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PSYC 218 – Assignment 3 – Testing Single Sample and Paired Samples Data

This assignment will give you an opportunity to practice calculating and interpreting single sample t tests, paired samples t tests, Confidence Intervals, Cohen’s d, and power. Before you begin, you should review Chapter 8 of “A Student Guide to SPSS" as well as Chapters 8 and 9 of “Essentials of Statistics for the Behavioral Sciences,” and our in-class Lab from Week 8 Friday (which includes some tips about the most recent version of SPSS). 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 3. Use the SPSS file “Assignment 3 Data 2023 TO POST.sav” to complete the assignment. The SPSS file contains all the data from before, as well as the new False Memory data. Download the Word document “2023 Assignment 3.docx” and TYPE your answers in the spaces provided. You may insert additional spaces after any question as needed. Always use proper symbols and notation wherever possible (e.g., M, s², m, t_obt, d, s_M) in your answers, and properly round all of your final answers to 2 decimal places (but don’t round too early in the calculation to avoid errors in the final answer). 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).

Submission. Return to Assignment 3 on Canvas to submit two documents: your assignment (which must be in pdf (preferably) or Word 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, which is followed by the three variables resulting from the False Memory (FM) CogLab, then the data from the Change Detection, Stroop, and class Survey data from before.

1. First, let us explore our class’s perceptions of well-being on the following survey questions: In general, I consider myself a happy person (happy), and I am satisfied with my life (satisfied). One way to understand our class means would be to compare them to another sample or to a specific population. Instead, we are going to compare them to a specific numerical standard. Do PSYC 218 students, on average, significantly agree or disagree with these statements? In other words, is our class mean significantly different from the scale midpoint of 4, which indicates “neither agree nor disagree”? Conduct the appropriate hypothesis test using alpha = .05, 2 tailed.

a. State the null and research hypotheses using scientific notation. These hypotheses will be the same for both survey questions. [1 point]  

b. Conduct one-sample t tests: one for the happy survey question, and one for the satisfied survey question. Report the results of the t tests using APA style notation, paying close attention to correct use of italics and decimal places. [2 points]

c.  Based on your answer to question 1b, state whether you should reject or retain each H₀ and provide conclusions about how happy and how satisfied our class is. [1 point]

d.  Report the Cohen’s d effect sizes for both of these survey questions, and provide a precise interpretation for each of them. [4 points]

e.  Recall from the demo a few weeks ago that our class was significantly less happy than the general world population represented in the World Values Survey. Consider that result in light of the analyses you just conducted. Is there reason to be worried about the happiness of our class? Why or why not? Explain your answer. Hint: There isn’t a single right answer here. The point is to get you thinking about how to reconcile these results. What have we learned about The Humans? [1 point] 

2. In the False Memory CogLab, you saw a list of original words (e.g., "bed," "drowsy," "tired," "dream") in a study phase. During the subsequent test phase you were shown words and were asked to indicate whether the word was old (shown in the study phase) or new (not shown in the study phase). The test phase lists contained three types of words. Some were original old words that were shown in the study phase (e.g., "bed"); others were unrelated new words that served as meaningless distractors (e.g., "cup"); and others were related new words that were semantically related to words shown in the study phase but had not been presented (e.g., "sleep").  The independent variable was the type of word presented at test, which had three levels: original list word, unrelated distractor word, semantically related distractor word. The dependent variable was the percentage of each type of words chosen. This design resulted in three columns of data:

· FMOriginalListWords = Percent of original List Items correctly identified by the participant

· FMUnrelatedNewWords = Percent of unrelated distractor lures falsely identified by the participant

· FMRelatedNewWords = Percent of semantically related distractor lures falsely identified by the participant

a. According to CogLab, on average in the population, people falsely identify 74.433% of semantically related lure words as having been on the list. Without knowing the population standard deviation, we can only conduct a one-sample t test (rather than a z test) to help us evaluate our class data. Does our class mean on this variable (FMRelatedNewWords) significantly differ from the population?

i. State the null and research hypotheses using scientific notation. [1 point]   

ii.  Conduct the one-sample t test to test this hypothesis using conventional alpha. Write a sentence to report the results of this hypothesis test, including the APA style statistical information (sample mean and standard deviation, t-test summary statement at the end), like shown in class. (In other words, what does this tell us about The Humans?) [2 points]

b. Are people in our class equally likely to correctly identify original items as they are to falsely identify semantically related lure words?

i. State the null and research hypotheses using scientific notation. [1 point]  

ii.  Conduct a paired samples t test to evaluate this question using conventional alpha. Write a sentence to report the results of this hypothesis test, including the APA style statistical information (variable means and standard deviations, as well as the test summary at the end), like shown in class. (In other words, what does this tell us about the humans?). [2 points]  

iii.  State the 95% Confidence Interval for m_D (the difference between these two memory scores), as reported in the output [1 point]. Interpret what this range of scores is indicating [1 point]. Do we expect it to include zero (why or why not)? [1 point]

iv.  Report the estimate the effect size of m_D, as stated in the output [1 point]. Then, use SPSS to conduct an a priori power analysis with that value. Let’s make the common assumption that we want 80% power to detect the effect, and continue with our 2 tailed alpha of .05. Report the number of people we need in a future study to detect an effect (assuming it’s real and is about this size). [1 points]