Assignment 3: t Tests and ANOVA NURS 8200

Assignment 3: t Tests and ANOVA NURS 8200

Independent t Test Exercises

Part 1

  1. How many women were employed versus not employed in the sample?

A total 436 women were employed while 524 were not employed.

  1. What is the total sample size?

The sample size is 960

  1. What are the mean and standard deviation for the CES-D scores for each group?

The mean and standard deviation for CES-D scores are


Group Statistics
  Currently employed? Mean Std. Deviation
CES-D Score No 20.8965 12.46425
Yes 15.8239 10.13655


  1. Interpret the Levene’s statistic. (Hint: Is the assumption of homogeneity of variance met?

The assumption of homogeneity of variance is met considering that the p-value is less than 0.05. 

  1. Are equal variances assumed or not assumed?) Why?

The equal variance is not assumed because the F-statistics is 23.615 which is significantly high. 

  1. What is the value of the t-statistic, number of degrees of freedom and the p-value?


  t df Sig. (2-tailed)
CES-D Score Equal variances assumed 6.825 958 .000
Equal variances not assumed 6.954 957.514 .000
  1. Does the data support the hypothesis? Why or why not?

Yes, there is a significant difference in the levels of depression between the working women and those who are not working. The p-value is less than 0.05; therefore, the hypothesis is accepted.

Part II

  1. What is the total sample size?

The sample size is 157

  1. What are the mean and the standard deviation of the CES-D scores at wave 1 and wave 2?
Paired Samples Statistics
  Mean Std. Deviation
Pair 1 CES-D Score 18.5516 11.87462
CESD Score, Wave 1 17.8344 11.49908
  1. What is the mean difference between the two time periods?

The mean diffwerence = 0.7172

  1. What is the value of the t-statistic, number of degrees of freedom and the p-value(sig)?


  t-statistics Degrees of freedom P-value
Pair 1 CES-D Score – CESD Score, Wave 1 .709 156 .480


  1. Does the data support the hypothesis? Why or why not?

Yes, the p-value is greater than p=0.05; therefore, the null hypothesis is rejected.

Part 3

The results indicate that the level of education attainment does not influence the depression level, mental health and physical health components. The p-values for the test were below 0.05 and this indicated that the characteristics in the stress level, mental and physical health components were almost similar regardless of the level of education attained. Furthermore, the assumption of equal variance was met because the F-statistics value was below 1.5.

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Week 5 ANOVA Exercises

  1. What is the total sample size?

The total sample size is n=935

  1. How many women were in each of the different hprobgrp groups?


No Housing Problem 367
One Housing Problem 264
Two or More Housing Problems 304


  1. What are the mean and standrad deviation (SD) overall satisfaction scores for each group?
  Mean Std. Deviation
No Housing Problem 12.71 2.353
One Housing Problem 11.97 2.588
Two or More Housing Problems 10.57 2.594
  1. Interpret the Levene’s statistic. (Hint: Is the assumption of homogeneity of variance met? Are equal variances assumed or not assumed?)

The assumption of homogeneity of variance is met because the p-value is lower than 0.05.

  1. What is the value of the F-statistic, number of degrees of freedom and the p-value?
  df F Sig.
Between Groups 2 61.674 .000
Within Groups 932    
  1. Is there a significant difference in the overall satisfaction level of women in each of the hprobgrp groups?

There is a significant difference in the overall satisfaction level of women in each of the hprobgrp groups.

  1. Interpret the post hoc test. When interpreting the post hoc test indicate the mean and standard deviation for each group and indicate which group was signifantly higher or lower from the other. If there is no difference between two groups indicate that as well.

The turkey post-hoc test result uindicated that the level of satisfaction difefred significantly between the groups based on the housing problem. Though, there was no significant difference in level of satisfaction between those people with one housing problem and those with two or more housing problem.

Statistical analysis is a powerful tool that helps researchers gain valuable insights into a set of data and make informed decisions based on the results. Therefore, it is important for nurses and other professionals to have adequate knowledge regarding statistical analyses. There is also a need to know which statistical tests should be used based on the nature of the data set and the purpose of the analysis. Two types of statistical tests that have widely been applied in research are Analysis of Variance (ANOVA) and T-tests (Mishra et al.,2019). ANOVA is applied in to determine whether three or more groups or populations are statistically different. On the other hand, t-tests are applied to determine whether two groups are statistically different (Liang et al.,2019). Therefore, these two tests play a key role since they offer the researcher a chance to understand the nature of variations between variables in research. Therefore, the purpose of this assignment is to summarize the interpretation of the ANOVA statistics provided in the SPSS Output.

The data provided is on the overall satisfaction and material well-being. The data provided covers descriptive statistics, tests for homogeneity of variance, ANOVA and multiple comparisons. The descriptive table shows the standard deviation, mean and 95% confidence interval for the dependent variables for each separate group, which forms part of the study. From the data provided, the mean for “two or more housing problems” was 10.57, the mean for “one housing problem” was 11.97, and the mean for “No housing problem” was 12.71. The standard deviations observed for the three categories are 2.594, 2.588, and 2.353.  It is also important to note that the overall mean for all three groups represented in the study was 11.80.

