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Lecture 10

stats Lecture 10.pdf

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Douglas Bors

Lecture 10 - STATS In repeated measure, you put a dot for each condition and then you draw a line to connect them and put an error bar above and below the dot T test is like a bar graph - remember digital lab coat RELATIONS B/W TWO VARIABLES Regression and correlation - In both cases, y is a random variable beyond the control of experiment - In case of correlation, x is also random variable - In case of regression, x is treated as fixed variable - as if there is no sampling error in x - Regression: you wishing to predict the value of y of basis of value of x - asking if they are related - is column one related to the other - if one event does not predict the probability of another event  independent events - Correlation: you are wishing to express the degree the relation b/w x and y COVARIANCE - Covariance: number reflecting degree to which two variables vary or change in value together - Knowing whether someone is slow or fast does not determine accuracy - COVARIANCE = product of the difference scores divided by n-1 - n is number of subject not the number of scores that you have - The absolute value of covariance if a function of variance of x and variance of y - thus, covariance could reflect strong reflection when two variances are small, by maybe express weak relation when variances are large - covariance is not standardized in any way LINEAR RELATIONS - Relation can be most accurately represented by straight line - Linear transformations - Equation for a straight line - y = bx + a (a is the y intercept and b is the slope of the line) When relation is imperfect (not all points fall on straight line) - points are not on straight line because there are other influences that cause points to not fall on straight line We draw best-fit using "least squares" criterion - we try to minimize square deviations and use world operates in squares so we use squares - If there is no slope, y is the best predictor - In some situations, the y intercept is worthless cause it is not possible STANDARD ERROR OF ESTIMATE: similar to SD - Where relation is imperfect, there will be prediction error, whether one used mean or regression line - (should be r squared) - Use n-2 because there are two means that went into the prediction - Residual variance (variance around regression line) - Make sure you use the transformed equation - R = correlation coefficient (an average product of the z scores) - To standardize, we divide covarianc
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