Unit 8 Workshop 2023

pdf

School

Dalhousie University *

*We aren’t endorsed by this school

Course

2450

Subject

Statistics

Date

Apr 3, 2024

Type

pdf

Pages

Uploaded by ElderMoonSwan35

PSYO2501 Fall 2023 1 Unit 8 Workshop: One-Way Analysis of Variance (ANOVA) Quiz Due Date: Friday, Nov 24 at 11:59pm PRACTICE QUESTIONS BEGIN (ANSWER KEY POSTED ON BRIGHTSPACE) 1a. Below is a partially filled-in ANOVA table. Calculate the F-test, p-value, and ω 2 value based on only this information. One you have the F-test, you can look up the p-value using the F- distribution app in the links below: F-distribution App Try this link first: https://psyo2501.shinyapps.io/fdist/ Mirror (use if the first link doesn’t work): https://shiny.rit.albany.edu/stat/fdist/ Source SS Df MS F p ω 2 Group 18.76 4 4.691 Error 70.62 70 1.009 Total 89.38 2. In this next question, you will explore an online app (and will return to using it for an assessment question later in the workshop!). Use the “ANOVA Playground” App for this section Use this Link: https://psyo2501.shinyapps.io/anova2/ When you open up the app, it generates a random dataset. That is, it essentially uses a random number generator to create 5 different groups and analyzes it with one-way ANOVA. In this first part, you will play around with a few settings to see how it impacts the ANOVA. Play around with the different data visualization options to get a feel for the data. You might also try refreshing the browser to get a new random dataset and try it again to get a sense of the pattern. 2a. What happens to the data visualizations and F-test when you adjust the variation between groups ? The closer you go to +10, the more between-groups variation you add. As you get closer to -10, you have increasingly less between-groups variation. 2b. What happens to the data visualizations and F-test when you adjust the variation within groups ? The closer you go to +10, the more within groups variation you add. As you get closer to -10, you have increasingly less within-groups variation.

PSYO2501 Fall 2023 2 2c. Play around with the group sample size and see how it changes the data visualizations. When you have a small number of data points (say, N = 10), which data visualization (dot plot, box plot, density plot) seems to give the most useful information? When you increase to a large sample (say, N = 300) which data visualization seems best? IMPORTANT: CLOSE THE WEB BROWSER TAB WITH THE ANOVA APP BEFORE PROCEEDING! ASSESSMENT QUESTIONS BEGIN (QUIZ QUESTIONS ON BRIGHTSPACE) 3. Dr. Colourful is brought in by SmartyPants University to do a study on the calming effects of different paint colours. The University believes that they should paint the walls a colour that calms their students, so students perform better on tests. Specifically, they think that colours like purple or baby-blue will be calming, while in contrast, they think red will make people less calm. They think that grey is a neutral color that probably doesn’t affect calmness. Finally, they also think students might feel even calmer in a baby-blue room over purple, because that’s school logo’s primary colour. They design an experiment where students complete a questionnaire evaluating state-calmness level (current level of calmness compared to when they are typically at the University) in one of four rooms, each painted a different color: (a) purple; (b) baby-blue; (c) red; (d) grey. Calmness is rated on a visual analogue scale from -10 to +10, with -10 representing feeling very restless, 0 being neutral, and +10 representing peak calmness levels. They use a between-subjects design. They hypothesize that: (H1) Students completing the survey in the baby-blue room will have higher calmness ratings than those in the grey room. (H2) Students completing the survey in the purple room will have higher calmness ratings than those in the grey room. (H3) Students completing the survey in the red room will have lower calmness ratings than those in the grey room. (H4) Students completing the survey in the baby-blue room will have higher calmness ratings than those in the purple room. However, they are using two-sided tests so are open to the possibility the reverse is true. 3a. Assuming a one-way ANOVA is used to analyze the data, what is the null and alternative hypothesis for the overall F-test? 3b. If Dr. Colourful wanted to do every possible pairwise comparison (i.e., as many unique t- tests as possible), how many separate post hoc tests would they be conducting?

