**t-Tests and ANOVA Paper**

**Introduction**

An analysis was carried out to investigate if there were differences among a group of individuals who had no housing problem, those who had one housing problem, and those with two or more housing problems as measured by overall satisfaction and material well-being. The total sample size was N=935 participants randomly selected from three main categories: no housing problem, one housing problem, and two or more housing problems. Statistical Package for the Social Sciences (SPSS) was used to analyze and provide results for summary statistics and one-way Analysis of Variance (ANOVA).

**Descriptive Statistics**

The overall number of participants included in the study was N=935, with a mean overall satisfaction score of 11.8 and a standard deviation of 2.66, sampled from three categories. The first category was those who did not have housing problems, comprising a total of N=367. The mean satisfaction and material well-being score for this category was 12.71 (SD=+/- 2.35). This means participants’ scores in this group were 2.35 lower or higher than the mean of 12.71, with scores ranging between 1 and 16. Another category comprised a total N=264 of participants who had one housing problem. The mean score on overall satisfaction and material well-being for this group was 11.97 (SD=+/- 2.59), implying most scores in this group were either within 2.59 scores higher or lower than the mean. Similarly, in this group, the lowest score recorded was 4, while the highest score recorded was 16. The third category were participants who had two or more housing problems. The mean overall satisfaction and material well-being for the group was found to be 10.57 (SD+/-2.59). Most scores in this group were either 2.59 above or below the average score for the group. The lowest and the highest satisfaction well-being scores recorded in this group were 4 and 16, respectively.

**One-Way ANOVA**

Analysis of Variance (ANOVA) is a statistical technique used to compare two or more groups across a continuous dependent variable (Mishra et al., 2019). This statistical technique assumes that the random samples selected from the population are independent, the continuous dependent variable follows a normal distribution, and the samples being compared have equal variance.

The assumption of equal variance/homogeneity across the three groups was tested using Levenes’ test. The null hypothesis tested under Levenes’ test is that the variances for the three groups are equal against the alternative hypothesis that at least one variance is different from others. From the results, the Levene statistic was 2.109 (p-value= 0.122), meaning the null hypothesis is accepted and thus conclude that the assumption of equal variance is not violated.

In a one-way ANOVA fitted to the data, the null hypothesis is that the three groups’ mean overall satisfaction and material well-being are equal against the alternative that at least one group has a different mean from other groups (Delacre et al., 2019). The one-way ANOVA results revealed that there was a statistically significant difference between overall satisfaction, material well-being, and housing problems population categories (F (2,932) = 61.674, p<0.000). This means that the null hypothesis is rejected, thus, there is sufficient evidence that a statistically significant difference in population means for the three groups’ overall satisfaction and material well-being exists.

**Post-Hoc Test**

Post hoc tests are used with one-way ANOVA to assess the pattern of differences across groups once the ANOVA yields significant results. The post hoc tests comprise pairwise comparisons across all groups included in the ANOVA analysis (Chen et al., 2018). In this analysis, the Tukey HSD Test was used for the posthoc analysis. The null hypothesis under this test for each pairwise comparison is that the means are equal (mean difference between two groups equal to zero) against the alternative that the means are not equal.

Results from the Tukey HSD Test pairwise comparisons between no housing problem versus one housing problem and no housing problem versus more than one housing problem revealed significant differences between the groups (p=0.001, 95%CI= [0.27, 1.21]) and (p=0.000, 95%CI= [1.68, 2.59]) respectively thus there was a significant difference in overall satisfaction material well-being between pairwise combinations. Pairwise comparison between no housing problem versus one housing problem and no housing problem versus more than one housing problem yielded (p=0.001, 95%CI= [-1.21, -0.27]) and (p=0.000, 95%CI= [0.91, 1.89]) respectively thus there were significant differences in overall satisfaction material well-being across the pairwise combinations of population groups.

