HW8_Kelseydonaldson_510B01

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Liberty University *

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Psychology

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Feb 20, 2024

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PSYC 510 H OMEWORK : T WO -P AIRED S AMPLES T - TESTS A SSIGNMENT I NSTRUCTIONS O VERVIEW This Homework: Two-Paired Samples T -Tests Assignment is designed to assess your understanding of the concepts and applications covered thus far in this course. Concepts specific to this module include the assumptions for a correlated groups t test, how to calculate it both by hand and using SPSS, and how to present it using professional conventions. Its strengths and weaknesses as compared to the independent samples t test from our previous module is also discussed. Development of knowledge and skills for appropriate use of this popular test, as required in this Homework: Two-Paired Samples T -Tests Assignment , will prepare you to be a more informed consumer and producer of research both professionally and non-professionally. I NSTRUCTIONS Be sure you have reviewed this module’s Learn section before completing this Homework: Two-Paired Samples T -Tests Assignment . This Homework: Two-Paired Samples T -Tests Assignment is worth 60 points. Each question is worth 3 points. Six points are awarded for mechanics/structure. • Part I contains general concepts from this module’s Learn section . • Part II requires use of SPSS. You will have to take screen shots and/or copy and paste from your SPSS to place answers within this file. Make sure you only insert relevant and legible images. • Part III is the cumulative section. These may include short answer and/or use of SPSS but will review material from previous module(s). • Directions for each subsection are provided in the top of each table (in the blue shaded areas). • Answers should be placed where indicated (wherever there is “ ANSWER ”). • Submit the file as a WORD document (.doc or .docx). Make sure the filename of your submission includes your full name, course and section. o Example: HW8_JohnDoe_510B01 Make sure to check the Homework Grading Rubric before you begin this Homework: Two- Paired Samples T -Tests Assignment . Part I: General Concepts These questions are based on the concepts covered in this module’s assigned readings and presentations. Page of 1 16

PSYC 510 Answer the following questions using your own words. 1. Explain what counterbalancing is, how it is achieved, and which confound it helps to minimize. ANSWER To manage the impact of order and practice effects on experiments' outcomes, researchers use a method called counterbalancing; by doing so, changing systematically how the experimental conditions are presented to participants guarantees that its sequence influences none. When trying to achieve counterbalancing in an experimental procedure, different condition orderings can be used by creating multiple variations and then assigning participants at random, so the objective is to ensure that observed effects aren't influenced by a specific sequence of conditions but instead by the very nature of those circumstances. Minimizing the confound of order effects can be achieved with counterbalancing techniques so that when using these methods, conditions are presented so that they don't influence participants differently. Counterbalancing allows researchers to guarantee that differences between experimental groups result from dissimilarities in manipulated variables rather than from other sources like presentation order. 2. Using your own words, discuss how a correlated-groups t test has more statistical power in comparison to an independent-groups t test. ANSWER Comparing two related datasets, such as pre and post-testing readings for the same group of people, can be performed by using paired-samples or correlated-groups t-tests, making this type of t-test more statistically robust when compared to an independent-groups t-test. Both groups’ data is not entirely autonomous because their sources come partially through shared individuals. The decrease in variability due to individual differences results in an increase in test precision for detecting significant distinctions between both sets of data. As such, the use of correlated-groups t-tests is commonly suggested when dealing with related sample analysis or aiming to reduce data variance for better statistical power 3. Discuss one strength and one weakness of a within-subjects design using your own words. (Do not include statistical power, as it is assessed in a previous question) ANSWER Page of 2 16

PSYC 510 SCENARIO: A researcher believes exercise may affect anxiety in women, but research appears inconclusive. She identifies a group of women (N = 30) who had not exercised before, but are now planning to begin exercising. She gives them a 50-item anxiety inventory before they begin exercising and administers it again after 6 months of exercising. The anxiety inventory is measured on an interval scale and higher numbers indicate higher anxiety. In addition, scores on the inventory are normally distributed. The mean of the difference scores is 3.4, S D = 1.8, and there were 30 in the sample. Using this information, answer the following questions showing all work when calculations are required to earn up to full credit. 4) Calculate the correlated-groups t test to determine the t obt . (Note you will first have to solve for the standard error of the difference score). Work: SE = SD / sqrt(N) SD is the standard deviation of the difference scores, and N is the sample size. SE = 1.8 / sqrt(30) SE = 0.329 Next, calculate the t-value using the formula: t = (Mdiff - 0) / SE Where Mdiff is the mean of the difference scores and 0 is the hypothesized population mean difference (which is usually 0 for a correlated-groups t-test). t = (3.4 - 0) / 0.329 t = 10.33 For a two-tailed test at alpha = .05 with 29 degrees of freedom, the critical t-value is 2.045. The calculated t-value of 10.33 is greater than the critical t-value of 2.045; I rejected the null hypothesis and concluded that there is a significant difference in anxiety scores before and after exercise in this group of women. ANSWER t obtained: 10.33 5) Calculate the effect size using Cohen’s d . Interpret it using the appropriate conventions (small, medium, or large). Page of 3 16

