Psyc 203 1st Edition Lecture 7Outline of Last Lecture I. Review II. Bar Graphs III. SkewnessIV. CorrelationOutline of Current Lecture I. Reviewa. Skewness Statistic b. Description of kurtosis c. Correlation coefficients II. Strength or Degree III. Sum of Products IV. Restriction of Range V. Outliers Current LectureI. Reviewa. Skewness Statistic i. Mean>Median = Positive Skewii. Mean<Median = Negative Skewb. Correlation coefficients i. A numerical index that reflects the relationship between 2 variables ii. Ranges between -1 to 1 II. Strength or Degree i. A correlation coefficient tell us about the pattern of the association for an entire sample. Unless there is a perfect 1.0 or -1.0 correlation, you are guaranteed to find exceptions to the overall pattern!ii. Pearson correlation: variables that can I assume any value along some underlying continuum1. For example: height, age, test score, incomeb. Direct correlation: when variables change in the same direction (positive correlation)c. The absolute value of the coefficient reflects the strength of the correlationd. You can use a scatterplot to visually represent a correlatione. Coefficient of determination: percent of variance in one variable that is accounted for by the variance in another variablef. Square the correlation coefficient to determine exactly how much of a variance inone variable can be accounted for by the variance and another variablei. Four example: GPA and the number of our studied equals .7 R squared equals .7 squared which equals 491. 49% variance in GPA can be explained by variance and studying timeg. The stronger the correlation the more variance can be explainedh. Unexplained variance qualification of alienationIII. Sum of Products a. Similar to SS (sum of squared deviations)b. Measures the amount of covariability between two variablesc. SP = · XY − · X ·Y /nIV. Restriction of Rangea. Fact: The obtained value of correlation is affected by the range of scores in the data. b. Ideally, you will have the full range of X and Y observations. c. Otherwise, the sample correlation can be distorted. d. People often assume that restriction of range makes the observed correlation smaller than the population value. This is not always the case! V. Outliersa. Extreme observations (on X,Y) are more likely to influence the correlation than more typical observations b. The distortion can be dramatic with even one
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