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This study guide provides an in-depth exploration of the pearson correlation coefficient, a statistical measure used to determine the linear relationship between two continuous variables. The difference between experimental and correlational approaches, the question addressed with correlational research, the bivariate distribution and scatter plots, the definition and interpretation of pearson r, and the computation of the correlation coefficient. It also includes examples and exercises to help students understand the concepts.
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Okun PSY 230 STUDY GUIDE # Pearson Correlation Coefficient I. Pearson Correlation Coefficient
Person Manual Number of Typing Errors (Y) Dexterity (X)
Fred 50 15 Gene 50 12 Heidi 100 12 Irene 150 6 Janet 150 0
Mean 100 9 Standard Deviation 50 6
A researcher is interested in determining whether there is a relationship between a manual dexterity test and number of errors made on a typing test. She draws a sample of 5 high school students learning to type. Below are the scores on the manual dexterity test and number of errors made on the typing test. In addition means and standard deviations are provided for both variables. Raw Data for Computing the Correlation between 2 Interval Variables Person Manual # of Typing Errors (Y) Dexterity (X)
Fred 50 15 Gene 50 12 Heidi 100 12 Irene 150 6 Janet 150 0
Mean 100 9 Standard Deviation 50 6
for the X variable, z = [Xi- M x] /Sx for the Y variable, z = [Yi- M y] /Sy
Steps in Computing Power. STEP 1: Determine gamma (), the population effect size. In the case of the correlation coefficient, gamma equals the absolute value of A. STEP 2: Determine delta (). Delta combines the estimate of the population effect size and sample size.
delta = /A/ x N- STEP 3: Enter Table H with an a priori specified value for and the value of delta that was just computed.
Given the desired power, , and A how can the sample size be determined for a study examining a Pearson correlation coefficient? STEP 1: Entering Table I with the desired power and a priori specified value of , determine delta. STEP 2: Solve for n using the formula, n = (DELTA/A)^2 + 1.