| Course | RES 710 Statistical Research Methods and Design I (RES/710) |
|---|---|
| Week | 5 |
| Paper type | Doctoral t test analysis |
| Length | about 1,156 words, 4 double-spaced pages plus title page and references |
| Format | APA 7 student paper |
| School | University of Phoenix |
| Program | DBA |
| Updated | October 2026 |
Free sample paper for RES 710 Week 5
Comparing Two Groups: Independent and Paired t Tests on Wait Times and Satisfaction
[Student Name]
University of Phoenix
RES/710: Statistical Research Methods and Design I
Week 5 Assignment
[Instructor Name]
[Date]
The learner, the credit union, its members and all data are composites written for a model paper.
Week 4 tested the credit union board's claims against fixed benchmarks. This paper compares groups within the composite Grand Rapids member survey, addressing the core research question from Week 1: does waiting relate to satisfaction, and does it matter how members are served? Three comparisons answer different parts of that question, each with a different form of the t test.
Choosing the Test
An independent-samples t test compares means of two separate groups; a paired-samples test compares two measurements from the same people; a one-sample test, used in Week 4, compares a mean with a fixed value. The tests assume independent observations, roughly normal sampling distributions for the means and, for the classic independent test, equal variances in the two groups.
Delacre et al. (2017) showed through simulation that Student's t test can produce misleading error rates when variances and sample sizes differ, while Welch's test, which does not assume equal variances, performs well in both situations and loses little when variances are equal. They recommended Welch's test as the default. Ruxton (2006) made a similar case, noting that Welch's test is also preferable to switching to a rank-based test simply because variances differ. The learner uses Welch's test for every independent comparison.
Comparison 1: App Versus Branch Satisfaction
H0: mean satisfaction is equal for app and branch members. H1: the means differ.
App members (n = 248) had a mean satisfaction of 6.0 (SD = 0.9); branch members (n = 645) had 5.3 (SD = 1.3). The standard deviations differ noticeably, which supports Welch's test. The difference of 0.7 points gave t(643) = 9.12, p < .001, with the difference's 95 percent interval running from 0.55 to 0.85. Cohen's d, using the pooled standard deviation of 1.20, was 0.58, a medium effect by the conventions Cohen proposed for standardized differences (Cohen, 1992).
Why Comparison 1 Is Not the Answer
App members are younger, with a median age of 34 against 49 for branch members, use the credit union for simpler tasks and never wait in a physical line. The higher satisfaction could reflect any of these. A t test compares groups; it cannot separate channel from the characteristics of the people who choose it. The learner reports the result as a descriptive difference and turns to a comparison within one channel.
App users are happier, but the t test cannot say whether the app makes them happier or happier people choose the app.
Comparison 2: Long Versus Short Waits at Branches
H0: among branch members, mean satisfaction is equal for those who waited more than 10 minutes and those who waited 10 minutes or less. H1: the means differ.
The 10-minute cut point was set in advance, since the credit union's service standard promises service within 10 minutes. Branch members who waited longer (n = 150) had mean satisfaction of 4.6 (SD = 1.4); those who waited 10 minutes or less (n = 495) had 5.48 (SD = 1.2). Welch's test gave t(219) = 6.96, p < .001, and the difference's interval ran from 0.63 to 1.13. Cohen's d was 0.70, a medium-to-large effect.
Splitting a continuous variable discards information, so this comparison is a first look aligned with the service standard. Week 6 will treat wait time as continuous in correlation and regression.
Comparison 3: Perceived Versus Recorded Wait
For the 992 members with recorded waits, the survey also asked how long they felt they waited. Because both values come from the same member, a paired test is correct; an independent test would ignore that each member's two values are related.
H0: the mean difference between perceived and recorded wait is zero. H1: the mean difference is not zero.
Perceived waits averaged 1.6 minutes longer than recorded waits, with a standard deviation of the differences of 4.8 minutes. The paired test gave t(991) = 10.50, p < .001, with a 95 percent interval of 1.30 to 1.90 minutes. The standardized effect, the mean difference divided by the standard deviation of differences, was 0.33.
Because the differences were skewed, the learner also ran a Wilcoxon signed-rank test, which ranks the differences rather than using their values. It gave the same conclusion, so the result does not depend on the normal approximation.
Reporting Effect Sizes
Lakens (2013) explained that effect sizes allow readers to judge practical importance and compare results across studies and that the formula for Cohen's d differs between independent and paired designs, so researchers should state which version they report. The learner labels the paired effect clearly as based on the standard deviation of differences, so readers do not compare it directly with the independent-group values.
Checking Assumptions
Independence holds across members, though members are clustered in branches; a sensitivity check that averaged satisfaction within branch and compared branch means gave the same direction of results. The satisfaction samples are large enough for the central limit theorem to cover mild skew. Box plots showed no extreme satisfaction values. For the paired test, the 12 outage-related waits from Week 2 were removed in a second run, which reduced the mean difference slightly to 1.5 minutes without changing the conclusion.
Group Descriptives Table
App members: n = 248; satisfaction M = 6.0, SD = 0.9.
Branch members: n = 645; satisfaction M = 5.3, SD = 1.3.
