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# week 3 class notes PSYCH240

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This 4 page Class Notes was uploaded by Nate Dickstein on Friday February 6, 2015. The Class Notes belongs to PSYCH240 at a university taught by Jeffrey Starns in Fall. Since its upload, it has received 179 views.

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Date Created: 02/06/15

Class 42315 Section 3 Proportion number of elements with a certain characteristic divided by the total number of elements percentage proportion times 100 Zscores tells you the number of standard deviations that a score falls above or below the mean even if a score is far away from the mean it still might be a typical score because of a certain deviation from the mean ZXMS ZZscore Xraw score Mmean Sstandard deviation The height of American females has the mean of 64 inches and a standard deviation of 3 inches 80 M64 and 83 what is the Z score for a woman 70 inches tall X70 Z706432 so the woman is two standard deviations taller than the average regardless of the original distribution the Zscore distribution will have a mean of zero MO a standard deviation of 1 81 and the same shape as the original distribution ZO means that the score equals the mean so basically the score is very typical Higher 23 indicate more atypically higher scores Lower 23 indicate more atypically lower scores You can also get back to a raw score from a Zscore XZSM US females have an average height of 64 inches with a standard deviation 3 Sandra has a z score of 6 How tail is she X6364622 Section 4 Correlation and Prediction how do u take one variable and use it to predict another variable or how its related to another variable scatterplot a graph in which the Xaxis is the score on one variable and the yaXis is the score on the other variable each point on the plot is one datacollection unit to define the relationship between the 2 variables mathematically well put in a line that shows how one variable tends to change across changes in the other variable this is called the LeastSquares regression line the regression line is defined by the linear equation YhatabX Yhat predicted score for variable Y Xvalue of score on variable X ayintercept or regression content predicted Y value when XO bslope or regression coefficient predicted change in Y for every unit change in X Y is the criterion variable what you try to example X is the predictor variable what you use to predict Y example Y is free throw percentage and X is height Yhat17260129X Slope you can calculate the slope given 2 X values and their corresponding Yhat values BYquot2Yquot1Xquot2Xquot1 Class 5 2515 0 Yintercept the predicted Y value when XO The Yintercept won t make sense if 0 is not a possible X value For instance this value suggests that players who are 0 inches tall will make over 100 of their free throws which is impossible of course In this case just think of the intercept value as something you need to move your line up or down to line it up with the data More generally fitting a regression function will rarely produce good predictions for the criterion variable outside of the range of data that you have for the predictor variable For example say I take the height of kids from their 6th to 10th birthdays and find a linear relationship such that predicted height increases by two inches per year It would not be reasonable to predict that the kids will grow another 120 inches 10 feet between their 10th and 70th birthdays Having data in the older age range would allow us to make a better prediction for height on their 70th birthday 0 Regression line Why is it called least squares the leastsquares regression line minimizes the sum of squared deviations between the predicted and observed Y values that is no other line will make better predictions for Y based on X 0 Strength of the relationship we need a way to express how strongly the two variables are related slope does not give this strength by itself slope is affected both by the strength of the relationship AND the relative scale of the two variables like using centimeters vs inches 0 A common measure of relationship strength is called proportion of variance accounted for r 2 This statistic measures how much better we can predict Y using information about X versus NOT using information about X you wont have to calculate this from scores but you will need to understand what it is r 2 is not affected by scale so we can use it as a pure measure of relationship strength rquot20 means there is no relationship between the two variables knowing about one variable does not help you predict the other variable at all rquot21 means there is a perfect relationship between the variables knowing about one variable allowed you to perfectly predict the value of the other variable every time 0 another way to measure the strength of a relationship is with correlation a correlation is the measure of the degree and direction of a relationship between 2 variables for a correlation we do a regular regression except that we convert both variables to z scores first because a scores puts everything on the same scale so a correlation is the slope you get from a regression on zscores o interpreting r sign orindicates direction of the relationship means the y variable increases as the x variable increases means the y variable is decreasing as the x variable is increasing the absolute value indicates the strength of the correlation O is weakest correlation 1 or 1 is strongest correlation you can get r 2 by just squaring the correlation coefficient r Linearity of relationship the correlation coefficient assumes a linear relationship between the two variables if the variables are related by any other type of function then the correlation coefficient might below even though the variables are strongly related you should always look at scatterplots to make sure the relationship between the variables is linear if it isn39t then don39t use linear regression or correlation 0 Non linear relationship relationship between variables that approximately follows pattern that is not a straight line 0 Causality 0 how do we figure out what39s causing what in a relationship between two variables 0 3 possibilitiesdirections of causality 1 X could be causing Y 2 Y could be causing X 3 another variable could be causing both X and Y 0 Correlation does not imply causation BUT all correlational evidence cannot be dismissed automatically you have to evaluate each case to figure out which pattern of causation is most likely o establishing causality what do we do when we want to make causal statements 1 run an experiment instead of just measuring two variables and trying to predict one with the other we directly manipulate an independent variable and measure its effect on a dependent variable all variables except for the independent variable are either held constant across conditions or randomly assigned conditions to prevent a systematic effect any changes in the dependent variable should be uniquely attributed to the independent variable 2 get more information on the time course of the relationship and possible outside variables that might produce the relationship if you can rule out plausible outside variables and establish the change in X precede changes in Y then you have stronger evidence that X causes Y 3 establish how one variable causes another variable we can develop theories of the mechanism by which one variable changes another and test these theories in controlled experiments with knowledge of the underlying mechanisms we can make stronger inferences about relationships we find in the real world 0 Section 5 0 Probability o Empirical probability the proportion of times that an outcome occurs in some number of observed attempts o theoretical probability objective definition the empirical probability we would get from an infinite number of attempts o probabilities can be expressed either as proportions or percentages you can either say a probability is 75 or 75 o Theoretical probability subjective definition the extent to which you should expect or believe something on days with a 95 chance of rain you should strongly expect that you will need an umbrella subjective probabilities are a great way to represent our degree of certainty or uncertainty if you know absolutely nothing every possible outcome is equally likely as far as you know if you know everything there is to know then you know for sure that one outcome will happen 100 probability and the others won39t 0 probability one outcome we are often interested in is whether or not our beliefs will turn out to be true subjective probabilities can represent how confident we are that we are right subjective probabilities represent our ignorance making probability statements does not necessarily mean that the world is inherently unpredictable even if events are actually deterministic we have to make probabilistic statements about them because we never know all of the determining factors

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