Walden University NURS 8201 WEEK 5 ASSIGNMENT: T-TESTS AND ANOVA-Step-By-Step Guide

This guide will demonstrate how to complete the Walden University NURS 8201 WEEK 5 ASSIGNMENT: T-TESTS AND ANOVA assignment based on general principles of academic writing. Here, we will show you the A, B, Cs of completing an academic paper, irrespective of the instructions. After guiding you through what to do, the guide will leave one or two sample essays at the end to highlight the various sections discussed below.

How to Research and Prepare for NURS 8201 WEEK 5 ASSIGNMENT: T-TESTS AND ANOVA                       

Whether one passes or fails an academic assignment such as the Walden University NURS 8201 WEEK 5 ASSIGNMENT: T-TESTS AND ANOVA depends on the preparation done beforehand. The first thing to do once you receive an assignment is to quickly skim through the requirements. Once that is done, start going through the instructions one by one to clearly understand what the instructor wants. The most important thing here is to understand the required format—whether it is APA, MLA, Chicago, etc.

After understanding the requirements of the paper, the next phase is to gather relevant materials. The first place to start the research process is the weekly resources. Go through the resources provided in the instructions to determine which ones fit the assignment. After reviewing the provided resources, use the university library to search for additional resources. After gathering sufficient and necessary resources, you are now ready to start drafting your paper.

How to Write the Introduction for NURS 8201 WEEK 5 ASSIGNMENT: T-TESTS AND ANOVA                       

The introduction for the Walden University NURS 8201 WEEK 5 ASSIGNMENT: T-TESTS AND ANOVA is where you tell the instructor what your paper will encompass. In three to four statements, highlight the important points that will form the basis of your paper. Here, you can include statistics to show the importance of the topic you will be discussing. At the end of the introduction, write a clear purpose statement outlining what exactly will be contained in the paper. This statement will start with “The purpose of this paper…” and then proceed to outline the various sections of the instructions.

How to Write the Body for NURS 8201 WEEK 5 ASSIGNMENT: T-TESTS AND ANOVA                       

After the introduction, move into the main part of the NURS 8201 WEEK 5 ASSIGNMENT: T-TESTS AND ANOVA  assignment, which is the body. Given that the paper you will be writing is not experimental, the way you organize the headings and subheadings of your paper is critically important. In some cases, you might have to use more subheadings to properly organize the assignment. The organization will depend on the rubric provided. Carefully examine the rubric, as it will contain all the detailed requirements of the assignment. Sometimes, the rubric will have information that the normal instructions lack.

Another important factor to consider at this point is how to do citations. In-text citations are fundamental as they support the arguments and points you make in the paper. At this point, the resources gathered at the beginning will come in handy. Integrating the ideas of the authors with your own will ensure that you produce a comprehensive paper. Also, follow the given citation format. In most cases, APA 7 is the preferred format for nursing assignments.

How to Write the Conclusion for NURS 8201 WEEK 5 ASSIGNMENT: T-TESTS AND ANOVA                       

After completing the main sections, write the conclusion of your paper. The conclusion is a summary of the main points you made in your paper. However, you need to rewrite the points and not simply copy and paste them. By restating the points from each subheading, you will provide a nuanced overview of the assignment to the reader.

How to Format the References List for NURS 8201 WEEK 5 ASSIGNMENT: T-TESTS AND ANOVA                       

The very last part of your paper involves listing the sources used in your paper. These sources should be listed in alphabetical order and double-spaced. Additionally, use a hanging indent for each source that appears in this list. Lastly, only the sources cited within the body of the paper should appear here.

Stuck? Let Us Help You

Completing assignments can sometimes be overwhelming, especially with the multitude of academic and personal responsibilities you may have. If you find yourself stuck or unsure at any point in the process, don’t hesitate to reach out for professional assistance. Our assignment writing services are designed to help you achieve your academic goals with ease. 

