Problem Description:
This assignment focuses on TwoPaired Samples TTests, exploring their principles and practical applications. It covers concepts like counterbalancing and statistical power, delves into realworld scenarios analyzing exercise's impact on anxiety, individuals' coping abilities, and the effect of inperson versus virtual meetings on information retention. Students perform calculations, use SPSS for data analysis, create graphs, and report results in APAstyle. The assignment enhances understanding of statistical tools and their realworld applications.
Part I: General Concepts
Overview: This section provides a deep understanding of the foundational concepts of twopaired samples ttests.
 Counterbalancing: Counterbalancing is a meticulous technique that involves randomizing the order in which participants receive interventions. This minimizes the potential bias stemming from the order of interventions, enhancing data quality and mitigating the influence of extraneous factors such as practice or fatigue.
 Question 1: Explain what counterbalancing and how to achieve it.
 Statistical Power: In comparison to independentgroups ttests, correlatedgroups ttests exhibit superior statistical power. The latter leverages related groups, which can significantly reduce variations between samples, thereby making it a more powerful statistical tool.
 Question 2: Discuss how correlatedgroups ttests have more statistical power in comparison to an independentgroups t test.
 Strengths and Weaknesses of WithinSubjects Design: Withinsubjects designs present distinct advantages and limitations. One key strength is their efficiency in terms of sample size as they require fewer participants. However, one notable weakness is the time factor, as the collection of data takes longer due to the administration of multiple treatment conditions.
 • Question 3: Discuss one strength and one weakness of a withinsubjects design using your own words.
 CorrelatedGroups ttest: Utilizing the provided data, we calculate a tvalue of 10.346, indicating a statistically significant difference in anxiety levels.
 Question 4: Calculate the correlatedgroups t test to determine the t_obs.
 Effect Size (Cohen's d): The effect size is 1.89, signifying a very large effect based on conventions.
 Question 5: Calculate the effect size using Cohen’s d.
 Directionality and Critical Value: This is a nondirectional study, and the t critical value is determined as 2.0452.
 Question 6: Is this a directional or nondirectional study, and what is the t_cv?
 95% Confidence Intervals: Employing the twotailed t_cv, we establish a 95% confidence interval of (2.727879, 4.072121).
 Question 7: Calculate the 95% confidence intervals (make sure you use the twotailed t_cv).
 APAStyle Results: The results indicate a significant impact of exercise on anxiety in women (t(28) = 10.346, p = 0.0000, d = 1.88, 95% CI [2.7279, 4.072121]).
 Question 8: Write an APAstyle Results section based on your analyses.
 CorrelatedGroups ttest: SPSS output confirms a significant difference in selfrating and peer rating (t(11) = 4.180, p = 0.002).
 Question 9: Conduct a correlated groups ttest. Paste the appropriate SPSS output below.
 Table 1: Paired Samples statistics
 Effect Size (r^2): The effect size is calculated as 0.61366, indicating a medium effect, following conventions for effect size interpretation.
 Question 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).
 SPSS Graph: An appropriate graph is created and included in the document.
 Question 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”.

Independent and Dependent Variables: In this scenario, the independent variable is the mode of attendance (in person or virtual), and the dependent variable is the amount of information retained.
 Question 12: Identify the independent and dependent variables.
Answer: The independent variable in the study is the mode of attendance retained (either in person or virtually), and the dependent variable is the amount of information.

Graph: An appropriate graph, complete with axes labels and error bars, is created.
 Question 13: Create an appropriate graph based on the data and paste it below (make sure to have axes labels and error bars).

APAStyle Results: There is a statistically significant difference in information retention between inperson (M=74, SD=7.90218) and virtual (M=82.8, SD=7.88529) meetings (t(18) = 2.493, p = 0.023, d = 0.26, 95% CI [16.21665, 1.38335]). As the pvalue is below the significance level (0.05), the null hypothesis is rejected.
 Question 14: Write an APAstyle Results section based on your analyses.
Answer: There was a statistically significant difference in the amount of information retained for Inperson (M=74, SD=7.90218) and Virtual (M=82.8, SD=7.88529). t(18)= 2.493, p=0.023, d=0.26, 95% CI [16.21665, 1.38335]. We reject the null hypothesis since pvalue is less than the significance level (0.05).