PSYO2501 Fall 2023 3 3c . How would you test Dr. Colourful’s hypotheses more specifically using post-hoc tests? Write out the null and alternative hypotheses for each post hoc test you will need to do to test these hypotheses. You should not write out EVERY pairwise comparison. In other words, write as many t-tests tests as would be needed to test all 4 hypotheses (i.e., a subset of the total number of tests in 3b). Assume they are using two-tailed tests, with an alpha of .01. 3d. If Dr. Colourful did only the number of post hoc tests you specified in 3c (i.e, a smaller subset of every comparison from 3b), what would the familywise error rate be? Assume they started with a critical value for alpha of .01. 3e. If Dr. Colourful did only the number of post hoc tests you specified in 3c (i.e, a smaller subset of every comparison from 3b), what would the Bonferroni critical p-value be? Assume they started with a critical value for alpha of .01. 4a. Dr. Colourful conducts this experiment and has 25 people in each of the 4 conditions for a total of 100 study participants. Below is an ANOVA table. The only parts that are filled in are the Group and Error Sums of Squares. Fill in all the other non-grey cells in this table based on only this info, and the info described above. The quiz online will ask you about some of these values, along with getting you to report the p-value; you will need to fill in all the numbers to get the p-value (except the ω 2 , but you will be asked about it!). Once you have the F-test, you can look up the p-value using the links provided in Practice Question 1. Source SS Df MS F p ω 2 Group 17.05 Error 87.25 Total

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

PSYO2501 Fall 2023 4 4b. What would you conclude from the analysis above? Is there evidence against the null hypothesis? Assume an alpha of 0.01. Additionally, explain what the ω2 value means. Return to the “ANOVA Playground” App for this section Try this link first: https://psyo2501.shinyapps.io/anova2 IMPORTANT TECHNICAL NOTE: If you left the app open and didn’t close it like instructions asked earlier, you may experience errors! When you play with the bars that “adjust variation between/within groups” in the practice question, it adds some random error to the data. This is as intended for practice question 2. However, if these bars are anything other than ZERO in the next step, then the results in question 5 where everyone is using the same dataset will be wrong, because the app will add random error to your answer (thus, making you get it wrong on your quiz!). Refreshing your browser prior to this analysis should also avoid this if you didn’t close and re -open. 5 . Ok, now we’re going to analyze an actual dataset using the app. Go to the Source data tab, click on the drop down box under Run the ANOVA using and select “an existing dataset.” This will use a specific dataset called “anova.fall2018.txt” instead of a randomly generated one. In this experiment, Dr. Feelgood wants to run an experiment to see if certain therapies can alleviate symptoms of psychological disorders. He uses a between-subjects design and examines the efficacy of three therapies: Cognitive-Behavioural Therapy (CBT), Interpersonal Therapy (IPT), and antidepressants. He also has a control group that was on a waitlist and did not have any treatment. At the end of 13 weeks, all three groups report on their symptoms of depression, anxiety, and somatoform disorder symptoms. He believes that people in the CBT, IPT, and antidepressant groups will have lower levels of psychological disorder symptoms relative to the control group. He additionally has a prediction that talk therapies (CBT & IPT) will work better than the antidepressant group at reducing symptoms. However, he’s not sure if CBT or IPT are better or worse than each other. Note: For Question 5, I want you to focus just on one outcome variable (anxiety symptoms) because I’m trying to make sure the workshop doesn’t take too long to complete this week! 5a. Assuming a one-way ANOVA is used to analyze the data when anxiety symptoms are the outcome, what is the null and alternative hypothesis for the overall F-test?

