Ch. 7

Statistical Significance of r is Affected by Three Things

-Sample size -Magnitude of the correlation -How careful you want to be not to draw an inaccurate conclusion about whether the correlation is .00

Correlation coefficient: direction

-The sign of a THIS indicates the direction of the relationship between the two variables -Variables can be either positively or negatively related -*Positive correlation* - a direct, positive relationship between two variables; as one variable increases, the other variable increases -*Negative correlation* - an inverse, negative relationship between two variables; as one variable increases, the other variable decreases

What does a significant correlation mean?

-X may cause Y. -Y may cause X. -A third variable may cause X and Y. 1. Spurious correlation - correlation between two variables due to their relation to other variables

Correlation coefficient

-a statistic that indicates the degree to which two variables are related to one another in a linear fashion

partial correlation

-correlation coefficient -the correlation between 2 variables with the influence of 1+ other variables statistically removed. -If a THIS between 2 variables (with the influence of a third variable removed) is significantly lower than the Pearson correlation between the two variables, then the correlation between them is at least partly due to the third variable (or to a variable associated with the third variable).

phi-coefficient correlational

-correlation coefficient -used when both variables are dichotomous

point biserial

-correlation coefficient -used when only one of the variables is dichotomous

Spearman rank-order

-correlation coefficient -used when variables are measured on an ordinal scale (the numbers reflect the rank ordering of participants on some attribute)

Correlation coefficient: magnitude

-expresses the strength of the relationship between the two variables -When r = .00, the variables are not related. -A correlation of .78 indicates that the variables are more strongly related than does a correlation of .30. -THIS is unrelated to the sign of r; two variables with a correlation of .78 are just as strongly related as two variables with a correlation of -.78. -A correlation of .00 indicates that there is no linear relationship between the two variables. -However, there could be a curvilinear relationship between them.

Underlying assumptions of Pearson correlational analyses

-normally distributed, linearly related, continuous variables

Pearson correlation coefficient (r)

-the most commonly used measure of correlation -Ranges from -1.00 to +1.00 -Indicates strength and direction of association

Correlational research

-used to describe the relationship between two or more naturally occurring variables -To what extent do two variables covary together? 1. Is age related to political conservativism? 2. Are highly extraverted people less afraid of rejection than less extraverted people? 3. Is depression correlated with hypochondriasis? 4. Is I.Q. related to reaction time?

Correlation coefficient: statistical significance

-when the correlation calculated on a sample has a very low probability of being .00 in the population from which the sample came

Factors That Distort Correlation Coefficients

1. *Restricted range* - data in which participants' scores are confined to a narrow range of the possible scores on a measure 2. *outlier* 3. *Reliability of a Measure* -- the less reliable a measure is, the lower its correlations with other measures will be.