Parametric analysis

Parametric analysis is the data collected by production engineers with well modeling and decision-making techniques. (OspreyData Marketing. 2021). A non-parametric analysis does not mean that our engineer does not know about the population, but it means that the collected data does not have a normal distribution. In case of not normal distributed data, we conduct those tests made for non-parametric statistics such as Wilcoxon signed-rank test or others that we explain here in more detail.

T-Test

The t-test is an inferential statistical analysis used to study two different groups. Mathematically, a t-test addresses the problem by assuming that the means of the two groups' distributions are equal with a null hypothesis of (H0: u1=u2). The t-test will show a high probability of differences in these two groups when rejected (H0: u1=u2). 
More importantly, a t-test is conducted for a group of 20 to a maximum of 30 people; otherwise, it is not suggested. However, other tests can maximize the analysis accuracy for more than 30 people in groups. (Fernandez, 2021)  
The t-test could be used for a parametric analysis to draw out the inference about data from different groups; however, the engineer failed to comply with this article's parametric analysis data collection, so we can not use the t-test for that purpose.

F-Test

The f-test or f-distribution or ANOVA is used when at least three groups of samples exist to analyze. F-test conducts for a parametric analysis to get the results of the equality of groups' variances. F-test is called a "parametric test" also because of the "presence of parameters in the F- test. These parameters in the F-test are the mean and variance." (Lani, 2021) Therefore, our engineer of this article can not use the f-test because of failing to comply with the parametric test.

Chi-square test

The Chi-square test (distribution-free test) is especially non-parametric analysis statics, and it is used for data when the level of data is nominal or ordinal. Therefore, this test fits our analysis in this article when our engineer's data collection is not complying with parametric statistics.

Mann–Whitney U test

The Mann–Whitney U test is a non-parametric data analysis tool for the independent samples and groups. This test compares the means of different and separate groups of data. So, Mann–the Whitney U test is also a good technique for our engineer to conduct the analysis.

Wilcoxon signed-rank test

The Wilcoxon signed-rank test is a non-parametric data analysis and is the best fit for our analysis, and we can use this test for our collection of data in this article.

Kruskal–Wallis test

The Kruskal–Wallis test is an extended version of the Wilcoxon signed-rank test and a one-way analysis of variance (ANOVA). Kruskal–Wallis test is a non-parametric analysis, so that we can use this test for our purpose also.

Reference

1. Fernandez, J. (2021, December 14). The statistical analysis t-test is explained for beginners and experts. Medium. Retrieved 2022, from https://towardsdatascience.com/the-statistical-analysis-t-test-explained-for-beginners-and-experts-fd0e358bbb62

2. Lani, J. (2021, July 27). F-test. Statistics Solutions. Retrieved 2022, from https://www.statisticssolutions.com/f-test/

3. OspreyData Marketing. (2021, June 14). What is Parametric Analysis? OspreyData. Retrieved 2022, from https://ospreydata.com/what-is-parametric-analysis/