Our team of experienced writers is well-versed in academic writing and familiar with the specific requirements of the NURS 8201 WEEK 5 ASSIGNMENT: T-TESTS AND ANOVA assignment. We can provide you with personalized support, ensuring your assignment is well-researched, properly formatted, and thoroughly edited. Get a feel of the quality we guarantee – ORDER NOW. 

T-TESTS AND ANOVA NURS 8201

T-TESTS AND ANOVA NURS 8201

Student t-test is often applied in the statistical analysis to test hypothesis. In the SPSS output, the results of t-test can be translated in different ways. In other words confidence interval can be applied as well as the significant values obtained. T-test is a form of inferential statistics that is always applied to determine if there is a significant different between the means of two variables or two groups in a dataset (Kim, 2015). The two variables may be related in certain features. While performing t-test, there are always assumptions that have to be made. For example, there is always assumption of equality of variance. Some other assumptions that are always made include normality of data distribution, adequacy of sample size, the data is also assumed to be randomly sampled. The independent sample t-test or two sample t-test is always performed when one variable being considered is categorical while the other is continuous. The continuous variable must have a normal distribution (Delacre et al., 2017).

T-distribution is always considered to be a continuous probability distribution that often arise from the estimation of the mean of a given population with a normal distribution. In most cases t-test is applied in proving hypothesis (Champely et al., 2017). There are different approaches that can be applied in either rejecting or accepting null hypothesis (Test et al., 2018). In t-test, there is always the testing of the difference between the two samples under consideration when the variances of the two variables are unknown. Assumptions of normality are essential in ensuring accurate or effective processes in the statistical analysis. There is always the need to consider the scale of measurement in the process of undertaking t-test. In most cases, the scale of measurement applied to the data under analysis should always follow an ordinal or continuous scale. Homogeneity of variance is another assumption that is always made regarding t-test (Kim & Park, 2019). In other words, the variance of data under each variable should be equal to ensure that there is effective outcomes in the process of comparing the means using t-test.   

Click here to ORDER an A++ paper from our Verified MASTERS and DOCTORATE WRITERS: T-TESTS AND ANOVA NURS 8201 

Two sample t-test or the independent sample t-test is often used in data analysis to compare the means of two independent groups to test whether there is a statistical evidence that the associated population means have a significant difference. Just like any other t-test, the independent t-test is a parametric test. The independent sample t-test is always recommended when one variable is categorical while the other variable is continuous and normally distributed. In this case, weight is a continuous variable while sex is a categorical variable (Jeanmougin et al., 2018).

The independent sample t-test is most commonly applied in testing the statistical difference between the means of the given two groups. It can also be applied in the determination of the statistical difference between the means of two interventions. Finally, independent sample t-test can be applied in the determination of statistical difference between the means of two change scores. The independent sample t-test can only be applied in comparing the means for two and only two groups (Kruschke, 2018). 

Two sample t-test or the independent sample t-test is often used in data analysis to compare the means of two independent groups to test whether there is a statistical evidence that the associated population means have a significant difference. Just like any other t-test, the independent t-test is a parametric test. The independent sample t-test is always recommended when one variable is categorical while the other variable is continuous and normally distributed. In this case, weight is a continuous variable while sex is a categorical variable (Jeanmougin et al., 2018).

The independent sample t-test is most commonly applied in testing the statistical difference between the means of the given two groups. It can also be applied in the determination of the statistical difference between the means of two interventions. Finally, independent sample t-test can be applied in the determination of statistical difference between the means of two change scores. The independent sample t-test can only be applied in comparing the means for two and only two groups (Kruschke, 2018). 

An example of a research question that can be explored using a nonparametric test is; what is the effect of media advertisements on the perception of body image by teenage girls? This question has both dependent and independent variables. The dependent variable is the perception of the body image. It is the dependent variable since it is the outcome measure in the research. It can also be influenced by the independent variable. The independent variable in this type of research question is media advertisements. It is an independent variable because it cannot be manipulated. It also influences the behavior or the outcomes of the dependent variable. The levels of data include nominal, ordinal, ratio, and interval levels of measurement. The nominal level is the lowest in the rank while the ratio level is the highest that has a true zero (Weaver, 2017). The variables in this research topic are ordinal level variables. An example of a non-parametric test that can be used to measure these variables is Mann-Whitney U test. This is a non-parametric test of t-test. It will provide insight into whether there is similarity in distribution in two independent samples (Corder & Foreman, 2014). The test will tell whether the distribution of the samples had an effect on the outcomes or not.

