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Stats I Final Pitt 3
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What is
correlation
?
correlation
measures the relationship between two variables
there are more than one type of correlation (depending on level of measurement)
Pearson product moment correlation
correlation
between interval/ratio variables
most widely used measure of correlation
has the most assumptions
Speraman rank correlation
correlation
between ordinal variables
Phi coefficient
correlation
between dichotomous variables
point-biserial correlation
correlation
between a dichotomous & interval/ration variables
ex: right or wrong of an exam item and total score
biserial correlation
correlation
between a dichotomous (w/ underlying continuum) & interval/ratio variables
ex:anxiety (low, high) & depression
polyserial correlation
correlation
between a polytomous (3 or more levels) (w/ underlying continuum) & interval/ratio variables
ex: anxiety (low, medium, high) & depression
tetrachoric correlation
correlation
betwee dichotomous variables (w/ underlying continuum) and depression
ex: anxiety (low, high) & depression (low, high)
polychoric correlation
correlation
between polytomous variable (w/ underlying continuum)
Pearson Product Moment Correlation Assumptions
correlation
No Outliers
Linearity
Normal Distribution
Pearson Assumptions:
No Outliers
correlation
no extreme scores
two types:
-univariate
-multivariate
Pearson Assumption: No Outliers -
Univariate
correlation
an extreme score that is far away from the distribution of a variable
-only one variable
Pearson Assumption: No Outliers -
Multivariate
correlation
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
Pearson Assumption:
Linearity
correlation
variables should
NOT
show any non-linear pattern
Pearson Assumption:
Normal Distribution
correlation
distribution of a variable should be
univariate
normal
distribution of variables should be
multivariate
normal
Range of Correlation
correlation
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
Scatterplot
correlation
when the correlation is r=
+
1, the scatterplot appears in a straight line
as the correlation approaches 0, the variability of scores increases
Covariance
correlation
measures of relationship between two variables in raw units (
unstandardized correlation
)
possible range is -infinity to +infinity
Types of Research Questions
correlation
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?
Sampling Distribution Correlation
correlation
in not normal
except
when r=0 due to restricted range of the correlation
-bound between -1 & +1
One-sample t-test for correlation
correlation
For testing H
_{0}
:
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 to us
r
-critical
correlation
when testing more than one correlation becomes tedious
easier to compute r-critical value as long as there are same N
Fisher's
r-
to-
z
transformation
when to use
correlation
For testing a H
_{0}
:
p = p
_{0}
_{ }
For difference in a correlation between groups
For confidence interval of a correlation
Convert r to z-score
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Author
Anonymous
ID
187294
Card Set
Stats I Final Pitt 3
Description
Stats I Finall Pitt part 3
Updated
2012-12-05T15:55:31Z
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