PSYCH 240 1st Edition Lecture 5Section 3: Z-ScoresZ-Scores-Z-scores: indicates the number of standard deviations that a score falls above or below the mean-z=(X-M)/Soz=z scoreoX=raw scoreoM=meanoS=standard deviation-Regardless of the original distribution, the z-score distribution will have a mean of zero, a standard deviation of 1, and the same shape as the original distribution-z=0 means that the score equals the mean (the score is very typical)-Higher z's indicate more atypically high scores-Lower z's indicate more atypically low scores Z-Scores to Raw Scores-You can also get back to a raw score from a z-scoreoX= zS + M Objectives--Understand what a z-score is, and how z-scores provide a measure of how “typical” a score is on a distribution. --Be able to compute a z-score given a raw score and the mean and standard deviation of a distribution. Also, be able to compute a raw score given a z-score and the mean and standard deviation. (You may also need to compute the mean and variability for yourself given the entire set of scores). --Know how converting all of the scores in a distribution to z-scores affects the mean, standard deviation, and shape of the distribution.Section 4: Correlation and PredictionThese notes represent a detailed interpretation of the professor’s lecture. GradeBuddy is best used as a supplement to your own notes, not as a substitute.Scatterplots-Scatterplot: a graph in which the x-axis is the score on one variable and the y-axis is the score on the other variable; each point on the plot is one data collection unitoLeast-Squares Regression Line: to define the relationship between the two variable mathematically, we'll put in a line that shows how one variable tends to change across changes in the other variable-Y-hat = a + bXY-hat= predicted score for variable YX= value of score on variable Xa= y-intercept or "regression constant" - predict Y value when X=0b= slope or "regression coefficient" - predicted change in Y for every unitchange in XY= criterion variable (what you predict)X= predictor variable (what you use to predict Y) Slope (b)-You can calculate slope given two X values and their corresponding Y-hat values-oThis formula nicely shows the meaning of the slope parameter. Slope it how much out prediction for the Y variable changes when the X variable increases by one measurement unitoIt doesn’t matter which scores you consider the first value and the second
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