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# Principles of Assessment PSY 3430

SUU

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This 3 page Class Notes was uploaded by Adrienne Lueilwitz on Tuesday October 20, 2015. The Class Notes belongs to PSY 3430 at Southern Utah University taught by Staff in Fall. Since its upload, it has received 5 views. For similar materials see /class/225494/psy-3430-southern-utah-university in Psychlogy at Southern Utah University.

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Date Created: 10/20/15

PSY 3430 Standard Error Standard errors are like standard deviations for samples estimates and measures Standard Error 0f the Mean SE Mean If you take a sample from a population measure any trait ht wt siblings intelligence etc and compute the mean you have an unbiased estimate of the population or a single value that best represents the overall mean of the population But how representative is it really That depends on a lot of factors If you randomly take the sample and obtain a mean you get a number Then you randomly take another sample and measure the same variable and compute the mean the value may be the same or it may be different higher or lower Then randomly take another sample and take the mean the value may be the same or it may be different from the last two higher or lower etc If this process is repeated many times usually thousands you will get many different numbers representing the mean of the population In fact if you plot these sampling means you will see a normal distribution with the majority of scores clustered around the center and more dispersed toward the tails and symmetrical in shape The value at the center of the distribution will likely be the population mean Usually we don t have the time or resources to take thousands of random samples in order to compile a distribution of sampling means The best we can do is estimate how good the mean of our sample is at re ecting the population by making some adjustments Two pieces of information are necessary the sample size and the standard deviation of the sample The standard deviation is divided by the square root of the sample size The quotient is the Standard Error of the Mean It is the theoretical standard deviation of the sampling distribution the thousand random samples of the population As with any standard deviation it can be used to create a range in which the likelihood of a true population mean falls can be calculated using what we know about the normal distribution I can be 68 confident that the true population mean ranges between the 1 standard error below the sample mean and 1 standard error above the sample mean Z i 10 SEMean I can be 95 con dent that the true population mean ranges between 2 times the standard error below the sample mean and 2 times the standard error above the sample mean Z i20 SEMean I can be 99 con dent that the true population mean ranges from 3 times the standard error below the sample mean and 3 times the standard error above the sample mean Z i30 SEMean The value of the standard error decreases as the sample size increases better representes the population and the standard deviation decreases more consistent scores are easier to estimate Standard Error 0f the Estimate SE Estimate In any given regression equation an estimation of the DV by the known values of the IV is of interest what is your likely weight based on your height Similarly you may wish to predict something using scores on a test success in school based on ACT scores These types ofvariables are called predictors ones on which the prediction is based IV s and criterion the thing being predicted DV s The accuracy of these predictions is determined in part by how good the test is at measuring what it is supposed to be measuring validity You could give the test thousands of times and measure how accurately it predicted the criterion each time You will likely encounter different predicted values of the criterion for each time you make a prediction These different values will vary in regard to how accurate they are Some will be really close to the actual value of the criterion some will miss it by a long way If you plot how much each prediction missed the true value the residual value the results will be normally distributed with most misses being relatively close and fewer toward the extreme values The standard deviation of this distribution is called the Standard Error of the Estimate and can be used to calculate confidence intervals for the predictions made I can be 68 con dence that the actual value of the criterion will fall between 1 standard error of the estimate below and one standard error of the estimate above the predicted value i SEEstimate If my regression equation predicts that someone 6 tall would weigh 208 and the standard error of the estimate is 10 then I am 68 confident that someone who is indeed 6 tall would weigh between 198 and 218 based on my sample I can be 95 confident that hisher weight would range between 2 times the Stande Error of the Estimate below to 2 times the Standard Error of the Estimate above the estimated value someone 6 tall would weigh between 188 and 228 based on my sample i 2SEEstimate I can be 99 confident that hisher weight would range between 3 times the Stande Error of the Estimate below and 3 times the Standard Error of the Estimate above the predicted value someone 6 tall would weigh between 178 and 238 based on my sample i 3SEEstimate The higher the correlation between my predictor and criterion the smaller the Standard Error of the Estimate and the more confident I am in my predictions The Standard Error of the Measure SE Meas Test scores are made up of one s actual ability and error some random and some systematic If you score 110 on an IQ test that score re ects your actual IQ and some measurement error If I gave you the same test a thousand times your scores would vary Many scores would be close and some would be higher and some lower If these scores were plotted they would re ect a normal distribution with most scores clustered around the mean and the rest spread toward the tails in a normal fashion Since your intelligence theoretically does not change the variability in the test is due to error in measurement The standard deviation of this distribution is called the Standard Error of the Measure The SE Meas can be used to calculate con dence intervals for any measure I can be 68 con dent that the value of whatever trait I am measuring falls between one SE Meas below and one SE Meas above the test score that the person got If the SE Meas of the IQ test was 10 I would be 68 con dent that your actual IQ score ranged between 100 and 120 Again the variability in the IQ is not because your IQ changes rather because of error in measurement I would be 95 con dent that your true IQ ranged from 90130 2 times the SE Meas above and 2 times the SE Meas above your test score I would be 99 con dent that your actual IQ ranged from 80140 3 times the SE Meas below and 3 times the SE Meas above your test score Of course giving an IQ test to the same person a thousand times is impractical and generally a bad idea this value can be estimated with the following procedure Take the Standard Deviation and multiply it by the square root of 1 minus the reliability of the test EXtrapolating from this process if the Standard deviation of the test is high the SEMeas will be higher if the Standard Deviation is low the SEMeas will be lower but if the Reliability is high the SEMeas will be low A low SEMeas is good and re ects a better test more accurate and less error The reliability is extremely important So what is the reliability of a test

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