Internal Validity Threat: In this research scenario, one potential threat to internal validity is selection bias. As participants chose their mode of attendance, the study lacked random assignment, potentially introducing bias into the results.
 Question 15: Discuss one threat to internal validity as it specifically relates to this research scenario.
Answer: In relation to this research scenario, Selection is a threat to internal validity, since participants got to choose whether they attend a quarterly meeting in person or via Google Meet, there was already a selection bias as random assignment was not done.
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.

Based on the data above:
 Question 16: What is the z score for someone being diagnosed with dementia at age 65 (can round to two decimal places)?
 Z score = 0.7142857
 Percentage of people with dementia = 23.75%
Answer: Counterbalancing involves randomizing the order in which participants will receive a given intervention, so that the order the interventions are received will be identical amongst all participants. It minimizes the influence of extraneous factors, such as practice or fatigue, on experimental results.
Answer: Correlatedgroups t test has more statistical power than independentgroups t test because while Correlatedgroups t test use the same participants or related groups and this reduces, if not eliminates, completely the variation between the samples as compared to independentgroups t test where groups are independent.
Answer: One strength of a withinsubjects design is sample size. The design does not require a large sample size since its subjects or participants provide repeated measures for each condition. One weakness of a withinsubjects design is time. It takes a longer time to gather data since more than one treatment condition is given to one participant, as opposed to betweensubjects designs.
Scenario: A research study investigates whether exercise has an impact on anxiety in women. Thirty women are subjected to an anxiety assessment before and after six months of exercise. The mean difference in anxiety scores is 3.4, with a standard deviation of 1.8.
Work: t_obs = x̅_d / (S_D⁄√n) = (3.4) / ((1.8)⁄√30) = 10.34587
Answer: t obtained: 10.34587
Work: d = x̅_d / S_D = (3.4) / (1.8) = 1.89
Answer: 1.89
Work: It is a nondirectional study. df = n1 = 301 = 29 t_cv = t_(1α/2, df) = t_(1(0.05)/2, 29) = t_(0.975, 29) = 2.0452
Answer: 2.0452
Work: 95% C.I. = n x̅_d ± t_CV * S_D⁄√n = 3.4 ± 2.0452 * 0.3286335 = (2.727879, 4.072121)
Answer: (2.727879, 4.072121)
Answer: There was a significant effect of exercise on anxiety in women t(28) = 10.346, p = 0.0000 d=1.88, 95% CI [2.7279, 4.072121].
Part II: SPSS Application
Overview: This segment involves applying SPSS for analyzing data related to people's selfrating and peer rating of their coping abilities in challenging situations.
Scenario: Participants rated their mood in response to a negative event and imagined how the same event would affect a peer.
Answer:
Paired Samples Statistics  

Mean  N  Std. Deviation  Std. Error Mean  
Pair 1  Self_rating  5.58  12  1.929 
Peer_rating  4.83  12  1.697  
Paired Samples Test  
Mean  Std. Deviation  Std. Error Mean  95% Confidence Interval of the Difference  
Lower  
Pair 1  Self_rating  Peer_rating  .750  .622  .179 
Work: r^2 = t^2 / (t^2 + df) = 〖4.180〗^2 / (〖4.180〗^2 + 11) = 0.61366
Answer: 0.61366  This implies a medium effect size.
Part III: Cumulative
Overview: In this part, you'll analyze data concerning information retention in meetings, comparing inperson and virtual attendance.
Scenario: Participants were given the choice to attend quarterly meetings either in person or via Google Meet. Afterward, they underwent an assessment of information retention.
Work: Z = (x  µ) / σ = (65  70) / 7 = 0.7142857
P(Z < 0.7142857) = 0.2375
23.75% of people might start to show signs of dementia before 65.
Answer:
Conclusion
In conclusion, this assignment on TwoPaired Samples TTests equips students with the knowledge and practical skills necessary to harness the power of statistical analysis in realworld scenarios. From understanding the intricacies of counterbalancing to conducting SPSS analyses, the journey through these concepts is both enlightening and essential. By applying these techniques to scenarios like exercise's influence on anxiety or information retention in meetings, students gain a deeper appreciation for the practical applications of statistics. This assignment serves as a stepping stone towards becoming proficient data analysts and informed consumers of research.