Final Review.docx

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Ramesh Balasubramaniam

KIN 1G03: FINAL REVIEW Theme 1: Correlation and Causation - How do we relate two variables? - How are their central tendencies and dispersion related? - Pearson r A statistic that represents the extent to which the same individual or event occupies the same relative position on two variables; - The Pearson r statistic ranges from -1.00 to 1.00 - In a perfect negative correlation, r = -1.00 - In a perfectly positive correlation , r = +1.00 - There is no apparent relationship, r = 0.00 R provides some indication of the degree of relationship between the two variables. `Degrees of relationship` To calculate this level of reliability (statistical significance) 1. Determine df: df = npairs – 2 (df compensates for small n by requiring a large absolute r) 2. Formulate hypothesis (H0= no relationship, H1 = true reliable relationship) - Value of sig tells you how probable is it that the value you got is due to chance Theme 2: Bivariate Regression - One useful function of correlational analysis is that they can be used to predict the outcome of a variable - If the existing correlation is reasonably high we can predict what the value of y will be if we know x - 1. Calculate r, r , k - 2. Regression line: two important characteristics: o 1. Intercept (a), slope (b) (change in Y resulting from change in one unit of x) o Regression line = Line of best fit 2 2 - Slope (b) = by= [sumXY – (sumx)(sumy)/N ] [sumX – (sumx) /N] - a = meanY – bmeanX - Y’ (predictive value) = a + bx - Deviation around the regression line (residual) Is much smaller than deviation around the mean - To draw the line, use (x=0) and (x=anotherscore), then connect the dots - Our predication is only as good as the relationship between the two variables - If r = 0, best guess would be the mean - If there is no relationship it doesn’t matter how much you know about one variable seeing as it has no influence on the other Summary: - Regressio nrepsents two things: - 1) attemps to predict Y from X (DV from IV) - 2) A statement of how confident we are in this prediction 2 - If k = 0, we are totally confident Standard Error of the Estimate - Recall that: Standard deviation s = sqrt [sum(Y-Ymean) /N] 2 - The equivalent for regression is the standard error of the estimate - Estimates variability about the regression line - Sesty = sqrt [sum(Y-Y’) /N] - Table: Y (Y Observed) Y’ (Y Predicted) (Y-Y’) (Y-Y’)2 - Sesty = variation around regression line? - OR: Sesty = s (yqrt (1-r ))2 - Sy = sqrt (SSy (sum of squares of y) / n) - Thus, because ew know that 68% of the time the true score will fall between z score of -1.00 and 1.00, we are now 68% certain that june got 91.blahblah +/- Sesty score… (6.67) - What are the chances she got a diff mark? - Y’ = 91.38 (predicted score) - Sesty= 6.67 (our margin) - Z 83(Y – Y’ ) / Sesty = (83 – 91.38) / 6.67 = -1.257 - To change confidence to LOC 95%, multiply 6.67 by 1.96 AND +/- the predicted score by that # Testing For Significant Differences One convenient an dpowerful method to test the relative difference between two means is the t-test Student’s t test Allow sus to test the likelihood that two means are “equal” Tests the statistuical diff btwn two means against ht ebackground of within-group variabuility Difference can be affected It does this calculating a t value (t obtained) This value is compared to a critical t value (t critical) T critical represents the point One tailed T – test - Two variables, X1 and X2, find the mean of each - In this caes ew have two independent groups.. eg old style vs new style - T test compares the mean of these groups to determine if they are diff - Df In a correlation = (n-1) + (n-1) - Look at overlap of one particular tail - T = meanx1 – meanx2 / sqrt (summed standard error of means squared of each variable added together) - Compare value to t table values in a standard table Non Parametric Stats Multi-Category Chi Sq
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