mare 250 dr. jason turner
DESCRIPTION
Correlation. MARE 250 Dr. Jason Turner. 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 - PowerPoint PPT PresentationTRANSCRIPT
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MARE 250Dr. Jason Turner
Correlation
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Correlation Coefficient (r)(Pearson) – measures the extent of a linear relationship between two continuous variables (responses) H0: r = 0Ha: r ≠ 0
Pearson correlation of cexa Ant and cexa post = 0.811P-Value = 0.000
IF p < 0.05 THEN the linear correlation between the two variables is significantly different than 0
IF p > 0.05 THEN you cannot assume a linear relationship between the two variables
Correlation Coefficient
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Correlation CoefficientCorrelation 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. RegressionCorrelation 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 OutliersOutliers 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
Leng
th (
cm)
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 example…You 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 – SimpleEnter 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