PSYO2501 Fall 2023 5 5b. Assuming that Dr. Feelgood wants to do all possible pairwise comparisons for anxiety symptoms as post-hoc tests, what are the null and alternative hypotheses for these tests? He wants to use two-tailed tests when he is not sure of the direction, and one-tailed tests for effects where he is sure which mean should be higher than the other. 5c. Run the one-way ANOVA for ANXIETY SYMPTOMS and report the F-tests. The alpha is .15. You can report the F-tests below in APA format, F(df1,df2) = X.XX, p = .XX, where df1 = Group degrees of freedom and df2 = Error degrees of freedom. IMPORTANT NOTE: You will need to interpret the p-values for the quiz questions, but will not have to report the exact p-values (so no need for questions about how to round or report the p- value in Brightspace). 5d. Run the post-hoc tests for the anxiety symptoms variable only (under the tab “Student’s t - test). Which of the six tests are statistically significant, after applying the Bonferroni correction to the original alpha of .15? He is doing 6 post hoc tests, so .15/6 = .025 is our new cut-off. To get used to seeing values in this way, you can report the t-tests in APA format: t(df) = X.XX, p = .XX. 5e. Based on the F-tests, data visualizations, and post-hoc tests what are your conclusions for this study for ANXIETY SYMPTOMS. The course material in this file has been posted for your personal educational use only. Copying this file for distribution (e.g. uploading material to a commercial third-party or public website, or otherwise sharing these materials with people who are not part of the class) outside of this site may be a violation of Copyright law. If you have questions regarding the use of the materials in this file, please contact Dr. Mackinnon at mackinnon.sean@dal.ca .

PSYO2501 Fall 2023 6 Practice Question Key Here is the answer key for the self-graded questions. Please make sure you try all these question before looking at the key, or you will not learn as much! Assessment questions will never be posted in a digital file like this; instead, you will only see the answers through the Quiz feature in Brightspace, and only after all students have finished the quiz.\ 1a. Below is a partially filled-in ANOVA table. Calculate the F-test, p-value, and ω 2 value based on only this information. One you have the F-test, you can look up the p-value using the F- distribution app in the links below: F-distribution App Try this link first: https://psyo2501.shinyapps.io/fdist/ Mirror (use if the first link doesn’t work): https://shiny.rit.albany.edu/stat/fdist/ Source SS Df MS F p ω 2 Group 18.76 4 4.691 Error 70.62 70 1.009 Total 89.38 F = MSG / MSE F = 4.691 / 1.009 F = 4.65 P = 0.00219 ω 2 = ( SS G - (df G * MSE)) / (SS T + MSE) ω 2 = ( 18.76 - (4 * 1.009)) / (89.38 + 1.009) ω 2 = ( 18.76 - 4.036) / (89.38 + 1.009) ω 2 = 14.724 / 90.389 ω 2 = 0.163 group membership explains 16.3 % of the variance

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

PSYO2501 Fall 2023 7 2a. What happens to the data visualizations and F-test when you adjust the variation between groups ? The closer you go to +10, the more between-groups variation you add. As you get closer to -10, you have increasingly less between-groups variation. As variation between groups increases, the means of the different groups get increasingly different from one another. As a result, the value for the F-test gets larger and larger the more between-subjects variation you add. 2b. What happens to the data visualizations and F-test when you adjust the variation within groups ? The closer you go to +10, the more within groups variation you add. As you get closer to -10, you have increasingly less within-groups variation. When you increase the within-groups variation, the spread of the data within each group gets larger (so the data visualizations get wider!). In contrast, as you get closer to -10, the spread of the data within the groups gets narrower (until at -10, everyone has exactly the same value within their groups!). This is what is meant by within-group variation. As a result, the F-test gets larger when there is LESS within-group variation. 2c. Play around with the group sample size and see how it changes the data visualizations. When you have a small number of data points (say, N = 10), which data visualization (dot plot, box plot, density plot) seems to give the most useful information? When you increase to a large sample (say, N = 300) which data visualization seems best? With a small sample, the dot plot is probably most useful, and the density plot is misleading. With a large sample, the dot plots are ugly and hard to read, but the density plots shine. The box plot works reasonably for both (but probably provides less info, and is less intuitive and aesthetically appealing, so it is better as a supplement).

Unit 8 Workshop 2023

Related Documents