criterion variable) for each value of X (the predictor variable).