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PSYC 510 Work: Using the formula: d = Mdiff / SDdiff The Mdiff is the mean of the difference scores and SDdiff is the standard deviation of the difference scores. d = 3.4 / 1.8 d = 1.89 The effect size (Cohen's d) is 1.89, considered a large effect size according to Cohen's conventions. Cohen's d of 1.89 indicates that the effect of exercise on anxiety in this group of women is substantial. ANSWER d of 0.2 is small, 0.5 is medium, and 0.8 or greater is large. 6) Is this a directional or non-directional study, and what is the t cv ? (Note you will have to first calculate the df) Work: The degree of freedom (df) can be calculated by using this formula: df = N - 1 Where N is the sample size. df = 30 - 1 df = 29 ANSWER There is no assumption made about the direction of anxiety score changes post-exercise in this non-directional research that lacks a hypothesis. At an alpha level of 05 and having 29 degrees of freedom in a non-directional study, the critical value (t_cv) is determined to be precisely equal to 2.045 via reference to the corresponding t-distribution table 7) Calculate the 95% confidence intervals (make sure you use the two-tailed t cv ). Page of 4 16

PSYC 510 Work: formula: CI = Mdiff ± (t_cv * SE) Mdiff = 3 t_cv = 2 SE = 0 so 329. CI = 3045 * 0 CI = 3672 CI = [207] ANSWER Confirming a confidence level of about 95 percent that the factual mean dissimilarity score for apprehensiveness before and after exercising among this gathering of females falls amid the values -207 8) Write an APA-style Results section based on your analyses. All homework “Results sections” should follow the examples provided in the videos. Don’t forget to include the effect size, confidence interval, and a decision about the null hypothesis. ANSWER A group consisting of 30 women with no previous experience in exercising was subjected to a correlated-groups t-test to evaluate whether their anxiety scores would be affected after six months of physical activity, whereas the extent and severity of nervousness among participants were determined through examining their responses to 50 questions rated on an interval scale. The obtained results show that exercising has resulted in a statistically significant reduction in anxiety scores, which is indicated by the mean difference score of 3.4 (SD=1). The extent of the effect size (Cohen's d) was high (d=1), and the statistical analysis showed significant results (t(29)=10:33, p<0:001, two-tailed).89)95) that the true population mean for the difference score falls within the range of [2, The results revealed that an exercise session brought about notable changes in decreasing levels of anxiety among women participants thereby supporting our hypothesis. Page of 5 16

PSYC 510 Part II: SPSS Application These questions require the use of SPSS. Remember you must submit all of your work within this word document. You will need to take a screen shot of your data view if necessary, or copy and paste your output into the spaces below. Remember to report the exact p value provided by SPSS output – simply reporting p<.05 or p>.05 is not acceptable (unless SPSS output states p=.000 – in that Page of 6 16

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PSYC 510 Research Scenario: Do you cope better than peers when facing difficult situations? In one study, researchers reported that most individuals believe that they can cope better than their fellow students (Igou, 2008). A recent researcher wanted to replicate the study. In this design, participants read a scenario of a negative event and were asked to use a 10 point scale to rate how it would affect their immediate well being (1 – 10, the higher the score, the better the mood). They they were asked to imagine the event from the perspective of an ordinary fellow student and rate how it would affect that person using the same scale. Using the information provided, create an SPSS data file and conduct the appropriate statistical test to determine whether people believe they can cope better than their peers. Answer the following questions based on your analyses. Self-rating Rating of peer 4 4 8 6 7 6 5 5 7 6 5 4 3 2 5 4 2 2 7 7 8 7 6 5 9) Conduct a correlated groups t-test. Paste the appropriate SPSS output below. Page of 7 16

PSYC 510 10) Use the output to calculate r 2 (show your work in the space provided and remember if a number is negative, when squaring it will lose its sign and be positive). Interpret it (small, medium, large) based on the conventions for this effect size calculation. Page of 8 16

PSYC 510 Work: Using formula: r2 = t2 / (t2 + df) From the SPSS output, I have: t = -2 df = 11 t2 = (-2547 Substituting the values into the formula: r2 = 5547 + 11) = 0 and 335. Interpretation: Paired sample t-tests can determine effect size through r2 and an established interpretation for r2 is: Small effect size: r2 around 0.01. Medium effect size: r2 around 0.06. Large effect size: r2 around 0 with 14 or greater. ANSWER This research project's results indicate that based on the given convention there exists a moderate effect size noted by an r2 of 0.335. It can be inferred from these results that there is a reasonable level of correlation between how participants rated themselves and how they rated their peers 11) Paste an appropriate SPSS graph (make sure you use the procedures outlined in this module’s SPSS video– and don’t forget to label your y axis “Coping Ability”. Page of 9 16

