MARE 250

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Correlation
MARE 250 Dr. Jason Turner
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Correlation Coefficient
Correlation Coefficient (r)(Pearson) measures
the extent of a linear relationship between two
continuous variables (responses) H0 r 0 Ha r
? 0
Pearson correlation of cexa Ant and cexa post
0.811 P-Value 0.000 IF p lt 0.05 THEN the
linear correlation between the two variables is
significantly different than 0 IF p gt 0.05 THEN
you cannot assume a linear relationship between
the two variables
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Correlation Coefficient

Correlation test is used to determine the
relationship between two responses Specifically
it gives you two pieces of information 1)
p-value is used to determine whether a linear
relationship exists i.e. - is relationship
significantly different than zero 2)
Correlation value (R) used to determine
strength and direction of the relationship -
value between 0 -1 or 0 1. Closer to 1 or -1
the stronger the linear relationship positive
number positive direction of relationship,
negative number negative direction of
relationship
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Correlation Coefficient
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Coefficient Relationships
The coefficient of determination (r2) is the
square of the linear correlation coefficient
(r) We will use coefficient of determination in
regression (next week)
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Correlation vs. Regression
Correlation coefficient (Pearson) measures the
extent of a linear relationship between two
continuous variables (Responses) Linear
regression investigates and models the linear
relationship between a response (Y) and
predictor(s) (X) Both the response and predictors
are continuous variables (Responses)
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When Correlation vs. Regression?
Correlation coefficient (Pearson) used to
determine whether there is a relationship or
not Linear regression - used to predict
relationships, extrapolate data, quantify change
in one versus other is weighted direction
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When Correlation vs. Regression?
IF Correlation variables are equally weighted
in both direction IF Regression then it
matters which variable is the Response (Y) and
which is the predictor (X) Y (Dependent
variable) X (Independent) X causes change in Y
(Y outcome dependent upon X) Y Does Not cause
change in X (X Independent)
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Effects of Outliers
Outliers may be influential observations
A data point whose removal causes the correlation
equation (line) to change considerably Consider
removal much like an outlier If no explanation
up to researcher
r -0.728
r -0.852
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Correlation vs. Causation
Two variables may have a high correlation without
being related/connected For exampleYou might
find a strong correlation between depth and
urchin density at Onekahakaha when possibly there
is little true causation (cause-effect
relationship) In actuality the relationship is
probably driven by salinity being very low in
shallow, nearshore waters and higher in deeper
waters further from the freshwater outflow
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Correlation vs. Causation
THEREFORE You must determine whether there is a
scientific basis for the comparison before you
test for it
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Correlation How to?
STAT Basic Statistics - Correlation
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Correlation How to?
Enter all response variables of interest into
Variables box
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Correlation How to?
Output is a matrix table with Pearson Correlation
scores and p-values
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Correlation How to?
GRAPH Scatterplot Simple Enter all response
variables of interest into Variables box as X
Y combinations
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Correlation How to?
Scatterplots are valuable graphic tools
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Correlation How to?
For more than 2 variable use a matrix plot