Another important aspect of this data output is the test of Homogeneity of Variances. Levene’s test was used to accomplish this analysis. This analysis of the F-test when testing the null hypothesis that the variance is equal across all the groups tested (Yi et al.,2022). It is observable that the p-value obtained from Levene’s tests was 0.122, which means that they are not significantly different as the value is greater than 0.05.

The ANOVA output also showed the interaction within the group and between the groups of  “material well-being” and “overall satisfaction” as part of the statistical tests. From the results, it is evident that there was a statistically significant difference between the group means. The p-value obtained for this analysis is 0.000, a value above 0.05, indicating statistical significance. As such, the mean of material well-being and overall satisfaction is statistically significant. Nonetheless, it is not possible to have an idea of how the groups under consideration are different from each other using this test. As such, it is important to apply a computation of multiple comparisons with a Tukey post hoc test.

The next important part of the analysis is the multiple comparisons of “material well-being” and “overall satisfaction”, with a 0.05 used as the level of significance. The analysis shows that the difference between the means of the tested groups is statistically significant. As earlier indicated, a deeper study of the groups requires the use of Tukey post hoc tests, which is the test known and used in accomplishing post hoc tests on one-way ANOVA tests. Therefore, this study employed the Tukey post hoc test since it forms a vital ANOVA. When ANOVA is used to test the similarity of three or more groups’ means, the statistical significance results would show that not all the tested group means are similar (Uysal, et al., 2019).

The ANOVA output fails to identify the particular differences between the mean pairs that are significant. As such, the post hoc tests are key to determining the differences between the means of multiple groups while controlling the standard errors. The difference in overall satisfaction between one housing program and no housing problems was found to be 0.739, which is significant.  The difference in overall satisfaction between no housing problems and two or more housing problems was 2.139, which is also significant. In addition, the difference between one housing problem and two or more housing problems was 1.401, which is also significant.

It is also evident from the table that there was a statistically significant difference between one housing problem and no housing problem since the obtained p-value was 0.001. The p-value of 0.001 was obtained for the comparison of no housing problem and two or more housing problems means, which is also statistically significant. Besides, the difference between one housing problem and no housing problem was also statistically different, with a p-value of 0.001 observed.


This assignment has focused on the t-tests and ANOVA for the provided data. The provided data was mainly on overall satisfaction and material well-being. Therefore, various analyses have been performed and reported. Descriptives, Tests of Homogeneity of Variance, ANOVA and multiple comparisons have all been explored.


Liang, G., Fu, W., & Wang, K. (2019). Analysis of t-test misuses and SPSS operations in medical research papers. Burns & Trauma7.

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 Anaesthesia22(4), 407.

Uysal, M., Akyuncu, V., TanYıldızi, H., Sümer, M., & Yıldırım, H. (2019). Optimization of durability properties of concrete containing fly ash using Taguchi’s approach and Anova analysis.  DOI: 10.7764/RDLC.17.3.364

Yi, Z., Chen, Y. H., Yin, Y., Cheng, K., Wang, Y., Nguyen, D., … & Kim, E. (2022). Brief research report: A comparison of robust tests for homogeneity of variance in factorial ANOVA. The Journal of Experimental Education90(2), 505-520.


Since entering the career of nursing, I believe that most nurses would like to gather as much experience as they can to become a proficient and well-rounded staff in this profession. Being a nurse for about six years now, I have spent the last two and a half years working my way up to become an intensive care unit (ICU) nurse. Being an ICU nurse is a specialty in itself that provides many nursing with the competitive pay, comprehensive benefits, and extensive learning experience in critical level of care. As the ICU can be a stressful environment for patients and families, with established long term consequences, the impact that this unique environment can have on healthcare professionals is increasingly being recognized.

What I have noticed while being a nurse in the critical care environment, I have noticed a significant increase in our nurse turnover rates for both local and traveling nurse staff. For as long as I have been working in this hospital (in a different unit at the time), many nurses are either not trained properly and/or experiencing burnout early on in their career due particularly in the ICU unit. The exposure of  nurses within a high acuity nursing environment without the proper support from our management has led to burnout. Furthermore, I have noticed that the ICU unit is the only unit with the least amount of local nurses that stay employed for at least two years into their career life.

Most of the staff nurses that I have worked with have expressed the desires to leave off-island in search for better opportunities or change in nursing career. Our hospital is going through a constant battle with recruiting and retaining their nursing staff, specifically more significant in the ICU unit. Our medical director is currently working alongside the hospital administrators about looking for ways to address the increase burnout that the staff nurses are experiencing and construct a resilient healthcare system. For as long as I have been working in this hospital (in a different unit at the time), many nurses are either not trained properly with the advanced skills needed dealing with life threatening illnesses and/or lack the skills to tackle critically ill conditions. As a result overall, burnout causes decrease in quality of care, poor performances, increase mortality in patients, and errors in the healthcare environment.

