# NUR 705 Discussion 12.1: Alternate Statistical Tests

## NUR 705 Discussion 12.1: Alternate Statistical Tests

I remember a short research project of testing the effectiveness of different water conditioners when I was in a 7th grade science class. The dependent variables were the three different water conditioners I chose to test. The independent variable was the degree of pH balance each water conditioner produced. If the measurements were normally distributed I could use the one way analysis of variation (ANOVA) to measure the difference in proportions of the water conditioner ability to correct the pH. In the case of the measurements not being normally distributed, an alternative test to propose would be the Kruskal-Wallis test. This alternative test scores and ranks the different groups. In this study the Krystal-Wallis test would rank the effectiveness of the water conditioners. I would use this test because it would determine which water conditioner is the most effective.

References

Polit, D. F., & Beck, C. T. (2021). Nursing research: Generating and assessing evidence for nursing practice (11th ed.). Wolters Kluwer.

Stephanie,

I love how an experiment from the 7th grade was relatable to the content we are discussing this week. In terms of a research study, can you elaborate more on the purpose? I know that you noted the study evaluated hair conditioners and looked at the pH value; however, what did researchers want to find? Did you want a high or low pH? What is the scale that determines the effectiveness of a conditioner? Perhaps you may want to identify the favorable outcome of this study to help create more of an understanding of what is favored in terms of pH balance. Looking at the variables of the study, have you considered looking at the pH balance as the dependent variable and the type of conditioner used as the independent variable? The reason I consider this is because an independent variable is explained as “A variable that stands alone and isn’t affected by other variables that the study is trying to understand. Independent variables influence dependent variables” (National Library of Medicine, 2022). That said, I was viewing your study to comprehend the variables from an opposite outlook. The ANOVA test was your choice of test if the data were in a normal distribution. The Krystal-Wallis test is your test of choice if the data was not normally distributed. I was reading more on this test and found a great source from the University of Virginia. The reference goes through what a Krystal-Wallis test is and the process of conducting this test. I thought it would be an extra useful source for you to look into!

-Rana

References

National Library of Medicine. (2022). *Dependent and Independent Variables. *https://www.nlm.nih.gov/nichsr/stats_tutorial/glossary.html#IndependentVariable (Links to an external site.)

Lomuscio*. *(2021, December 7). *Getting Started with the Kruskal-Wallis Test*. The University of Virginia. https://data.library.virginia.edu/getting-started-with-the-kruskal-wallis-test/ (Links to an external site.)

Rana, thank you for your reply. This research project aimed to test the different water conditioners used for fish tanks to determine if one was better. The pH was adjusted to ensure the water was habitable for fish. When I initially wrote this post, I thought that it had been included. Sorry for leaving that out. I agree with your recommendations regarding the ANOVA and Krystal-Wallis tests based on the data distribution. In truth, I wish I had known about those types of tests when I had been in 7th grade because it would have been a great addition to my project! If I recall correctly, all three water conditioners that were tested properly balance the pH. Thanks again for your reply.

Hello Stephanie.

I very much agree with you analysis. It is in order to use Kruskal-Wallis test instead of ANOVA in case that data presented does not exhibit a normal distribution. The choice of ANOVA statistical test is important in your case given the dependent variables are three (MacFarland & Yates, 2018). There are a few general guidelines that can help you decide which test to use. If your data are normally distributed, then you should use ANOVA (Rayner & Livingston, 2020). If your data are not normally distributed, then you should use the Kruskal-Wallis test. Additionally, if you have more than two groups of data, you should use the ANOVA test. If you have only two groups of data, you should use the Kruskal-Wallis test. The Kruskal-Wallis test is a nonparametric statistical test used to compare the medians of three or more groups (Cabral & Lucena, 2020). It is often used when the data are not normally distributed. The Kruskal-Wallis test is an alternative to the one-way ANOVA, and it is particularly useful when there are an uneven number of observations in the different groups. Nice work!

**References**

Cabral Júnior, J. B., & Lucena, R. L. (2020). Analysis of precipitation using Mann-Kendall and kruskal-wallis non-parametric tests. *Mercator (Fortaleza)*, *19*. https://doi.org/10.4215/rm2020.e19001 (Links to an external site.)

MacFarland, T. W., & Yates, J. M. (2018). Kruskal–Wallis H-test for oneway analysis of variance (ANOVA) by ranks. In *Introduction to nonparametric statistics for the biological sciences using R* (pp. 177-211). Springer, Cham. https://link.springer.com/chapter/10.1007/978-3-319-30634-6_6 (Links to an external site.)

