Overview
PSY 230: Psychological Statistics and Measurement
University of Arizona Spring 2025 Written Assignment 1: Hypothesis Testing ***due on Friday March 28 at 11:59 pm*** Overview Imagine that you are a psychologist who has invented a new medication (“Wildcatozine”) to treat people with depression. You predict that depressed individuals who take Wildcatozine will experience fewer depression symptoms than depressed individuals who do not take the medication, but now you need to test this hypothesis. You recruit a sample of n = 30 college students who have been diagnosed with depression, and you give them all Wildcatozine. Several weeks later, you give all participants a questionnaire about their depression symptoms. This questionnaire gives each participant a depression score from 0 (not at all depressed) to 10 (extremely depressed). You may assume that this questionnaire has been widely used previously with other depressed students. As such, we know that the population of untreated depressed individuals has an average score (μ) of 7.00 on this scale, with a standard deviation (σ) of 2.50, and that this distribution is normally distributed. Your job is to analyze the data from the Wildcatozine study, and to write a paper about whether the medication significantly decreased symptoms of depression. The goal is not necessarily to mimic the results section of a published research article. Instead, the goal is to clearly explain the analyses that you have conducted, and how you interpret the results. Sample Data After several weeks of taking Wildcatozine, these are the depression scores reported by your sample of n = 30: 7, 9, 6, 7, 10, 6, 3, 8, 1, 9, 2, 4, 3, 9, 5, 8, 6, 4, 7, 4, 10, 7, 3, 5, 5, 4, 2, 9, 0, 7 ***For this assignment, please round all calculations to 2 decimal places.***
Paper Requirements Your paper should include answers to the following questions: • Descriptive statistics of central tendency: o What is the mean (M) for your sample? Briefly describe how you calculated it. (2 points) o What is the median for your sample? Briefly describe how you calculated it. (2 points) o What is the mode for your sample? Briefly describe how you calculated it. (2 points) • Descriptive statistics of variability: o What is the range for your sample? Briefly describe how you calculated it. (2 points) o What is the variance (s 2 ) for your sample, rounded to two decimal places? Briefly describe how you calculated it. (2 points) § Hint #1: You will first need to calculate the “sum of squared deviations” (SS) before you can calculate sample variance. § Hint #2: Remember that you are dealing with a sample, not a population. Be careful when calculating variance! o What is the standard deviation (s) for your sample, rounded to two decimal places? Briefly describe how you calculated it. (2 points) • z-score information for your sample: o Transform your sample mean (M) into a z-score. Briefly describe how you did this. (3 points) § Hint: Remembering that you are calculating a z-score based on a sample mean. You will first need to calculate the “standard error” before you can calculate the z-score. See Chapter 7 for reminders about this process. You can round these calculations to two decimal places. o Explain what that z-score means, as if you were explaining it to someone who has never taken a statistics course (but they do know what a standard deviation/standard error is). In other words, what can you say about your sample once you know its z-score? (3 points) o Among the entire population, what proportion of scores falls above your sample mean? What proportion of scores falls below your sample mean? Briefly describe how you used the unit normal table (available in the Course Support section of MindTap) to find these proportions. (3 points) • Hypothesis testing information: o Step 1: State the hypothesis. § What is the null hypothesis (H 0 ) in this study? (1 point) § What is the alternative hypothesis (H 1 ) in this study? (1 point) § Is the alternative hypothesis directional or non-directional? How do you know? And based on this answer, will you be conducting a one-tailed test or a two-tailed test? (3 points) o Step 2: Set the criteria for a decision about H 0 . § If you decide to use an alpha level of .05, what is the z-score that you will use as a cutoff score for the hypothesis test? (1 point) § If you decide to use an alpha level of .01, what is the z-score that you will use as a cutoff score for the hypothesis test? (1 point) § If you decide to use an alpha level of .001, what is the z-score that you will use as a cutoff score for the hypothesis test? (1 point)
o Step 3: Collect data & compute sample statistic (in this case, the sample statistic is a z-score). § What is the sample mean (M)? What is the z-score that corresponds with this sample mean? (4 points) • Hint: You already calculated both of these statistics earlier in the paper! o Step 4: Make a decision about H 0 . § Does the sample z-score exceed the cutoff for p < .05? Based on your answer, what decision do you reach about the null hypothesis (reject or fail to reject)? (1 point) § Does the sample z-score exceed the cutoff for p < .01? Based on your answer, what decision do you reach about the null hypothesis (reject or fail to reject)? (1 point) § Does the sample z-score exceed the cutoff for p < .001? Based on your answer, what decision do you reach about the null hypothesis (reject or fail to reject)? (1 point) • Type I & Type II Errors o Although you cannot definitively know this as a researcher, it is possible that your p < .05 conclusion is a Type I error? Is it possible that it is a Type II error? Briefly explain your answers. (2 points) o Although you cannot definitively know this as a researcher, it is possible that your p < .01 conclusion is a Type I error? Is it possible that it is a Type II error? Briefly explain your answers. (2 points) o Although you cannot definitively know this as a researcher, it is possible that your p < .001 conclusion is a Type I error? Is it possible that it is a Type II error? Briefly explain your answers. (2 points) • Summary Statement o Assuming that you did not make any Type I or Type II errors, briefly summarize the three results of your hypothesis test (one result per alpha level). Taking all three of these results into consideration, do you think we can make a valid claim that Wildcatozine is an effective antidepressant? (3 points) § Hint: There are multiple “correct” ways to answer this last question! Think critically about your three results and what they tell you about Wildcatozine. • Your paper should be organized, easy to follow, and free of grammatical and spelling errors. (5 points)
Miscellaneous Notes • It is fine if you work with classmates on this paper, and it’s also fine if you have the same answers to the questions. (Every student who does the problem correctly SHOULD have the same answers!). However, it is extremely important that you write your paper independently. You can work through the math with classmates, and you can compare your answers to each other. However, you absolutely MUST write your paper independently. The mathematical answers might be the same as other students, but the explanations MUST be your own. I want to see that you, as an individual, understand how to conduct a hypothesis test. All submissions will be screened with plagiarism- checkers. Please be sure to avoid any issues by writing your own paper, from scratch. • Make your explanations complete, but concise. The list of questions above should guide you through your data analysis, so it is a good idea to structure your paper in that sequence. • You will be graded based on your answers to the questions above, not on paper length. We are not going to be picky about formatting, APA style, etc. Make it easy for your TA to find your answers. • Upload your completed paper to the Written Assignment 1 folder in the D2L Assignments tab. • Please ask us questions! The TAs and I are here to help you.