PSYC 317 Ch. 7 Correlational Research

Negative correlation

as one variable increases, the other variable decreases

Positive correlation

as one variable increases, the other variable increases

A correlation

between two scales can never be higher than either scale's Cronbach's alpha * Cronbach's alpha about .70

Phi coefficient

used when both variables are dichotomous ex. Gender and virginity

Spearman rank-order correlation

used when one or both variables are on an ordinal scale ex. Placing in marathon and age

Point-biserial correlation

used when only one variable is dichotomous ex. Gender and height

Magnitude of a correlation expresses

the strength of the relationship r = .78: variables more strongly related than r = .30

Straight Line

= perfect correlation

Correlation and Causation

A correlation between two variables does NOT imply that one causes the other -Even a perfect correlation of 1.00 does not mean causality * can always be a 3rd variable that might influence X & Y variable

Coefficient of Determination

Correlation between stroke patient functioning and caregiver mental health r = .35 .35 x .35 = .1225, or 12.25% shared variance - The other 87.25 % is due to other factors "more variables helps explain more variance"

3 criteria for Inferring Causality

Covariation, Order in time, Removal of all other variables

Factors that distort correlation coefficients

Restricted range, Outlier, On-line Outlier, Off-line Outlier, Measure Reliability

Statistical significance affected by 3 things

Sample size: more participants = more sig Correlation magnitude: larger r = more sig How careful we want to be in our conclusion that the correlation in the population is not .00 : move alpha from .05 to .01 or .001

Other types of Correlations

Spearman rank-order correlation, Point-biserial correlation, Phi coefficient

Correlational Research

Used to describe the relationship between 2 or more naturally occurring variables ex. Is blondness related to intelligence? Are children's and parents' IQ's related?

What does a significant correlation mean?

X may cause Y: High drinking lowers GPA. Y may cause X: Low GPA increases drinking. A third variable may cause X and Y: People with large social networks may have lower GPAs and drink more.

Correlation Coefficient

a statistic indicating the degree to which two variables are related in a linear fashion

Removal of all other variables

all other variables that may affect the relationship between the two variables are controlled or eliminated

Covariation

changes in one variable are associated with changes in the other variable

Spurious correlation

correlation between two variables due to their relation to other variables aka: third variable problem

Partial correlation

correlation between two variables with the influence of one or more other variables statistically removed ex. If drinking and GPA are still correlated when removing the effect of social network, can conclude social network is not causing the correlation -If no longer significant relationship is partly due to social network or to another variable associated

On-line outliers

fall in the same pattern as the data and artificially inflate r

Off-line outliers

fall outside of the pattern of the data and artificially deflate r

Scatter plot

graph of participants' scores on two variables

p-value

index of how likely the true correlation in the population is different from .00 Rule: if less than 5% probability the size of the samples correlations is due to chance ( p < .05 ), results are considered "statistically significant" and reflect the larger population * ( p < .05 )

Sign ( - or + ) of a correlation coefficient

indicates the direction of the relationship Variables can be positively or negatively related

r^2

is on a ration scale and is easily interpretable "variance explained"

Pearson Correlation Coefficient ( r )

is the most commonly used measure of correlation -Ranges from -1.00 to + 1.00

Magnitude

is unrelated to the sign ( - or + ) -.78 is a larger (stronger) correlation than .52 +/- .10 = small, +/- .30 = medium, +/- .50 = large

Restricted range

participants' scores are confined to a narrow range of the possible scores on a measure * lowers the correlation coefficient - Artificially lowers correlations below what they would be if the full range of scores was present

Nondirectional hypothesis

predicts that two variables will be correlated but does not specify whether r will be positive or negative

Directional hypothesis

predicts the direction of the correlation (i.e., positive or negative) - More powerful and can reach statistical significance with fewer participants

Coefficient of Determination ( r^2)

proportion of variance in one variable accounted for by the other variable (systematic) -r is NOT on a ratio scale .80 is NOT twice as large as .40

Curvilinear Relationship

r = .00: indicates no linear relationship OR a curvilinear relations ( there is a relationship, but not a linear relationship)

Outlier

score so deviant from the data that one can question whether it belongs in the data set - Typically > 3 S.D. away from the mean, often delete

The less reliable a measure

the lower its correlations with other measures

Order in time

the presumed casual variable must occur before the other variable