References

Corder, G. W., & Foreman, D. I. (2014). Nonparametric statistics: A step-by-step approach. Hoboken, New Jersey: Wiley.

Weaver, K. F. (2017). An introduction to statistical analysis in research: With applications in the biological and life sciences. Hoboken, NJ : John Wiley & Sons, Inc.

The topic in which I focused on as a discussion, highlighted the point that there is an increasing number of nurse prescribers (NIP), however, there is little evidence that exists about their antibiotic prescribing practices (Ness, Currie, Reilly, McAloney-Kocaman, & Price, 2021). The article reports that the objective of the study was to measure nurse independent prescribers, who are managing the care of patients presenting with an upper respiratory tract infection for the first time, without prescribing an antibiotic, and assess what are the determinants for not prescribing antibiotics (2021).

The literature shared that the inferential analysis was carried out using Spearman’s correlation to explore the relationship of the direct and indirect measures (independent variables) with intention (dependent variable) (2021). The analysis identified the significant predictors of intention for the multiple linear regression model, which was used due to the ordinal nature of the data and lack of normality. Also, the researchers used the Test-retest reliability to carry out the study by asking participants to complete the questionnaire again two weeks later and Spearman’s ρ correlation coefficient was used to check for stability of indirect measures. In my opinion, this strengthened the research (2021).  In my opinion, this standard of practice strengthened. 

Study Findings

The findings from 184 participants it was found that NIPs intended to manage their patients who presented with a URTI for the first time, without prescribing an antibiotic (2021). Key determinants were perceived norm, perceived behavioral control, and moral norm for this study (2021).

ANOVA

Calculating statistical data to obtain the mean is often a long and tedious process (Rosenfeld, 2021). The t-test and the one-way analysis of variance (ANOVA) are the two most common tests used for this purpose (2021). The literature reports that in the first decades of the twentieth century, an Englishman by the name of Ronald Aylmer Fisher radically changed the use of statistics in research (2021). He invented the technique called Analysis of Variance and founded the entire modern field called Design of Experiments (2021). ANOVA is a test that provides a global assessment of a statistical difference in more than two independent means (Sullivan, 2021).

ANOVA Example

A clinical trial is run to compare weight loss programs and the participants are randomly assigned to one of the comparison programs and these individuals are counseled on the details of the assigned program (Sullivan, 2021). Partakers in the test followed the assigned program for 8 weeks. The outcome of interest focused on is weight loss, in which is defined for the study as the difference in weight measured at the start of the study (baseline) and weight measured at the end of the study (8 weeks), measured in pounds.

The trial included three popular weight loss programs. The first one is a low-calorie diet. The second is a low-fat diet and the third is a low carbohydrate diet. For comparison purposes, the team built in a fourth group as a control lineup (2021). The trial implemented the ANOVA by using the following five-step approach.

 Set up hypotheses and determine the level of significance

Select the appropriate test statistic

Set up decision rule.

Compute the test statistic

Conclusion

T-Test

William Sealy Gosset introduced the t-statistic in 1908 (Peckinpaugh, 2018). The t-test is a statistical hypothesis test where it follows a Student’s t – distribution if the null hypothesis is supported (2018). The t-test conveys how significant the differences between groups are; In other words, the t-test identifies if the differences (measured in means) could have happened by chance (2018). With that being said, both the t-test as well as the ANOVA looks at the difference in means and the spread of the distributions (i.e., variance) across groups; however, the ways that they determine the statistical significance are different (Peckinpaugh, 2018). The t-test is used when determining whether two averages or means are the same or different (2018). A t-test has more odds of committing an error when more means are used, which is why ANOVA is used when comparing two or more means (2018).