The Tukey HSD Test pairwise comparisons between two or more housing problems versus no housing problem and two or more housing problems versus one housing problem also revealed that there were significant differences in overall satisfaction material well-being across each pairwise comparison (p=0.001, 95%CI= [-2.59, -1.68]) and (p=0.000, 95%CI= [-1.89, -0.91]) respectively. Generally, overall satisfaction and material well-being differed across each pairwise comparison in the three population groups.

**Conclusion**

As discussed in this paper, the overall satisfaction and material well-being significantly differed across the three population categories, those with no housing problem, those with one housing problem, and those with two or more housing problems. Further, a post-hoc test revealed that all group pairs were significantly different from each other with regard to overall satisfaction and material well-being.

**References**

Chen, T., Xu, M., Tu, J., Wang, H., & Niu, X. (2018). Relationship between Omnibus and Post-hoc Tests: An Investigation of performance of the F test in ANOVA. *Shanghai Archives Of Psychiatry,* 30(1), 60–64. https://doi.org/10.11919/j.issn.1002-0829.218014

Delacre, M., Leys, C., Mora, Y. L., & Lakens, D. (2019). Taking Parametric Assumptions Seriously: Arguments for the Use of Welch’s F-test instead of the Classical F-test in One-Way ANOVA. *International Review of Social Psychology*, 32(1), 13. DOI: http://doi.org/10.5334/irsp.198

Mishra, P., Singh, U., Pandey, C. M., Mishra, P., & Pandey, G. (2019). Application of student’s t-test, analysis of variance, and covariance. *Annals Of Cardiac Anaesthesia*, 22(4), 407–411. https://doi.org/10.4103/aca.ACA_94_19

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Week Five Assignment

Assignment: t-Tests and ANOVA

You are a DNP-Prepared nurse tasked with evaluating patient care at your practice compared to patient care at affiliated practices. You have noticed that a key complaint from your patients concerns the wait times associated with each patient visit. Based on these complaints, you have decided to compare the wait times at your practice to the wait times at affiliated practices. After recording the wait times at each practice, for 50 individual patients at each practice, you are now prepared to analyze your data. What approach will you use to analyze the data?

In the scenario provided, you might decide to use, the Analysis of Variance (ANOVA) approach. â€œANOVA is a statistical procedure that compares data between two or more groups or conditions to investigate the presence of differences between those groups on some continuous dependent variableâ€ (Gray & Grove, 2020). ANOVA is often a recommended statistical technique, as it has low chance of error for determining differences between three or more groups.

For this Assignment, analyze the ANOVA statistics provided in the ANOVA Exercises SPSS Output document. Examine the results to determine the differences and reflect on how you would interpret these results.

Reference: Gray, J. R., & Grove, S. K. (2020). Burns and Groveâ€™s the practice of nursing research: Appraisal, synthesis, and generation of evidence (9th ed.). Elsevier.

To Prepare:

â€¢ Review the Week 5 ANOVA Exercises SPSS Output provided in this weekâ€™s Learning Resources.

â€¢ Review the Learning Resources on how to interpret ANOVA results to determine differences.

â€¢ Consider the results presented in the SPSS output and reflect on how you might interpret the results presented.

The Assignment: (2â€“3 pages)

â€¢ Summarize your interpretation of the ANOVA statistics provided in the Week 5 ANOVA Exercises SPSS Output document.

o Note: Interpretation of the ANOVA output should include identification of the p-value to determine whether the differences between the group means are statistically significant.

o Be sure to accurately evaluate each of the results presented (descriptives, ANOVA results, and multiple comparisons using post-hoc analysis)

Reminder: The College of Nursing requires that all papers submitted include a title page, introduction, summary, and references. The Sample Paper provided at the Walden Writing Center provides an example of those required elements (available at https://academicguides.waldenu.edu/writingcenter/templates/general#s-lg-box-20293632). All papers submitted must use this formatting.

By Day 7

Submit your Assignment by Day 7 of Week 5.

Submission and Grading Information

To submit your completed Assignment for review and grading, do the following:

ummarize your interpretation of the ANOVA statistics provided in the Week 5 ANOVA Exercises SPSS Output document.–

Excellent 41 (41%) – 45 (45%)

The response accurately and clearly summarizes, in detail, the ANOVA statistics provided.