The impact that this unique environment can have on healthcare professionals is increasing therefore, as a DNP prepared nurse, to gain a more complete understanding of critical care well-being requires commitment to measure, develops interventions, and re-measure them. An analysis variation or ANOVA tests done for each survey or experimental results are significant and help us figure out if the studies prove our hypothesis. Inferential statistics takes data from samples and make generalizations about a population. Experimental analysis using t-test, to compare the means of two groups or ANOVA (analysis of variance) to analyze the difference between the means of more than two groups, would help make estimates about the population at study (nurses) and testing hypothesis to draw conclusions (Bhandari, 2020).

One of the chosen inferential articles that describe the prevalence of burnout in the ICU healthcare assessed in the included analysis of variance study (ANOVA) through PubMed, Medline, and a web of sciences article reviews and observational study designs. Within the articles, the most commonly used instruments for data collection include the Maslach burnout inventory (MBI), professional quality of life scale, work related behavior, and experience patterns. According to a 4 large scale research study reported that the burnout prevalence rates ranges between 28%-61%; this study suggests that ICU workers were slightly (about 20%) more prone to burnout than the average healthcare (Chuang, Tseng, Lin, Lin & Chen, 2016). The following risk factors reported include: age, sex, marital status, personality traits, work experiences, work environment, workload, shift work, ethical issues, and decision making choices.

In another article review done by Kerlin, McPeake & Mikkelsen (2020), being that ICU can be a stress environment for both patients and families; the impact that this environment can have on healthcare environment is being increasingly recognized. Challenging situations, exposure to high mortality and daily difficult workloads can lead to excessive stress and resultant in moral distress, leading to burnout syndrome. This cross-sectional study, most critical care nurses experience about 81% of one or more burnout symptoms. The framework presented in this article implies that multidisciplinary and coordinated cares are essential components to high quality critical care delivery. The publications are assessed for relevance to using data to support observational study designs that examine associations between any risk factors and burnout in the ICU setting.

In a systematic meta-analysis done by Ramirez-Elvira (2021), the ANOVA is  carried out with different articles and journals from Medline and CINAHL following the PRISMA (preferred reporting item for systematic reviews and meta-analysis), with a sampling of N= 1989; there was an estimate of about 31% prevalence for high emotional exhaustion, 18% high depersonalization, and 49% low personal achievement (p.2). Furthermore, in an inferential statistical cross-sectional total population study among N=60 nurses using a self-administered MBI questionnaire resulted into a high burnout percentage of about 62% (Cishahayo, Nankundwa, Sego, & Bhengu, 2017). Burnout is measured through high emotional exhaustion (48%), high depersonalization (25%), and low personal accomplishment (50%).

On a much larger and international scale, in study done by Bhagavathula (2018), an institution based teaching hospital with a cross-sectional study conduced among healthcare providers N=500 serving about >50,000 population in Ethiopia; a questionnaire with sociodemographic details using descriptive analysis using correlation and multivariate logistic regression studied ANOVA using survey questionnaires of MBI scale. The overall prevalence of burnout is about 14%, respondents with debility was 53%, increase self criticism of about 56%, and depressive symptoms of about 46%. As a result, the nursing profession was a significant determinant for emotional exhaustion and burnout.

In conclusion, most inferential studies summarized above strengthens the application of evidenced based practices in promoting recruitment and retention policies in decreasing the risk of burnouts. Critical care courses and educational programs should be established by the support faculty to meet the needs of critical care assessments and criteria. Practice variability that necessitates changing for better conditions in a resource limited setting may excavate the underlying factors associated with nursing burnout.



Bhagavathula, A., Abegaz, T., Belachew, S., Gebreyohannes, E., Gebresillassie, B., & Chattu, V.

(2018). Prevalence of burnout syndrome among healthcare professionals working at Gondar University Hospital, Ethiopia. Journal of Educational Health Promotion 7(145). Retrieved from;year=2018;volume=7;issue=1;spage=145;epage=145;aulast=Bhagavathula

Bhandari, P. (2020). An introduction to inferential statistics. Scribbr Statistics. Retrieved

Chuang, C., Tseng, P., Lin, C., Lin, K. & Chen, Y. (2016). Burnout in the intensive care unit

professionals. Medicine Baltimore Journal. 95(50). Retrieved from

Cishahayo, E., Nankundwa, E., Sego, R., & Bhengu, B. (2017). Burnout among nurses working

in critical care settings: A case of a selected tertiary hospital in Rwanda. International Journal of Research in Medical Sciences. 5(12). Retrieved from

Kerlin, M., Mc Peake, J., & Mikkelsen, M. (2020). Burnout and joy in the profession of critical

care medicine. BMC Critical Care Journal. 24(98). Retrieved from

Ramirez-Elvira, S., Romero-Bejar, J., Suleiman-Martos, N., Gomez-Urquiza, J., Monsalve-

Reyes, C., Canadas-Delafuentes, G…Albendin-Garcia, L. (2021). Prevalence, risk factors, and burnout levels in intensive care unit: A systematic review and meta-analysis. International Journal of Environmental Research and Public Health. 18.Retrieved from