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Statistics 401, Week 4

by: Wendy Liu

Statistics 401, Week 4 01:960:401

Marketplace > Rutgers University > Statistics > 01:960:401 > Statistics 401 Week 4
Wendy Liu
GPA 4.0

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Covers bivariate data representation, correlation, correlation coefficients, and linear regression
Basic Statistics for Research
Hei-ki Dong
Class Notes
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This 3 page Class Notes was uploaded by Wendy Liu on Thursday September 29, 2016. The Class Notes belongs to 01:960:401 at Rutgers University taught by Hei-ki Dong in Fall 2016. Since its upload, it has received 57 views. For similar materials see Basic Statistics for Research in Statistics at Rutgers University.


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Date Created: 09/29/16
Week 4: Bivariate Data 27 September 2016 Basic Statistics for Research Professor HK Dong Wendy Liu Bivariate/multivariate data – observations on two or more variables Marginal totals – total frequency of any row or column of a data table, given in the right-hand margin or bottom margin Simpson’s paradox – reversal of conclusions from a data table after combining several data tables together due to appearance of unreported variables Experimentation  Random assignment – subjects placed randomly into control/experimental groups  Placebo effect – subject’s expectations of a treatment to work cause positive results, even though the treatment itself has no therapeutic value o Placebo – treatment that has no physiological effect; usually a sugar pill, for drug testing  Double-blind procedure – experimenters don’t know which subjects are in which group, and subjects themselves don’t know what group they are in o eliminates placebo effect and experimenter bias Scatter diagram/plot – pairs of observations plotted as dots on a graph, with one observation as one variable (x,y) Positive correlation – x and y increase/decrease together Negative correlation – x and y increase/decrease in opposite directions Correlation coefficient r – measures strength and direction of linear relationship between x and y  Ranges from -1 ≤ r ≤ 1 o Magnitude of r indicates strength  |r| = 1, perfect linear relationship o Sign of r indicates direction  r > 0, positive correlation  r < 0, negative correlation o r = 1, perfect positive correlation o r = -1, perfect negative correlation o r = 0, no correlation  r: sample correlation coefficient  ρ: population correlation coefficient Calculating r: Definitional formulas: sum of squared deviations of x: sum of squared deviations of y: sum of cross products of x & y deviations: Alternative formulas: sum of squared deviations of x: sum of squared deviations of y: sum of cross products of x & y deviations: Example calculation of r w/ definitional formulas: n = 4 for (2,5) (1,3) (5,6) (0,2) 2 5 0 1 0 1 0 1 3 -1 -1 1 1 1 5 6 3 2 9 4 6 0 2 -2 -2 4 4 4 Example calculation of r w/ alternative formulas: n = 4 for (2,5) (1,3) (5,6) (0,2) 2 5 4 25 10 1 3 1 9 3 5 6 25 36 30 0 2 0 4 0 Spurious correlation – observed correlation btwn two variables that is false, due to influence by a third variable (the lurking variable) Predictor/input/independent variable – denoted by x Response/output/dependent variable – denoted by y Method of Least Squares – for the line of best fit – minimizes the average amount of residual  residual (SSE) – vertical error btwn data point and line of best fit o sum of squared error:  regression equation for line of best fit: o slope: o intercept: 2 Coefficient of determination r – amount (%) of variation in Y due to variation in X


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