Branch, wait over 10 minutes: n = 150; M = 4.6, SD = 1.4.
Branch, wait 10 minutes or less: n = 495; M = 5.48, SD = 1.2.
Perceived minus recorded wait: n = 992; mean difference 1.6 minutes, SD 4.8.
What the Results Mean for the Credit Union
Within branches, members who waited longer than the service standard rated satisfaction almost a point lower, a gap large enough to matter for advocacy and retention. And members feel their waits are longer than the clock shows, especially when waits are long, which suggests that managing perception, through visible queue displays or seating, could help alongside staffing. The channel difference is real but cannot be attributed to the app itself without further analysis. Branch managers can act on the wait result now, since the service standard already gives them a target to staff toward.
Limitations of Two-Group Tests
Each test compares only two groups and adjusts for nothing. Wait time is related to branch, time of day and staffing, and satisfaction may also depend on transaction type and member tenure. Correlation in Week 6 and regression models in RES 720 will consider several factors at once.
Conclusion
Welch's independent test, a paired test with a rank-based check and complete reporting of effects and intervals answered three questions: app members are more satisfied, branch members with long waits are notably less satisfied and members perceive waits as longer than they are. The first result needs careful interpretation, since groups differ in more than channel. Week 6 will examine wait and satisfaction as continuous variables through correlation.
References
Cohen, J. (1992). A power primer. Psychological Bulletin, 112(1), 155-159. https://doi.org/10.1037/0033-2909.112.1.155
Delacre, M., Lakens, D., & Leys, C. (2017). Why psychologists should by default use Welch's t-test instead of Student's t-test. International Review of Social Psychology, 30(1), 92-101. https://doi.org/10.5334/irsp.82
Lakens, D. (2013). Calculating and reporting effect sizes to facilitate cumulative science: A practical primer for t-tests and ANOVAs. Frontiers in Psychology, 4, 863. https://doi.org/10.3389/fpsyg.2013.00863
Ruxton, G. D. (2006). The unequal variance t-test is an underused alternative to Student's t-test and the Mann-Whitney U test. Behavioral Ecology, 17(4), 688-690. https://doi.org/10.1093/beheco/ark016
What the RES 710 Week 5 instructions ask
The fifth RES 710 paper asks doctoral learners to compare means with t tests. Tasks typically include choosing among one-sample, independent-samples and paired-samples tests, stating hypotheses, checking assumptions such as independence, normality and equal variances, running the analysis in SPSS or Excel, reporting t, degrees of freedom, p, an effect size and a confidence interval and interpreting the result for the research problem. Some prompts include a nonparametric alternative. Apply the tests to data tied to the learner's research question, explain each choice of test, cite statistics sources in APA and discuss what a group comparison can and cannot show about cause.
How this RES 710 Week 5 example is built
Our sample paper begins with app versus branch members. Because their variances differ, it uses Welch's test, following research that recommends it as the default: app users rate satisfaction 0.7 points higher, t(643) = 9.12, with a medium-to-large effect. Since app users never wait in line and are younger, the paper then compares branch members who waited more than 10 minutes with those who waited less, finding a gap of 0.88 points, d = 0.70. A paired test shows members believe they waited 1.6 minutes longer than the queue system recorded. Each result comes with an effect size and interval, following a primer on reporting effects, and a rank-based check confirms the paired result despite skew.
RES 710 Week 5 grading rubric: where the points go
Doctoral graders reward t test work that matches the test to the design and report results completely. Strong papers explain why each comparison is independent or paired, check assumptions with evidence and choose Welch's test or a nonparametric alternative where assumptions fail. Credit goes to full APA reporting of t, degrees of freedom, p, effect size and confidence interval, and to interpretation that weighs practical meaning and alternative explanations such as confounding. Graders also value clear tables of group descriptives and a short note on which tests will follow to address what the t tests leave open. Sound statistical references and consistent APA style complete a strong paper.
RES 710 Week 5 help: mistakes to avoid
t test papers often use an independent test on paired data, such as before and after scores from the same people, which wastes information. Match the test to the design. Another frequent gap is assuming equal variances by default; Welch's test is safer. Learners also report only the p value; add the effect size and confidence interval. Some papers conclude that one group causes higher scores when groups differ in other ways, such as age. Name confounders and say what further analysis could address them. Finally, check outliers and skew before testing and run a rank-based check where they are severe. Keep cut points, such as a service standard, fixed before analysis. A tutor can help you read SPSS t test output line by line.
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RES 710 Week 5 questions, answered
What does RES 710 Week 5 usually cover?
It usually covers t tests: one-sample, independent-samples and paired-samples tests, their assumptions, effect sizes and interpretation.
Where can I find a free RES 710 Week 5 sample paper?
The RES 710 Week 5 t test paper comparing credit union members is above, free to read in full.
When should you use a paired t test?
When the two sets of scores come from the same people or matched pairs, such as perceived and recorded wait time for each member.
What is Welch's t test?
A version of the independent-samples t test that does not assume equal variances in the two groups, recommended by many statisticians as the default.
What effect size goes with a t test?
Usually Cohen's d, the mean difference divided by a standard deviation, reported with a confidence interval for the difference.
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