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Assignment 2 – Standardization and Hypothesis Testing with the z Test

This assignment will give you an opportunity to practice calculating and interpreting standardized scores using SPSS, and conducting z Tests with large datasets. Before you begin, you should review Chapters 1 and 2 of “A Student Guide to SPSS" as well as Chapters 6 and 7 of “Essentials of Statistics for the Behavioral Sciences.” You may consult others throughout the process, but your assignment should be the result of your own work.

Files. The files you need can be found by going to the “Assignments” area on Canvas and clicking on Assignment 2. Use the SPSS file “Assignment 2 Data 2023 FINAL TO POST.sav” to complete the assignment. The SPSS file contains all the Stroop Effect data and Survey data from before, as well as the new Change Detection data. Download the Word document “2023 Assignment 2.docx” and TYPE your answers in the spaces provided. You may insert additional spaces after any question as needed. In addition, always use proper symbols and notation wherever possible (e.g., ) in your answers, and properly round all of your answers the appropriate number of decimal places. Whenever you’re reporting a value, include the appropriate symbol (if any), = sign (if relevant), the number, and its units (whenever it makes sense to include units). (Don’t have Word? Please download it for free here: https://it.ubc.ca/services/desktop-print-services/software-licensing/office-365-students)

Submission. Return to Assignment 2 on Canvas to submit two documents: your assignment (which must be in Word or preferably pdf format, i.e., with file extensions .doc, .docx, or .pdf) and your accompanying SPSS output file (i.e., the single .spv file that includes the results of all your final analysis – just delete any extra analyses that you might have run but not needed). This file is not essential, but will greatly help our TFs while grading. Your assignment will be graded by our TFs on Canvas.

To begin. Begin by opening the SPSS file. The variable labeled ‘CogLabID’ shows participants’ CogLab User IDs.

· An orientation to the new Change Detection data: Recall that the task involved judging whether two pictures were identical or different. In the no flicker condition, the pictures appeared one right after the other, and in the flicker condition, a gray box appeared between the two pictures. In the SPSS datafile, locate the four variables per participant: ProportionCorrectNoFlicker, ProportionCorrectFlicker, RTmsNoFlicker, and RTmsFlicker. RTms stands for “reaction time in milliseconds.”

· A reminder of the Stroop Effect data: The variable labeled 'rtsame' contains each participant’s mean reaction time (rt) on same trials, in units of milliseconds. Same trials are those for which the colour of the word matched the word itself (e.g., the word RED was printed in red ink). The variable labeled 'rtdifferent' contains each participant’s mean reaction times (rt) on different trials. Different trials are those for which the colour of the word did not match the word itself (e.g., the word RED was printed in blue ink).

1. According to the Stroop CogLab global data – which are based on a population of 107575 participants – the mean reaction time on different trials (i.e., trials where the colour of the word does not match the name of the word) is 1110.080 ms, and the standard deviation is 359.294 ms. Evaluate the hypothesis that the mean reaction time on different trials in our class is different from the mean reaction time in the population. Use an alpha level of .05, 2-tailed. [5 points total]

a. Specifically state the null and research hypotheses, using words. (1 point)

b. State the null and alternative hypotheses, using specific statistical language. (0.5 point)

c. Let’s now prepare to test this hypothesis using the z test. First, use SPSS to find the two pieces of descriptive information you will need to conduct this test. State those values here using proper notation. (0.5 point)

d. SPSS assumes you don’t have information about the population – so it doesn’t even give us the option to conduct a z Test! Use your knowledge from this course to conduct a z Test of the hypothesis you stated above. Report the result, including the precise, two-tailed p value. (2 points) Hint: Remember the two-tailed p value is the proportion of scores that are as extreme or more extreme than z_obtained (in either direction).

e. Based on your answer to part d, state whether you should reject or retain H₀ and write a sentence that draws a conclusion about the hypothesis. (1 point)

2. According to the Change Detection CogLab global data – which are based on a population of 84156 people – the mean proportion correct on flicker trials (i.e., trials where a grey box appeared between pictures) is .725, and the standard deviation is .164. Conduct a one-tailed z test (α = .05) to analyze whether our class was less correct in judging pictures, compared to the population, when this flicker was introduced. [5 points total]

a. State the null and alternative hypotheses in words and notation. (2 points)

b. Use your knowledge from this course to conduct a z Test of the hypothesis you stated above. Use SPSS to calculate the relevant descriptive statistics here. Report the following three values: Standard Error of the Mean σ_M, z statistic, precise p value (all to 4 decimals). (2 points)

c. Based on your answer to part b, state whether you should reject or retain H₀ and sentence that draws a conclusion about the hypothesis. (1 point)

3. Let’s now shift our thinking from the whole group to the individual participant. Specifically, let’s examine the Change Detection data for the participant whose CogLabID is PSYC218Jan23Skiba-444. [10 points total]

a. First, use the z score transformation function in SPSS to identify this participant’s z scores (relative to other scores in this sample) on two variables: RTmsNoFlicker and RTmsFlicker. (Hint: Consult Chapter 2, page 28-30, in the Cuttler Guide to SPSS for specific instructions to do this in SPSS rather than by hand.) [2 points]

b. If we assume, for now, that these variables are normally distributed, look up the z scores to identify the percent of the class is this person slower than. In a sentence or two, explain the results for both the No Flicker and the Flicker reaction times. Remember, a larger reaction time means slower performance. (Tip: sketch out a distribution while you work, so you can keep this key information in mind more easily. You don’t need to submit your sketch.) [2 points]

c. Examine the frequency distribution of scores for each of these z-transformed variables, and identify the values representing our target participant PSYC218Jan23Skiba-444. What % of scores actually fall below their score on RTmsNoFlicker? Does this number match the percentile you found in 3b? Why or why not? [2 points]

d. Let’s assume that in the population, these variables are normally distributed. According to the Change Detection global Reaction Time data (based on a population of 84156 people), μ_NoFlicker = 5251.024 ms (σ_NoFlicker = 40208.211 ms) and μ_Flicker = 8554.173 ms (σ_Flicker = 60066.434 ms). Use target participant PSYC218Jan23Skiba-444’s raw scores to calculate z scores relative to the population on both of these variables. [2 points]

e. Compare the z scores for this participant when comparing them to this sample versus to the population data. What do they mean? How do the z scores differ? Why do they differ? Write a couple of sentences to answer these questions by discussing these z scores. [2 points]

Total          /20

Late Deductions (2.5 points for each day late)

CogLab Deductions (5 points for failure to complete)

Final Assignment Grade will be worth 4% of your course grade.

Standard CogLab completion and Late Submissions: Like all sections of PSYC 218, if you did not complete the corresponding Coglab experiment, you will lose 1/4 of the total assignment grade (5 points). If your assignment submission is late, please submit to Canvas as soon as you have finished it (no need to wait for permission). You will lose 1/8 of the total assignment grade for each day it is late. Please see “What to do in Case of Personal Emergencies, Exceptional Challenges, and Missed Deadlines” Canvas page or section of the syllabus for 2022 updated information.