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Chapter 16

PSYC202 Chapter 16 Correlation.docx

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Department
Psychology
Course
PSYC 202
Professor
Ronald R Holden
Semester
Fall

Description
PSYC202 Chapter 16: Correlation 16.1 Overview ­ Correlation: a statistical technique that is used to measure and describe a relationship  between two variables ­ Two variables being observed occur naturally in the environment – not being  manipulated ­ Two scores per individual, variable X and Y ­ Data transferred to scatter plot ­ 3 characteristics of a correlation: 1. The Direction of the Relationship  ▯the sign of the correlation (+/­) ­ Positive Correlation: two variables tend to move in the same direction:  as X increases from one individual to another, the Y variable also tends to  increase; & vice versa ­ Negative Correlation: the 2 variables tend to go in opposite directions 2. The Form of the Relationship: linear or curved 3. The Strength of Consistency of the Relationship: ­ Whether Y increases same amount each time for each X increase, or  whether Y generally increases when X increases but not by same amount  each time ­ Perfect correlation  ▯+/­1.0 indicates perfect consistency ­ No correlation  ▯0 no consistency at all ­ Envelope  ▯a border drawn around all scatter plot points. When shape  looks like football, correlation around 0.7. When fatter than football,  indicates correlation closer to 0, when skinnier, closer to 1. ­ Application of correlations: 1. Prediction: 2. Validity: is the test measuring what its intended to measure? Ex.  if test is  measuring intelligence, the scores should correlate with other intelligence scores  like performance on learning tasks, problem­solving ability, etc. 3. Reliability: reliability produces stable, consistent measurements. When  reliability is high, correlation should be strong and positive 4. Theory of Verification: if theory predicts relationship between two variables,  correlation can be used to determine accuracy of theory 16.2 The Pearson Correlation ­ Pearson Correlation: measures the degree and direction of linear relationship between  2 variables. Written as ‘r’ ­ r = Covariability of X and Y  OR  r = SP variability of X and Y separately √SS XS Y ­ Sum of Products = SP = ∑(X­M )(Y­MX)     YR    SP= ∑XY ­ ∑X∑Y       n ­ Measures covariability between the variables (a version of SS) (numerator of  r) ­ M x ▯mean of X scores, M   Ymean of Y scores ­ SS measures variability/denominator of r. SS = ∑X  –  (∑X)     n ­ X and Y values can be transformed into z scores. This changes r = ∑z z X Y       (n­1) For a population: P =∑z z X Y    N 16.3 Understanding and Interpreting the Pearson Correlation ­ Correlation does not equal causation ­ Value of correlation can be affected greatly by range of scores ­ Extreme scores (‘outliers’) can have huge effect on correlation value ­ Correlation value should not be interpreted as proportion. To describe how accurately  one variable predicts another, you must square the correlation. (Ex. correlation value of  0.5 squared = 0.25 so one variable only predicts another 25% of the time) ­ If correlati
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