 T-Test Example

T-tests can be used in real life to compare averages (Glen, 2021). For example, a drug company may want to test a new cancer drug to find out if it improves life expectancy. In an experiment, there’s always a control group (Glen, 2021). The control group may show an average life expectancy of +5 years, while the group taking the new drug might have a life expectancy of +6 years (2021). It would seem that the drug might work. But it could be due to a fluke. To test this, researchers would use a t-test to find out if the results are repeatable for an entire population. There are three main types of t-test:

An Independent Samples t-test compares the means for two groups.

A Paired sample t-test compares means from the same group at different times (say, one year apart).

A-One sample t-test tests the mean of a single group against a known mean.

Use the following tools to calculate the t-test:

How to do a T-test in Excel.

T-test in SPSS.

T distribution on the TI 89.

T distribution on the TI 83.

Reference

 Circulation (2008). Analysis of variance Retrieved From https://doi.org/10.1161/CIRCULATIONAHA.107.654335Circulation. 117:115–121

 Glen, S., (2021). T-Test (Student’s T-Test): Definition and Examples From StatisticsHowTo.com: Elementary Statistics for the rest of us! https://www.statisticshowto.com/probability-and-statistics/t-test/

 Franscisco, (2017). Difference Between T-TEST and ANOVA. Difference Between Similar Terms and Objects. http://www.differencebetween.net/miscellaneous/difference-between-t-test-and-anova/.

 Ness, V., Currie, K., Reilly, J., McAloney-Kocaman, K., & Price, L. (2021). Factors associated with independent nurse prescribers’ antibiotic prescribing practice: a mixed-methods study using the Reasoned Action Approach. Journal of Hospital Infection, 113, 22–29. https://doi-org.ezp.waldenulibrary.org/10.1016/j.jhin.2021.04.008

 Rosenfeld, B., Vermont Mathematics Initiative (2021) https://higherlogicdownload.s3.amazonaws.com/AMSTAT/1484431b-3202-461e-b7e6-ebce10ca8bcd/UploadedImages/Classroom_Activities/HS_8__FISHER_and_Design_of_experiments.pdf

 Sullivan, L., (2021). Hypothesis Testing – Analysis of Variance (ANOVA). https://sphweb.bumc.bu.edu/otlt/mph-modules/bs/bs704_hypothesistesting-anova/bs704_hypothesistesting-anova_print.html

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?

Photo Credit: Dave and Les Jacobs / Blend Images / Getty Images

In the scenario provided, you might decide to use, the Analysis of Variance (ANOVA) approach.  “ANOVA 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 variable” (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 Grove’s the practice of nursing research: Appraisal, synthesis, and generation of evidence (9th ed.). Elsevier.}

To Prepare:

• Review the Week 5 ANOVA Exercises SPSS Output provided in this week’s Learning Resources.
• Review the Learning Resources on how to interpret ANOVA results to determine differences.
• Consider the results presented in the SPSS output and reflect on how you might interpret the results presented. 

The Assignment: (2–3 pages)

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

Main Post

Mental health research in genetic predisposition has been an interest for many researchers. Genetic testing has assisted researchers in detecting different disorders. One of the more fascinating studies is in the exploration of genetic factors that affect mental illness or can be identified (Andreassen, 2023). Mental health treatment has focused on clinical observation versus new approaches like genetic testing. So further understanding of how genetics can impact mental health treatment needs to be explored. Using inferential statistics, information can be computed to conclude and make inferences about the population based on a sample data set (Gray, 2020, p. 639). People are fascinated by the outcomes of genetic testing, especially for health conditions.

Genetic Testing

Polygenic risk score (PRS) measures the genetic contribution of a given trait or condition (Peck, 2022, p. 81). The study wanted to identify people’s motivation for seeking PRS, understanding the results, and their psychological reactions to receiving this information among individuals by uploading their DNA to third-party websites (Peck, 2022, p. 82). The study recruited staff from health and technology companies along with informed consent and genetic counseling about PRS (Peck, 2022). The study recruited users of Impute.me that identified 166 different conditions from genetic data (Peck, 2022, p. 82). A survey also involved demographic items (i.e., age, sex, gender, ethnicity, education level, household income, history of psychiatric illness, and time between receiving results from the tests (Peck, 2022, p. 82). 

