Chapter_12_Correlati - PSYC 310 Chapter 12 Correlational Research Correlation The relationship between two or more variables Correlation describes

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Unformatted text preview: PSYC 310 Chapter 12 Correlational Research Correlation The relationship between two or more variables. Correlation describes the direction and degree of relationship between two or more variables. No real manipulation of variables; just measure one and then the other. Correlation 5 6 7 7 8 8 9 10 110 112 118 120 122 122 130 140 Correlation The relationship between the variables can be visualized by means of a "scatterplot". X 5 6 7 7 8 8 9 10 Y 110 112 118 120 122 122 130 140 Variable X Correlation A line-of-best-fit (regression line) is drawn through the points. Variable X The closer the points are to the line, the greater the association between variables. Correlation - Direction The direction of the correlation indicates the nature of the changes in the variables. Positive Negative A B A B A B A B Correlation - Direction Positive Negative Correlation - Strength The degree of association between two variables is referred to as the strength of the correlation. It is expressed mathematically as a correlation coefficient. When the two variables are either ratio or interval, the strength is expressed as Pearson r. If one variable is ordinal and the other is ordinal or higher, we use the Spearman rrho. Correlation - Strength Correlation coefficients for both Pearson r and Spearman rrho can vary between -1.00 and +1.00 Strong Moderate Weak 0.70 1.00 0.30 0.69 0.00 0.29 Correlation Correlation - Significance In addition to considering the size of the correlation, you must also consider whether it is statistically significant. Small sample sizes are prone to producing large correlations, so the criteria for statistical significance is more stringent. Statistical significance is determined by consulting a table. The table takes into account sample size and alpha level. Correlation - Significance Level of Significance (p) for Two-Tailed Test df = n -2 1 2 3 4 5 6 7 8 9 10 .05 (research) .997 .950 .878 .811 .754 .707 .666 .632 .602 .576 .01(medical) .999 .990 .959 .917 .874 .834 .798 .765 .735 .708 To be significant, r must be equal to or larger than the value corresponding to the df and p level. (p level or alpha level) Shared Variance People run correlations to determine what percentage of changes in one variable (A) can be accounted for by changes in the other (B). This percent change accounted for is referred to as shared variance it is the shared common ground between variables A and B. If you want to be able to use one variable to predict another , you need to know the shared variance. Shared variance Shared Variance PROBLEM: Correlation values r are ordinal (not equal increments) an r of .80 is not twice as strong as r of .40. SOLUTION: Convert to ratio scale by squaring r. r 2 = shared variance. Shared Variance r = .00; r2 = .00 r = .20; r2 = .04 Shared variance = 0% Shared variance = 4% Shared Variance r = .40; r2 = .16 r = .60; r2 = .36 Shared variance = 16% Shared variance = 36% Shared Variance r = .80; r2 = .64 r = 1.00; r2 = 1.00 Shared variance = 64% Shared variance = 100% Multiple Correlation Sometimes we're interested in looked at the relationship between more than two variables. In this case, we run a multiple correlation. That is, we look at all the correlations among the variables of interest. We still consider the correlations in pairs, however. And the results are displayed in a correlation matrix Correlation Matrix A correlation matrix is when you measure more than 2 variables LOT LOT Anxiety Selfesteem Extrover sion 1.00 Anxiety -0.59 1.00 Selfesteem 0.35 -0.40 1.00 Extrover sion 0.20 -0.37 negative correlation 0.25 1.00 Correlation = Causality Correlation describes the relationship between two variables. What it DOES tell us: - when one variable is present, so is the other (contingency) - when one changes there is some corresponding change in the other. Correlation = Causality Correlation describes the relationship between two variables but it does not tell us about causality. Knowing that A & B are correlated does not tell us whether A causes B, B causes A, or if some other variable C causes both A and B. A B B C A B A Correlation Just because two things co-occur does not necessarily mean they are related! Correlation There may be another reason why these two events co-occur. Correlation Even when they appear related we can't say that one "caused" the other. Correlation But it may suggest the direction of influence...... In other words, which variable "preceded" the other. Correlation Correlation Correlation - Uses Correlations do not reveal causality BUT they do indicate relationships which can be investigated using more constrained techniques. Correlations are very useful for predictions. If A is known, and the correlation between A and B is known, then B can be predicted with an accuracy which depends on the strength of the correlation. Regression & Prediction Regression analysis is a way of using association between variables as a method of prediction. One variable is specified as the predictor variable and the other as the criterion variable. IQ (predictor) & academic success (criterion) family history (predictor) & breast cancer (criterion) Correlation - Uses Correlations can also be used to establish validity and reliability. - test-retest reliability - concurrent validity: 2 different methods that measure the same thing Correlation - Uses Correlations can also be used to evaluate theories, e.g., nature versus nurture. Potential Problems The Pearson correlation result will be misleading under two particular circumstances. Nonlinear relationships: Need to look at scatterplot to look at the shape of the relationship must be linear. Restricted range: If sample size is too small it will truncate the range of scores and underrate the correlation. Non-linearity The relationship must be linear a curvilinear relationship may give a misleading value. Other problems Truncated range 105 90 75 60 45 45 55 65 75 85 95 105 115 125 135 IQ between 85 & 130 Prediction is good at college level 95 90 85 80 75 70 100 110 120 130 140 IQ between 110 & 140 Data is only from the high end of the IQ distribution. Prediction in graduate school is poor Correlation Strengths & weaknesses: Record what exists naturally Cannot assess causality Helps identify where to look for causes Can investigate what is otherwise unethical to examine experimentally High external validity Low internal validity ...
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This note was uploaded on 04/29/2010 for the course PSYCH 310 taught by Professor T.bianco during the Winter '10 term at Concordia Canada.

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