Stats 2

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California Southern University *

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8740

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Psychology

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Apr 3, 2024

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Activity 5: Statistics Exercise II Caryn Patel MA MFT LPC California Southern University PSY-8740-8A: Statistical Methods and Analys Dr. Jamie Mills, Ph.D March, 21,2024

2 #1. Define "power" in relation to hypothesis testing. In the context of hypothesis testing, "power" refers to the probability that a statistical test will correctly reject the null hypothesis when it is false. In simpler terms, power is the ability of a statistical test to detect a true effect or difference when it exists. It's essentially the ability to avoid a Type II error, which occurs when the null hypothesis is not rejected even though it is false. High power indicates a greater likelihood of detecting a real effect if it's there, whereas low power suggests a higher chance of failing to detect a true effect, leading to a false conclusion of no effect (i.e., a false negative). Power is influenced by factors such as the sample size, the significance level chosen for the test, and the effect size of the phenomenon being studied. Increasing sample size generally increases power, while a smaller significance level (alpha) reduces power. #2. Alpha (a) is used to measure the error for decisions concerning true null hypotheses. What is beta (ß) error used to measure? Beta (β) error, also known as Type II error, is used to measure the error for decisions concerning false null hypotheses. In other words, beta error occurs when the null hypothesis is not rejected even though it is false. This means that the test fails to detect a true effect or difference when one exists in the population being studied. Beta error is directly related to the concept of statistical power. Power (1 - β) is the complement of beta error, so a lower beta error corresponds to higher statistical power. Reducing beta error involves designing studies with sufficient sample sizes, choosing appropriate statistical tests, and minimizing sources of variability to increase the likelihood of correctly rejecting a false null hypothesis when it should be rejected.

3 #3. In the following studies, state whether you would use a one-sample t test or a two- independent-sample t test. 1. A study testing whether night-shift workers sleep the recommended 8 hours per day:  In this study, you have one group of night-shift workers, and you want to compare their average sleep duration to the recommended 8 hours per day. Since you're comparing the mean of one group to a known value (8 hours), you would use a one-sample t-test. 2. A study measuring differences in attitudes about morality among Democrats and Republicans:  In this study, you have two independent groups (Democrats and Republicans), and you want to compare their attitudes about morality. Since you're comparing the means of two independent groups, you would use a two-independent-sample t- test. 3. An experiment measuring differences in brain activity among rats placed on either a continuous or an intermittent reward schedule:  In this experiment, you have two independent groups of rats (continuous reward schedule and intermittent reward schedule), and you want to compare their brain activity. Again, since you're comparing the means of two independent groups, you would use a two-independent-sample t-test. Use SPSS and the data file found in syllabus resources (DATA540.SAV) to answer the following questions. Round your answers to the nearest dollar, percentage point, or whole number. #4. Test the age of the participants (AGE1) against the null hypothesis H 0 = 34. Use a one- sample t-test. How would you report the results?

4 a. t = -1.862, df = 399, p > .05 One-Sample Statistics N Mean Std. Deviation Std. Error Mean Age 400 33.12 9.453 .473 One-Sample Test Test Value = 34 t df Significance Mean Difference 95% Confidence Interval of the Difference One-Sided p Two-Sided p Lower Upper Age -1.862 399 .032 .063 -.880 -1.81 .05 One-Sample Effect Sizes Standardizer a Point Estimate 95% Confidence Interval Lower Upper Age Cohen's d 9.453 -.093 -.191 .005 Hedges' correction 9.471 -.093 -.191 .005 a. The denominator used in estimating the effect sizes. Cohen's d uses the sample standard deviation. Hedges' correction uses the sample standard deviation, plus a correction factor. This is because the two-sided p-value is 0.05, which is less than the significance level of .05. Therefore, we reject the null hypothesis in favor of the alternative hypothesis, indicating that the mean age of the sample is significantly different from the test value of 34.

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