PSY 200: Chapter 8 and 9 Quiz 3
61 Cards in this Set
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Correlation
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Relationship between 2 variables
Linear relationship
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Correlation Coefficient
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Measure used to express extent or strength of relationship
Represented by r
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Positive Correlation
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0 < r < 1
Score high on 1 variable and score high on the other
Score low on 1 variable and score low on the other
Positive Slope
1.0= perfect correlation
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Negative Correlation
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-1 < r < 0
Score high on 1 variable and score low on the other
Negative Slope
-1= perfect correlation
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Zero
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0= no correlation
No linear relationship
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Linear Relationship
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Looking for linear relationship others may exist (u-shaped)
Correlation only measures linear
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Correlation RULE
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Correlation does not = Causation!!!
Just means that there was a relationship
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r < 0.29
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Small correlation/ weak relationship
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r 0.3-0.49
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Medium correlation/ relationship
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r 0.5 - 1.0
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Large correlation/ strong relationship
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Scatter diagram
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Graphic means to show data points and correlation and (later) regression
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Centroid
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(Mean of X, Mean of Y) This will be the central point (X,Y) of 2 variables
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When to use Pearson r
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Interval and ratio data
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Pearson r Z Score method
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r = sum (ZxZy)/N
Good if you already have Z scores
Answer must be between -1 and 1
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Correlation Coefficient Pearson r Raw score method
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Will have to find 8 sums
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Covariace
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Numerator
Degree to which 2 variables share common variance
Can be a negative number on top but not on bottom
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High Covariance
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More linear
Covariance closer to +/- 1
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Low Covariance
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Less linear
Closer to 0
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If r = +/- 1
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All data fall in a line
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If r < 1
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Data are scattered
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3 types of Variation
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Total= explained (r2) + unexplained (k2)
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Total Variation
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Graph with all arrows pointing at the mean line (middle horizontal line)
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Explained Variation
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Double arrows pointing from Mean line to regression line in 2 spots on either side of the centroid
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Unexplained Variation
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All arrows point toward regression line
Weighs how far away data is from where the regression line is
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If r = +/- 1
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All is explained
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If r= 0
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All is unexplained
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r2 Coefficient of Determination
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The proportion of 1 variable explained by the other
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k2 Coefficient of non-determination
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proportion of 1 variable not explained by the other
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toal = 1 or 100%
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1= r2 + k2
k2= 1-r2
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Cautions with pearson r
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Measures linearity so low r means not linear; could still have non-linear relationship
Distribution need not be normal but must be unimodal and skewed
If truncated will get spuriously low r (r is always lower when you truncate the data)
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Spearman r
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Used with ordinal data rs
Both variables must be rank ordered
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Non parametric test
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looks at ranks only
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Parametric Test
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Uses actual numbers
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D
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rank x- rank y
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Sum of D
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0
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Tied Scores and Spearman r
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If tied must take this into account to be fair
take the mean of the tied ranks and assign mean rank to both
If there are more than 2 take middle number
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Correlation Matrix
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Table to visualize many correlations
Correlate the most= Number closest to 1 or -1
Correlate the least= Number closest to 0
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If r is 0 or very low
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Does not mean no correlation at all it means that there is no linear correlation
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Share common variance
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If high relationship= linear and closer to 1 /-1
If Low relationship= less linear and closer to 0
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X Rank
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High to low
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Regression
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Allows you to predict relationships
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Regression Analysis Equation
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Y= a + by X
X, Y= Variables
by= slope, (m), (tilt)
a= y intercept (b) (where it hits y-axis)
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r = +/- 1
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It's easy to predict and draw the line
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r < +/- 1
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You must draw a "best fit" line
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Properties of the regression line
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Squared deviations around the line are minimal
Sum deviations = 0
New symbols X' and Y' are for predictions
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To find the regression line equation
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Use the formula with 3 formulas in it
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To draw the regression line for Y= a + by X
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1.) Pick 2 reasonable values for X
2.) Put in the equation and solve for Y
3.) plot the 2 pairs of X,Y points
4.) Connect the dots with a line
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X= a +bx Y
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In regression analysis you can also find X= a + bx Y and get 2 regression lines that have certain relationship
r = 1 Line is on the line
r = 0-75 line crosses through the line narrow
r = 0.25 line is quarter through
r = 0 the line is perpendicular
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r = +/- 1
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Superimposed
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r = 0
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Perpendicular
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Intersection point
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Mean of x, Mean of Y = Centroid
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Standard Error of the Estimate
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sesty
Estimate of the standard deviation of data around the regression line
k2 was a version of this but not really in terms of standard deviation
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r = +/- 1 and sesty
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sesty = 0 means no errors/ deviation
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r = 0 and sesty
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means sesty is maximal a lot of deviation
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Larger sesty means
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Less accurate predictions
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Y' and Y true
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Recall Y' was a prediction not a fact
Using sesty we can find an interval where are 68% sure that true Y will be
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Sesty and Y true
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are influenced by magnitude of X and Y
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Variance and sesty
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Low variance > better/ lower setsty > better Y true
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Homoscedasticity
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Where variance of 1 variable is constant at all levels of the other variable
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Heteroscedasticity
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Where variance of 1 variable is not constant at all levels of the other variable
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Post Hoc Fallacy
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Assuming a cause and effect relationship from correlation data
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PSY 200: EDP Quiz #2