Sample of Study

The study had 10.650 people eligible for analysis; 438, which was 4.1%, clicked on the link for more information, and 277 participated. Respondents were mainly female at 144, males at 82, White at 200, African at 2, South Asian at 3, East Asian at 4, Middle Eastern at 2, Hispanic/Latino at 2, Indigenous at 2, and others at 11. Education level was from less than high school to graduate degree level. Most respondents had a higher level of education, from some college to graduate. The income level was from less than 40,000 to 100,000+.  

Sources of Data

The surveys used a four-point Likert scale to rate the reasons for taking the test. The participants were also provided with a list of 58 conditions that were most inquired about. A yes and no statement was also to see if the participants understood the results. The FACToR scale has 12 items with subscales for negative emotions, positive emotions, uncertainty, and privacy concerns.

Data Analysis

The study was mainly descriptive but used exploratory statistics to explore relationships between the IES-R and FACToR. Other variables for demographics used t-test and ANOVA with posthoc Tukey to further examine significant relationships (Peck, 2022, p. 82)

Results

Most participants were interested in getting the results and accessing health information n=270. The condition frequently identified by participants was Alzheimer’s, anxiety disorder, major depression, type 2 diabetes, and breast cancer (Peck, 2022, p. 84). After examining the data, the use of t-test and ANOVA to address variables of adverse reactions was successful in the results—some further exploration and limitations of PRS. There were limitations to the study due to not being representative of the overall population, especially cultural significance.

References

Andreassen, O. H. (2023, December 27). New insights from the last decade of research in psychiatric genetics: discoveries, challenges, and clinical implications. World Psychiatry, pp. 22:4-24.

Gray, J. G. (2020). Burns and Grove’s the practice of nursing research: Appraisal, synthesis, and generation of evidence. St. Louis: Elsevier.

National Institute of Mental Health. (2023, December 27). Looking at my genes: What can they tell me about my mental health? Retrieved from National Institute of Health: https://www.nimh.nih.gov

Peck, L. B. (2022). Why do people seek out polygenic risk scores for complex disorders, and how do they understand and react to results? European Journal of Human Genetics, 30:80-87.

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:

• Please save your Assignment using the naming convention “WK5Assgn+last name+first initial.(extension)” as the name.
• Click the Week 5 Assignment Rubric to review the Grading Criteria for the Assignment.
• Click the Week 5 Assignment link. You will also be able to “View Rubric” for grading criteria from this area.
• Next, from the Attach File area, click on the Browse My Computer button. Find the document you saved as “WK5Assgn+last name+first initial.(extension)” and click Open.
• If applicable: From the Plagiarism Tools area, click the checkbox for I agree to submit my paper(s) to the Global Reference Database.
• Click on the Submit button to complete your submission.

Grading Criteria

To access your rubric:

Week 5 Assignment Rubric

Check Your Assignment Draft for Authenticity

To check your Assignment draft for authenticity:

Submit your Week 5 Assignment draft and review the originality report.

Submit Your Assignment by Day 7 of Week 5

To participate in this Assignment:

Week 5 Assignment

---

What’s Coming Up in Week 6?

Photo Credit: [BrianAJackson]/[iStock / Getty Images Plus]/Getty Images

Next week, you will continue your exploration of quantitative data. You will explore correlations and consider when it is best to utilize this statistical approach for quantifying relationships between variables. 

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.

Conclusion

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.

References

Liang, G., Fu, W., & Wang, K. (2019). Analysis of t-test misuses and SPSS operations in medical research papers. Burns & Trauma, 7. https://doi.org/10.1186/s41038-019-0170-3

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. https://doi.org/10.4103%2Faca.ACA_94_19

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 Education, 90(2), 505-520. https://doi.org/10.1080/00220973.2020.1789833