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# PSCH 343; Statistical Methods In Behavior Science. Week Eight Notes PSCH 343

UIC

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This 4 page Class Notes was uploaded by Katie on Monday March 7, 2016. The Class Notes belongs to PSCH 343 at University of Illinois at Chicago taught by Liana Peter-Hagene in Spring 2016. Since its upload, it has received 15 views. For similar materials see Statistics Methods In Behavioral Science in Psychlogy at University of Illinois at Chicago.

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Date Created: 03/07/16

• Hypothesis testing with Z-test Step 1. Research and null hypothesis Step 2: Determine the characteristics of the comparison distribution Known population mean Known population variance Step 3: Determine the cutoff score Depended only on significance level and one/two tailed test Step 4. Determine your sample’s score on the comparison distribution Step 5. Decide whether to reject the H 0 • Hypothesis testing with one-sample t-test Step 1. Research and null hypothesis Step 2: Determine the characteristics of the comparison distribution Step 3: Determine the cutoff score Step 4. Determine your sample’s score on the comparison distribution Step 5. Decide whether to reject the H 0 • Unknown population variance – Step 2 • We need to estimate population variance from the only data we have: • Assume the sample is part of the population (i.e., the null hypothesis) à the sample variance is a good approximation for population variance • BUT samples generally have less variability than populations à • Biased estimate: a parameter estimate that is systematically lower or higher than the actual value it is estimating • Like your friend who brags about how many games they won in highschool, but you know you should reduce that by at least 3. BIASED ESTIMATE ACTUAL PARAMETER • New formula for variance • We have to change the formula for sample variance so that it provides an unbiased estimate of the population variance • A couple of new concepts/notations • We will call the sum of squared deviations the sum of squares 2 Σ (X – M) = SS • Degrees of freedom: how many scores in a sample are free to vary when we estimate a population parameter based on those scores • (all but one: with a known mean, the last score HAS to be a certain value) N – 1 = df • The formula for estimating population variance is: • Calculate the standard error of the mean • You’re not done – you must now turn the population variance into the SE, just like we did for Z- tests • Example Strength model of self-control: When people engage in tasks that require self-control, they use up self-control resources and perform worse in other self-control tasks. Hypothesis: • Example • N = 16 • M = 846 calories at lunch • μ = 437 calories at lunch • Assume you calculated the SS - Σ (X – M) 2 • SS= 725904 Calculate the SE. Now you have completed Step 2: μ = 437, SE = ? • Hypothesis testing with one-sample t-test Step 1. Research and null hypothesis Step 2: Determine the characteristics of the comparison distribution Step 3: Determine the cutoff score Step 4. Determine your sample’s score on the comparison distribution Step 5. Decide whether to reject the H 0 • Determine cutoff score – Step 3 • Family of t-distributions • One t-distribution for each df • Page 677, Table A-2 • There is a specific cutoff corresponding to each df • As sample size increases, the cutoff decreases • (the larger the sample, the more accurate the estimate, the less we have to worry about Type 1 error) • Determine the df for our example: • Df = N -1 • What is the cutoff score corresponding to p =.05, two-tailed test, df = 15? • That is the cutoff you use instead of 1.96 – now it will change every time with sample size (df) • Calculate your test statistic – Step 4 • Same as for the Z-test: • Reject Null Hypothesis? – Step 5 • What if the researcher wants to be extra-sure the chance for Type I error is small, and sets the significance level at p < .01? • What is the new cutoff score? • What is the decision? • 2 example Assume you have the following reaction time data for an implicit attitudes test: You know the population mean is 1.23, but you don’t know the population variance Your sample of 12 scores has a mean of .86 You calculate the sum of squares and it is SS = 11.54 Would you reject the null hypothesis for significance level p < .05? What about p < .01? • 3 example For whatever you want to study… You know the population mean is 54.89, but you don’t know the population variance Your sample of 74 scores has a mean of 51.32 You calculate the sum of squares and it is SS = 12816.06 Would you reject the null hypothesis for significance level p < .05? What about p < .01?

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