What are the advantages and disadvantages of using parametric and non-parametric tests?

The first step before reaching for statistical software, is to use Professor Deming's Operational Definition to ask: "1. What are you trying to achieve?". If the answer to the question is that you have a process for which you want to ensure good quality, now and into the future, move to the next question: 2. "By what means?" The answer is the control chart. Testing for normality, then turning to non parametric methods is pure folly. Control charts work for any data distribution. Control charts incorporate the sequence of the data. They are the only way to ensure that your process is operating on target with minimum variance. The final part is: "3. How will you know?" If your control chart shows data within control limits ...

Parametric tests assume specific population distributions and require interval or ratio data. Advantages include high power and precision, but they demand strict assumptions. Non-parametric tests are distribution-free and applicable to ordinal or nominal data. They're robust but less powerful with smaller sample sizes. Choosing depends on data characteristics, with parametric tests preferred for normal data and larger samples, while non-parametric tests offer robustness in the face of skewed data or small sample sizes.

Choose between parametric and non-parametric tests based on your data characteristics, research objectives, and assumptions. Remember that robust statistical analyses play a crucial role in making informed decisions.

Parametric tests assume that the data being analyzed follows a specific distribution, usually a normal distribution. These tests are often more powerful than non-parametric tests, meaning they are better at detecting differences when they exist. They also tend to provide more precise estimates of the effect size. However, parametric tests require the data to meet certain assumptions, such as normality and homogeneity of variances. Violations of these assumptions can lead to inaccurate results. Additionally, parametric tests may not be suitable for small sample sizes or data that does not follow a normal distribution.

Non-parametric tests, on the other hand, do not rely on specific distributional assumptions. They are more robust to violations of assumptions, making them suitable for a wider range of data types. Non-parametric tests are particularly useful when dealing with ordinal or skewed data. However, non-parametric tests are generally less powerful than parametric tests, meaning they may be less likely to detect differences when they exist. They also tend to provide less precise estimates of effect size.

When choosing between parametric and non-parametric tests, one must consider the nature of the data and the assumptions underlying each test. Parametric tests, such as t-tests and ANOVA, are suitable for normally distributed data and require specific assumptions about the population parameters. Non-parametric tests, like the Mann-Whitney U test and Kruskal-Wallis test, are more robust to violations of assumptions and can be used with non-normal or ordinal data. Researchers should assess the distribution of their data, the level of measurement, and the assumptions of each test before making a selection. Consulting with a statistician or using software tools can also aid in making an informed decision.

The choice between parametric and non-parametric tests depends on several factors. If the data meets the assumptions of parametric tests and the sample size is adequate, parametric tests may be preferred for their greater power and precision. However, if the data does not meet the assumptions or if the sample size is small, non-parametric tests may be more appropriate due to their robustness.

In addition to the assumptions and sample size, other factors should be considered when choosing between parametric and non-parametric tests. These include the research question, the nature of the data, and the specific test being used. It is also important to consider the ease of interpretation of the results and the practical implications of the findings.