Rayner, J. C. W., & Livingston, G. (2020). The Kruskal–Wallis tests are Cochran–Mantel–Haenszel mean score tests. *Metron*, *78*(3), 353-360. https://link.springer.com/article/10.1007/s40300-020-00192-4

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For this example, I will look at the effects of gender on a person’s salary. The variables I would measure in this test are the gender of the participants and their average yearly salary. Gender pay gaps have been discussed for years and I would want to analyze that in nursing, there is a significance between gender and salary. The parametric statistical test I would run if the data was normally distributed is an independent samples t-test. I would use this test because I can compare the mean values of two samples to see if there is statistical evidence that gender has an effect on salary. If that data is non-normal or not normally distributed, I would use this test to analyze the data with a Wilcoxon rank-sum test, a non-parametric test. This test “compares the medians and rank order distribution of ordinal level data and skewed interval/ratio data, respectively” (McKechnie & Fisher, 2019). A t-test is considered a parametric test and is more used in research. Typically, parametric tests are preferred because they are generally better because they can distinguish data better than non-parametric tests, such as the Wilcoxon rank-sum test (McKechnie & Fisher, 2019). The method of testing and analyzing data depends on the variables, sample size, and other study factors. Of course, I would follow the steps of a study by formulating a hypothesis and null hypothesis, identifying the variables and external factors. That said, I would follow the methods of the tests provided (here being the Wilcoxon rank-sum test if the data is not normally distributed) and with those results of the compared medians analyze if the hypothesis is rejected or not. The method of testing and analyzing data depends on the variables, sample size, and other study factors. While this is just an example, this is one of the ways I can analyze data using a data set that is not normally distributed.

References

McKechnie & Fisher (2019). *Considerations when choosing a statistical method for data analysis*. Journal of the Australasian Rehabilitation Nurses’ Association (JARNA). https://doi.org/10.33235/jarna.22.3.20-29

Rana, great post!

I agree with your research study idea, and it would be interesting to see the results. I have heard of wage differences based on gender predominately in the corporate or business sector. Something to consider within your study are wages being compared equally to experience and education along with their respected genders. Another consideration would be location. Depending on what part of the country, urban or rural setting, and even the type of hospital could all be important factors within your analysis. What are your thoughts on comparing wages internationally as well? It may offer some interesting results. This is a great post, and I think you outlined how you would perform this study very well.

Hello Rana.

Great discussion. Your proposed study on the effects of gender on salary is a great example. I couldn’t agree more with you. I have learned that independent sample t-test is applied when one variable is continuous and normally distributed while the other one is categorical. The independent samples t-test is used to determine whether the means of two groups are statistically different from each other (Sanders et al., 2019). This test is most commonly used when the two groups are randomly sampled from a larger population. The independent samples t-test can be used to compare the mean scores of two groups on a single variable, or it can be used to compare the proportions of two groups who fall into different categories on a categorical variable. In order to use the test, data must meet several requirements: -The data must be continuous and measured on an interval scale. -The data must be randomly sampled from two distinct populations. -The sample sizes must be equal or nearly equal. When data is not normally distributed, Wilcoxon rank-sum test can be used instead of independent sample t-test (Kassambara, 2019). The Wilcoxon rank-sum test is a statistical test used to compare two samples. It is similar to the student’s t-test, but instead of using the means of the two samples, it uses the ranks of the values from each sample. The Wilcoxon rank-sum test is used when the two samples are not normal distributions (Liang et al., 2019). It is also used when the two samples have different sizes or when there are outliers in one or both of the samples. To calculate the Wilcoxon rank-sum test, first calculate the ranks for each value in both samples. Then add up the ranks for all of the values in each sample. Nice work!

**References**

Kassambara, A. (2019). Comparing groups: Numerical variables. http://www.datanovia.com/en/wp-content/uploads/dn-tutorials/book-preview/r-statistics-for-comparing-means_preview.pdf (Links to an external site.)

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 (Links to an external site.)

Sanders, K., Sheard, J., Becker, B. A., Eckerdal, A., & Hamouda, S. (2019, July). Inferential statistics in computing education research: A methodological review. In *Proceedings of the 2019 ACM conference on international computing education research* (pp. 177-185). https://doi.org/10.1145/3291279.3339408

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