Stats I Final Pitt 3

measures the relationship between two variables

there are more than one type of correlation (depending on level of measurement)

between interval/ratio variables

most widely used measure of correlation

has the most assumptions

between ordinal variables

between dichotomous variables

between a dichotomous & interval/ration variables

ex: right or wrong of an exam item and total score

between a dichotomous (w/ underlying continuum) & interval/ratio variables

ex:anxiety (low, high) & depression

between a polytomous (3 or more levels) (w/ underlying continuum) & interval/ratio variables

ex: anxiety (low, medium, high) & depression

betwee dichotomous variables (w/ underlying continuum) and depression

ex: anxiety (low, high) & depression (low, high)

between polytomous variable (w/ underlying continuum)

No Outliers

Linearity

Normal Distribution

no extreme scores

• two types:
• -univariate
• -multivariate

an extreme score that is far away from the distribution of a variable

-only one variable

an extreme score that is far away from the joint distribution of variables

it is possible for a case to be a multivariate outlier without bieng a univaritate outlier

variables should NOT show any non-linear pattern

distribution of a variable should be univariate normal

distribution of variables should be multivariate normal

• all correlation range from -1 to +1
• a measure of correlation is unitless (or standardized).

• r = -1 perfect negative relationship
• r = +1 perfect positive relationship
• r = 0 no relationship

when the correlation is r= +1, the scatterplot appears in a straight line

as the correlation approaches 0, the variability of scores increases

measures of relationship between two variables in raw units (unstandardized correlation)

possible range is -infinity to +infinity

1. Is there a significant relationship between x and y?

2. Is there a significant difference in the relationship of x and y between group 1 and group 2?

3. What is the (1-alpha)%CI of the correlation?

• in not normal except when r=0 due to restricted range of the correlation
• -bound between -1 & +1

For testing H₀: p = 0, Greek letter rho - population correltaion

df = N - 2

affected not only by N but also by r. Depends on the # of subjects & relationship

when testing more than one correlation becomes tedious

easier to compute r-critical value as long as there are same N

For testing a H₀: p = p₀

For difference in a correlation between groups

For confidence interval of a correlation

Convert r to z-score