# Session__12 - Correlation: Review A scatterplot is a...

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Correlation: Review

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A scatterplot is a graphical way to visualize the relationship between two variables. From http://www.mzandee.net/~zandee/statistiek/stat- online/chapter4/pearson.html
A correlation is statistical technique used to measure and describe a relationship between two variables. In a large sample, the correlation between wife’s age and husband’s age was r = 0.97.

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Relationships between variables can be characterized in three ways: 1. Direction of the relationship Positive or negative 1. Form of the relationship Linear or non-linear 1. Degree of the relationship How strong is the correlation?

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Pearson’s correlation is frequently used to measure the relationship between two variables. Designed as rho (ρ) in the population; r in the sample. Assumes a linear relationship between the variables. Ranges from -1 to +1 Sign indicates direction (positive or negative) Number indicates strength
Important points about correlations: 1. Correlation does not prove cause and effect. 2. The value of a correlation can be affected by the range of scores represented in the data. 3. Outriders, or extreme data points, can dramatically impact value of a correlation.

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Hypothesis testing for relationships using SPSS The steps for testing a value of r for significance are: 1. Set Hypothesis Ho: ρ = 0, no relationship in the population H1: 0, is a relationship in the population 2. Set significance level (α=.05) 3. Find out test statistic r from the output 4. Find out p value from the output. If p value <.05, reject null hypothesis If p value >.05 do not reject null hypothesis
SPSS Correlation Matrix

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Pearson’s r Definitional Formula: degree to which X and Y vary together degree to which X and Y vary seperately r = ( 29 ( 29 ( 29 ( 29 1 2 2 1 1 1 i i i i i X X Y Y n r X X Y Y n n = - - - =     - -         - -         ∑ ∑ ( 29 ( 29 XY x y COV r s s = ( 29 ( 29 1 XY X X Y Y COV n - - = -
Testing a value of r (manually) The steps for testing a value of r for significance are: 1. Set Hypothesis Ho: ρ = 0, no relationship in the population H1: 0, is a relationship in the population 1. Set significance level (i.e. α=.05) 2. Find critical value of r from Table J. 3. Calculate r. 5. If | r | > critical value, reject the null. A significant relationship does exist between the two sets of variables If | r | < critical value, then you fail to reject the null hypothesis and a significant relationship does not exist between the two sets of variables

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Example 1: Conduct a 5-step hypothesis test to see if there is a relationship between X and Y. Scores X Y 0 1 10 3 4 1 8 2 8 3 Xbar = 6 Ybar=2 Standard deviation of X = 4 Standard deviation of Y = 1 1. Hypotheses: Ho: ρ = 0 H1: 0 1. Alpha = 0.05 1. Find the critical value: 1. Calculate r
Example 1: Conduct a 5-step hypothesis test to see if there is a relationship between X and Y.

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## This note was uploaded on 01/27/2011 for the course EDPSY 400 at Pennsylvania State University, University Park.

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Session__12 - Correlation: Review A scatterplot is a...

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