Sharon Seidman Ph D CAS 301 Developmental Inquiry Methodology Correlations Linear Relations Between Variables Expectations Begins with hypothesis general concept or question Create specific testable prediction Prediction can specify relation or group differences Variable Definitions Concept Valid Face Predictive Concurrent Convergent Discriminant Operation Reliable Internal Test retest Inter rater Scale Ratio Interval Ordinal Nominal 1 Sharon Seidman Ph D CAS 301 Developmental Inquiry Methodology Describing Groups Central Tendencies Mean Median Mode Variability Range Standard Deviation Differences in Range Differences in Standard Deviation 2 Sharon Seidman Ph D CAS 301 Developmental Inquiry Methodology Normal Skewed Example Liking of Lizards Like Lizards 1 not at all 2 3 4 5 a lot Class 1 5 9 3 2 1 Class 2 1 4 10 4 1 Class 3 1 2 3 9 5 of Students Graph Liking for Lizards 12 10 8 6 4 2 0 Class 1 Class 2 Class 3 1 2 3 4 5 How Much Do You Like Lizards 3 Sharon Seidman Ph D CAS 301 Developmental Inquiry Methodology Class 1 Mode Median 10 of Students Like Class Lizards 1 1 not at all 5 2 9 3 3 4 2 5 a lot 1 Mean 2 25 8 6 4 2 0 1 2 3 4 5 Liking for Lizards More about Line Graphs One Variable Frequency Graph Y Axis Amount Count 60 of Children 50 Girls Boys 40 30 20 10 0 Not Yet Emerging Almost Fully 4 Sharon Seidman Ph D CAS 301 Developmental Inquiry Methodology Two Variable Graph Y Axis Second Variable Graphs Line graphs One vs two variables Single Y value for each X value Scatterplots Two variables Multiple Y values for each X values Two Variable Graph Mean Score for Group Members 5 Sharon Seidman Ph D CAS 301 Developmental Inquiry Methodology Two Variable Graph Individual Score for Each Person 106 PPVT R 104 102 100 98 96 94 92 90 88 86 4 5 6 7 Age Two Variable Graph Individual Score for Each Person 106 PPVT R 104 102 100 98 96 94 92 90 88 86 4 5 6 7 Age 6 Sharon Seidman Ph D CAS 301 Developmental Inquiry Methodology Pearson Product Moment Correlation Linear relation between 2 variables Represented by r Based on the line of best fit 7 Sharon Seidman Ph D CAS 301 Developmental Inquiry Methodology Line of best fit Smallest average distance between points and line Requires variable with mathematical properties Ratio Interval Likert Correlation Co efficient Strength Closeness of the line of best fit Ranges from 0 to 1 0 Direction Positive vs negative Nature of the relationship 8 Sharon Seidman Ph D CAS 301 Developmental Inquiry Methodology Representing Strength Direction 1 0 to 70 Strong Negative 69 to 30 Moderate Negative 29 to 00 Weak Negative 00 to 29 Weak Positive 30 to 69 Moderate Positive 70 to 1 0 Strong Positive Not the same as percentage Bi Variate Correlations Table 3 9 Sharon Seidman Ph D CAS 301 Developmental Inquiry Methodology Your Turn Let s look at the rest of Table 3 The Effect of Range Restricted Range Reduces Strength 10 Sharon Seidman Ph D CAS 301 Developmental Inquiry Methodology Restricted Range Reduces Strength Restricted Range Alters Curvilinear Distributions Restricted Range Alters Curvilinear Distributions 11 Sharon Seidman Ph D CAS 301 Developmental Inquiry Methodology Using Correlations to Make Predictions Regression Uses line of best fit Predicts individual score Regression 106 PPVT R 104 102 100 98 96 94 92 90 88 86 4 5 6 7 Age 12 Sharon Seidman Ph D CAS 301 Developmental Inquiry Methodology Improving Correlations Multiple Correlation Goal accuracy Real world multiple influences Use multiple variables to predict criterion Multidimensional math PPVT R Data Age Score Parent Ed Age Score Parent Ed 4 89 1 6 99 1 4 91 2 6 100 1 4 93 2 6 101 1 4 95 3 6 102 2 4 96 3 6 103 2 4 99 3 7 101 3 5 91 1 7 102 2 5 94 1 7 103 3 5 96 2 7 104 3 5 97 2 7 105 3 5 98 3 5 99 2 5 100 3 5 103 3 13 Sharon Seidman Ph D CAS 301 Developmental Inquiry Methodology One Predictor Variable 106 PPVT R Score 104 102 100 98 96 94 92 90 88 86 4 5 6 7 Age 2 Predictor Variables Regression Beta Weights Age 73 53 PPVT R Score Parent Education 39 15 14 Sharon Seidman Ph D CAS 301 Developmental Inquiry Methodology A Word about Standardization Unstandardized Coefficients B Model Constant Std Error Standardized Coefficients t Sig 29 2 000 Beta 76 199 2 607 Age 3 169 452 73 7 0 000 Parent Education 2 313 601 39 3 8 001 Your Turn Let s look at Table 5 page 1547 Related Analyses Structural equation models Structural models Path analysis Partial correlations 15 Sharon Seidman Ph D CAS 301 Developmental Inquiry Methodology Structural Equation Age Language Use PPVT R Score Parent Education 16