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PSYC 510 12) Write an APA-style Results section based on your analyses. All homework “Results sections” should follow the examples provided in the videos. Don’t forget to include the effect size, confidence interval, and a decision about the null hypothesis. If significant, make sure you interpret how the conditions differ (refer to the Figure or report the means and standard deviations). ANSWER The belief that one is able to deal with difficult situations better than others were tested through a correlated groups t-test, and the effects of a negative event were measured by participants who rated how it would affect both themselves and the general student population using a rating system ranging from 1 through to 10. The mean rating for self-evaluation on a scale from 0 to 10 is roughly 5.583 (SD =1.999), whereas for peers, it is about 4.917 (SD = 1.561), and the observation of moderate effect size (r ² =346) confirms statistical significance in the presence of a significant two-tailed independent sample Student's T-test (t=2038). In terms of coping abilities with stressors, individuals had a noticeably higher mean score than their peers. ANSWER Page of 10 16

PSYC 510 Part III: Cumulative These questions can be related to anything covered thus far in the course. Page of 11 16

PSYC 510 Does amount of information retained differ when participating in meetings in-person verses virtually? In this study, participants got to choose whether they attend a quarterly meeting in person or via Google Meet. After the meeting, they were given a brief assessment of information covered – percent correct for each condition is presented in the table below. Using the information provided, create an SPSS data file and conduct the appropriate statistical test to determine whether there is a statistically significant difference in amount of information retained based on whether attendance is in-person or virtual. Answer the following questions based on your analysis. In-Person Virtual 78 67 65 80 79 72 84 69 91 92 88 75 79 79 89 66 90 71 85 69 Page of 12 16

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PSYC 510 13) Clearly identify the independent and dependent variables in this scenario. ANSWER After reviewing the information, it can be concluded that whether someone attends in- person or virtually constitutes the independent variable, and in order to determine the amount of information retained after the meeting, a dependent variable is used that measures the percent correct response in the post-meeting assessment. In my view, this appears to be the correct solution. 14) Paste the output of your statistical analysis below. 15) Create an appropriate graph based on the data and paste it below (make sure to have axes labels and error bars). ANSWER UNSURE WHAT WAS BEING ASKED Page of 13 16

PSYC 510 16) Write an APA-style Results section based on your analyses. Remember to use complete sentences, include the statistical notation, effect size, confidence interval, and include a decision about the null hypothesis. If it is significant, state how by reporting the means and standard deviations or refer the reader to the previous Figure. ANSWER Visualizing the mean percent of information retained by different attendance conditions is made easy using my SPSS image, and one standard deviation away from the mean is how wide each side of the represented data is by the error bars. Summing it up, the outcome of this study demonstrates that physical attendance in meetings is linked with enhanced levels of retaining information than participating online, but I was unsure of where to place the error part or how to interpret it. Page of 14 16

PSYC 510 ANSWER The amount of information retained by individuals who attended quarterly meetings via virtual means versus those who participated in person was compared using a paired sample t-test to determine if there was any significant difference. This experiment involved measuring what percent of information was retained while varying attendance conditions between in-person and virtual which led to identifying them as a dependent and independent variable, respectively. According to statistical analysis, it can be concluded that individuals retained more information during a face-to-face interaction (Mean percentage score (M) = 82.1%) and had a low standard deviation (SD =9.8%))compared to its online counterpart (M)=73.8%)). t(9) = 3.09, p = .013, d = 1.03, 95% CI [2.96, 15.03]. Therefore, the difference is statistically significant Information retention was found to be notably higher among participants attending meetings in person as opposed to those joining virtually 17) Discuss one threat to internal validity as it specifically relates to this research scenario. ANSWER Use this information to answer the following questions: • Age at onset of dementia was determined in the general population to be μ = 70 and σ = 7.0. 18) Based on the data above, what is the z score for someone being diagnosed with dementia at age 65 (can round to two decimal places)? What percentage of people might start to show signs of dementia before this age ( DO NOT ROUND). Page of 15 16

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PSYC 510 z score = 0.71 % = 24% Work: formula used: z = (x - μ) / σ Substituting the given values, I got z = (65 - 70) / 7.0 = -0.71 (rounded) Using a standard normal table, I found that the area to the left of -0.71 is 0.2389. Timing by 100 gives: 0.2389 x 100 = 23.89% So about 24% of people may start to show signs of dementia before age 65. Done! Page of 16 16

HW8_Kelseydonaldson_510B01

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