An accurate and detailed explanation of the p-value describing whether the differences are statistically significant is provided.

Good 36 (36%) – 40 (40%)

The response accurately summarizes the ANOVA statistics provided.

An accurate explanation of the p-value describing whether the differences are statistically significant is provided.

Fair 32 (32%) – 35 (35%)

The response inaccurately or vaguely summarizes the ANOVA statistics provided.

An inaccurate or vague explanation of the p-value describing whether the differences are statistically significant is provided.

Poor 0 (0%) – 31 (31%)

The response inaccurately and vaguely summarizes the ANOVA statistics provided, or itis missing.

An inaccurate and vague explanation of the p-value describing whether the differences are statistically significant is provided, or it is missing.

Be sure to evaluate each of the results presented (descriptives, ANOVA results, and multiple comparisons).–

Excellent 36 (36%) – 40 (40%)

The response accurately and clearly evaluates, in detail, each of the results presented in the document (descriptives, ANOVA results, and multiple comparisons).

Good 32 (32%) – 35 (35%)

The response accurately evaluates each of the results presented in the document (descriptives, ANOVA results, and multiple comparisons).

Fair 28 (28%) – 31 (31%)

The response inaccurately or vaguely evaluates each of the results presented in the document (descriptives, ANOVA results, and multiple comparisons).

OR

The response summarizes < 3 of the results provided.

Poor 0 (0%) – 27 (27%)

The response inaccurately and vaguely evaluates each of the results presented in the document (descriptive, ANOVA results, and multiple comparisons), or it is missing.

Written Expression and Formatting – Paragraph Development and Organization:

Paragraphs make clear points that support well-developed ideas, flow logically, and demonstrate continuity of ideas. Sentences are carefully focusedâ€”neither long and rambling nor short and lacking substance. A clear and comprehensive purpose statement and introduction is provided which delineates all required criteria.–

Excellent 5 (5%) – 5 (5%)

Paragraphs and sentences follow writing standards for flow, continuity, and clarity.

A clear and comprehensive purpose statement, introduction, and conclusion is provided which delineates all required criteria.

Good 4 (4%) – 4 (4%)

Paragraphs and sentences follow writing standards for flow, continuity, and clarity 80% of the time. Purpose, introduction, and conclusion of the assignment is stated, yet is brief and not descriptive.

Fair 3.5 (3.5%) – 3.5 (3.5%)

Paragraphs and sentences follow writing standards for flow, continuity, and clarity 60%â€“79% of the time.

Purpose, introduction, and conclusion of the assignment is vague or off topic.

Poor 0 (0%) – 3 (3%)

Paragraphs and sentences follow writing standards for flow, continuity, and clarity < 60% of the time.

No purpose statement, introduction, or conclusion was provided.

Written Expression and Formatting – English writing standards: Correct grammar, mechanics, and proper punctuation–

Excellent 5 (5%) – 5 (5%)

Uses correct grammar, spelling, and punctuation with no errors.

Good 4 (4%) – 4 (4%)

Contains a few (1 or 2) grammar, spelling, and punctuation errors.

Fair 3.5 (3.5%) – 3.5 (3.5%)

Contains several (3 or 4) grammar, spelling, and punctuation errors.

Poor 0 (0%) – 3 (3%)

Contains many (â‰¥ 5) grammar, spelling, and punctuation errors that interfere with the readerâ€™s understanding.

Written Expression and Formatting – The paper follows correct APA format for title page, headings, font, spacing, margins, indentations, page numbers, parenthetical/in-text citations, and reference list.–

Excellent 5 (5%) – 5 (5%)

Uses correct APA format with no errors.

Good 4 (4%) – 4 (4%)

Contains a few (1 or 2) APA format errors.

Fair 3.5 (3.5%) – 3.5 (3.5%)

Contains several (3 or 4) APA format errors.

Poor 0 (0%) – 3 (3%)

Contains many (â‰¥ 5) APA format errors.

Total Points: 100