View
227
Download
0
Category
Tags:
Preview:
Citation preview
Bivariate Statistics
Nominal Ordinal Interval
Nominal 2 Rank-sum t-testKruskal-Wallis H ANOVA
Ordinal Spearman rs (rho)
Interval Pearson rRegression
Y
X
http://www.york.ac.uk/depts/maths/histstat/people/
Sir Francis Galton Karl Pearson
November 2, 2009
Source: Raymond Fancher, Pioneers of Psychology. Norton, 1979.
30 40 50 60 70 80
30
40
50
60
70
80
MATH
RDG
A correlation coefficient is a numerical expression of the degree of relationship between two continuous variables.
-1 r +1
-1 +1
Pearson’s r
Population
SampleA XA
µ
_
SampleB XB
SampleE XE
SampleD XD
SampleC XC
_
_
_
_
sa
sb
sc
sd
se
n
n
n
n n
Population
SampleA
SampleB
SampleE
SampleD
SampleC
_
XY
rXY
rXY
rXYrXY
rXY
-1 r +1
-1 +1
Pearson’s r
Pearson’s r is a function of the sum of the cross-product of z-scores for x and y.
Pearson’s r
r = zxzy
N
Population
SampleA
SampleB
SampleE
SampleD
SampleC
_
XY
rXY
rXY
rXYrXY
rXY
The familiar t distribution, at N-2 degrees of freedom, can be used to test the probability that the statistic r was drawn from a population with = 0
H0 : XY = 0
H1 : XY 0
where
r N - 2
1 - r2
t =
Some uses of r
• Association of two variables
• Reliability estimates
• Validity estimates
Factors that affect r
Non-linearity
Restriction of range / variability
Outliers
Reliability of measure / measurement error
-1 r +1
-1 +1
Pearson’s r
Pearson’s r can also be interpreted as how far the scores of Y individuals tend to deviate from the mean of X when they are expressed in standard deviation units.
-1 r +1
-1 +1
Pearson’s r
Pearson’s r can also be interpreted as the expected value of zY given a value of zX.
tend to deviate from the mean of X when they are expressed in standard deviation units.
The expected value of zY is zX*r
If you are predicting zY from zX where there is a perfect correlation (r=1.0), thenzY=zX.. If the correlation is r=.5, then zY=.5zX.
Recommended