STAT X2(3)

PSYC-FP4700 Assessment 3 Worksheet Assessment 3 – Hypothesis, Effect Size, Power, and t Tests Complete the following problems within this Word document. Do not submit other files. Show your work for problem sets that require calculations. Ensure that your answer to each problem is clearly visible. You may want to highlight your answer or use a different type color to set it apart. Hypothesis, Effect Size, and Power Problem Set 3.1: Sampling Distribution of the Mean Exercise Criterion: Interpret population mean and variance. Instructions: Read the information below and answer the questions. Suppose a researcher wants to learn more about the mean attention span of individuals in some hypothetical population. The researcher cites that the attention span (the time in minutes attending to some task) in this population is normally distributed with the following characteristics: 20  36 2 (μ σ )  . Based on the parameters given in this example, answer the following questions: 1. What is the population mean (μ)? _20_________________________ 2. What is the population variance ? 36. Square root of 36 is 6. _________________________ 3. Sketch the distribution of this population. Make sure you draw the shape of the distribution and label the mean plus and minus three standard deviations. 20 +- 3.6 =(2, 38) 1

Problem Set 3.2: Effect Size and Power Criterion: Explain effect size and power. Instructions: Read each of the following three scenarios and answer the questions. Two researchers make a test concerning the effectiveness of a drug use treatment. Researcher A determines that the effect size in the population of males is d = 0.36; Researcher B determines that the effect size in the population of females is d = 0.20. All other things being equal, which researcher has more power to detect an effect? Explain. Researcher A has more power to detect an effect because the effect size because there is a positive relationship between effect size and power of the test. ______________________________________________________________________ Two researchers make a test concerning the levels of marital satisfaction among military families. Researcher A collects a sample of 22 married couples ( n = 22); Researcher B collects a sample of 40 married couples ( n = 40). All other things being equal, which researcher has more power to detect an effect? Explain. The larger the sample size the greater the power. Researcher B has a larger sample size, therefore researcher B will have more statical power. ______________________________________________________________________ Two researchers make a test concerning standardized exam performance among senior high school students in one of two local communities. Researcher A tests performance from the population in the northern community, where the standard deviation of test scores is 110 ( ); Researcher B tests performance from the population in the southern community, where the standard deviation of test scores is 60 ( ). All other things being equal, which researcher has more power to detect an effect? Explain. 2

Data: Use the dataset minutesreading.jasp. The dataset minutesreading.jasp is a sample of the reading times of Riverbend City online news readers (in minutes). Riverbend City online news advertises that it is read longer than the national news. The mean for national news is 8 minutes per week. Instructions: Complete the steps below. 1. Download minutesreading.jasp. Double-click the icon to open the dataset in JASP. 2. In the Toolbar , click T-tests. In the menu that appears, under Classical, select One- sample t-test. 3. Select Time and then click Arrow to send it over to the Variables box. 4. Make sure the box is checked for Student. In the box labeled Test value , enter 8 . Hit enter. 5. Copy and paste the output into the Word document. One Sample T-Test One Sample T-Test   t df p Time -0.493 14 0.629 Note.  For the Student t-test, the alternative hypothesis specifies that the mean is different from 8. Note.  Student's t-test. 6. State the nondirectional hypothesis. Claim: the length of the Riverbend City online news being views is different than the population mean. Based on the claim, the null and alternative hypothesis would be: Null hypothesis, Ho; = 8 Alternative hypothesis, Ha ≠ 8 7. State the critical t for a = .05 (two tails). ± 2.145 8. Answer the following: Is the length of viewing for Riverbend City online news significantly different than the population mean? Explain. no, there is not significant difference to conclude that the length of viewing for Riverbend city online news is significantly different than the population. Note : You will continue to use this dataset for the next problem. 4

Problem Set 3.6: Confidence Intervals Criterion: Calculate confidence intervals using JASP. Data: Continue to use the dataset minutesreading.jasp. Instructions: Based on the output from Problem Set 3.5, including a test value (population mean) of 8, calculate the 95% confidence interval by following the steps below. 1. Check the box Location Estimate . 2. Check the box Confidence interval . Fill in the box with 95.0 %. 3. Copy and paste the output into the Word document. Table 2 Confidence Interval 95% CI for Mean Difference   t df p Mean Difference Lower Upper Time -0.493 14 0.629 -0.667 -3.564 2.231 Note.  For the Student t-test, location difference estimate is given by the sample mean difference d . Note.  For the Student t-test, the alternative hypothesis specifies that the mean is different from 8. Note.  Student's t-test. Problem Set 3.7: Independent Samples t Test Criterion: Calculate an independent samples t test in JASP. Data: Use the dataset scores.jasp. Dr. Z is interested in discovering if there is a difference in depression scores between those who do not watch or read the news and those who continue with therapy as normal. She divides her clients with depression into 2 groups. She asks Group 1 not to watch or read any news for two weeks while in therapy and asks Group 2 to continue with therapy as normal. The dataset scores.jasp is a record of the results of the measure, administered after 2 weeks. Instructions: Complete the steps below. 1. Download scores.jasp. Double-click the icon to open the dataset in JASP. 2. In the Toolbar , click T-tests. In the menu that appears, under Classical, select Independent-samples T-test. 3. Select Score and then click the top Arrow to send it over to the Dependent Variables box. 5

Problem Set 3.9: Independent t Test using Excel Criterion: Calculate an independent samples t test in Excel. Data: Use this data: Depression Scores: Group 1: 34, 25, 4, 64, 14, 49, 54 Group 2: 24, 78, 59, 68, 84, 79, 57 Instructions: Complete the following steps: a. Open Excel . b. On an empty tab, enter the data from above. Use column A for group 1 and column B for Group 2 . In Cell A1 , enter 1. In cell B1 , enter 2. c. d. Enter the data for each group below the label. e. Click Data Analysis , select t-Test: Two-Sample Assuming Equal Variances . Click OK. f. In Variable 1 Range enter $A$2:$A$8. (Or, click the graph icon at the right of the box and highlight your data for Group 1. Then, click the graph icon.) g. In Variable 2 Range enter $B$2:$B$8. h. Then click OK . Your results will appear on a new tab to the left. i. Return to your data. Click Data Analysis, select t-Test: Two-Sample Assuming Unequal Variances . Then click OK. j. In Variable 1 Range enter $A$2:$A$8. (Or, click the graph icon at the right of the box and highlight your data for Group 1. Then, click the graph icon.) k. In Variable 2 Range enter $B$2:$B$8. l. Then click OK . Your results will appear on a new tab to the left. m. Copy the results from both t tests below. Table 5 t-Test: Two-Sample Assuming Equal Variances Variable 1 Variable 2 Mean 34.85714 64.14286 Variance 483.4762 418.4762 Observations 7 7 Pooled Variance 450.9762 Hypothesized Mean 0 7

Difference df 12 t Stat -2.57996 P(T<=t) one-tail 0.01205 t Critical one-tail 1.782288 P(T<=t) two-tail 0.0241 t Critical two-tail 2.178813 t-test Two-Sample Assuming Unequal Variances Variable 1 Variable 2 Mean 89.9751 6 163.206 3 Variance 34950.0 5 49688.3 5 Observations 11 3 Hypothesized Mean Difference 0 df 3 t Stat - 0.52122 P(T<=t) one-tail 0.31912 2 t Critical one-tail 2.35336 3 P(T<=t) two-tail 0.63824 3 t Critical two-tail 3.18244 6 8