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8 Correlational research.docx

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PSYC 2001
Guy Lacroix

Correlational research Correlational research - What are correlations? • Scatterplots • Correlations and causality - What are regressions? • y = mx + b • Multiple regressions - Examples • Siddiqui, West, and Stanovich (1998) Correlational research - The purpose of correlational research is to establish that a relation exists between variables and to describe the nature of this relationship. • Rubin’s (1970) love scale and “being in love” • Reliability coefficient is .87 to 1.0 (Bowker et al., 2009) Pearson correlation coefficient - The Pearson correlation (r) coefficient is the statistic that indicates the degree to which two variables are related to one another in a linear fashion. - Range r is between – 1.00 and + 1.00 - Positive correlation (r > .00). Positive, direct relationship between two variables - Negative correlation (r < .00). Negative, inverse relationship between two variables No relation between the variables Perfect relation between the variables Strong relation between the variables Weak relation between the variables How can we tell that a correlation is significant? - What is the probability that a “lucky result” was obtained? - The probability is calculated using the Student’s t statistic. Critical values of r Number of participants Minimum r that is significant (for a p value of .05) 10 .52 20 .37 30 .30 40 .26 50 .23 60 .21 80 .18 100 .16 1000 .05 Correlation matrix - When multiple correlations are used, the results are typically shown in a correlation matrix. Index 1 2 3 1. Grades 1.0 - - 2. Performance IQ .65 1.0 - 3. Hours of study .34 .01 1.0 Correlations and causality - ACorrelation does not imply causality! - Three criteria must be satisfied to conclude that one variable causes another: • Covariation. There is a correlation between variables X and Y. • Directionality. Variable X (the cause) precedes Variable Y (the effect). • Elimination of extraneous variables. No other variable may be responsible for the relationship between X and Y. Directionality problem - Correlational studies do not allow us to determine which variable is the cause and which variable is the effect. - Self-esteem  school achievement (Stanovich example 2007) Third-variable problem - Although a correlational study may establish that two variables are related, it does not necessarily mean that there is a direct relationship between them. Linear regressions - Another way of looking at the relation between two variables. - The best fitting linear function is estimated and then used to “explain” the changes in one variable using a second variable. - Criterion. The variable to be explained. - Predictor. The variable used to predict, to “explain”. - Correlation between women owning a toasting and being on contraceptives; not causal y = mx + b Effect size for regressions - Using the regression equation, we know that the predictor (x) explains a 31% change in the criterion (y). 2 - r . The measure of effect size for regressions. Multiple regression - Regressions allow for multiple predictors. - Example. Suppose you want to explain grades using both IQ and number of hours of study. Index 1 2 3 1. Grades 1.0 - - 2. Performance IQ .65 1.0 - 3. Hours of study .34 .01 1.0 Multiple regression - R. Measure of relation for multiple variable. - R . The measure of effect size for multiple regressions Hierarchical multiple regressions - What if I want to see the relation between study time and grades independently of IQ? - Mathematically, the variance explained by IQ is removed after step 1. Hence, the variance explained by study time is “unique”. - Final F= probability that the result is due by chance • Percentage that results could be lucky; is it significant or not. 0.12 explains 12% of the leftover variable that has not be explained by IQ Criterion = Grades Variable R  R 2 Final F Step 1 1. IQ .65 .42*** 26.82*** Step 2 2. Study time .73 .12** 20.82*** Author Reco
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