*PUB 550 Explain the differences between parametric and nonparametric tests*

PUB 550 Explain the differences between parametric and nonparametric tests

The population distribution from which the sample was drawn is assumed to be uniform in parametric statistics. Nonparametric statistics don’t rely on presumptions; therefore, data can be gathered from samples that don’t fit any distribution.

Your data need not follow the normal distribution in order to use nonparametric tests. They are sometimes referred to as distribution-free tests, and in some circumstances they can be useful. In general, parametric tests are more familiar to those who do statistical hypothesis testing than nonparametric tests.

If your data is not normally distributed, it is recommended to utilize nonparametric tests, or something similar. Although it appears like a simple approach to decide, there are other factors to consider.

### Statistics using parametric and nonparametric methods

You should carefully assess the assumptions’ veracity and take into account a number of factors about the sample data and assumptions before deciding whether to employ parametric or nonparametric statistics.

### Benefits of parametric testing

Results from parametric tests can be trusted even when the distributions are skewed and non-normal.

When there is a difference in the degree of variability between the groups, parametric testing can produce reliable findings.

Greater statistical power is present in parametric tests.

Nonparametric Tests’ Benefits

Nonparametric tests measure the median, which is sometimes preferable for particular research topics.

When our sample size is small, and your data may not be normal, nonparametric tests are appropriate.

Ordinal data, ranking data, and outliers may all be examined using nonparametric tests.

### Reference:

Statistics – parametric and nonparametric. (2021). Retrieved from: https://www.ibm.com/docs/en/db2woc?topic=procedures-statistics-parametric-nonparametric

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**Parametric tests**

Has a higher statistical power. They are applied to normal or interval variables. They are used for large samples. Its data distribution is normal. They make a lot of assumptions. They require a higher condition of validity. Lower probability of errors.

The calculation is complicated to do. The hypotheses are based on numerical data. The calculations are too exact. It does not take missing values into account to obtain information.

**Nonparametric tests**

Lower statistical power means the test with less power is less likely to succeed in rejecting the null hypothesis. They are applied in categorical variables. They are used for small samples. The form of data distribution is not known.

They don’t make many assumptions. They require a lower condition of validity. Has a higher probability of errors. The calculation is less complicated to do. The hypotheses are based on ranges, median, and frequency of data. The calculations are not exact. And it considers missing values for information.

### Reference

Frost, J. (2022, June 2). *Nonparametric tests vs. parametric tests*. Statistics By Jim. Retrieved July 13, 2022, from https://statisticsbyjim.com/hypothesis-testing/nonparametric-parametric-tests/

### REPLY

With a non-parametric test, we are able to evaluate hypothesis for the entire population distribution. Non-

parametric tests are less powerful since they use less information in their calculations. A parametric correlation, for example, incorporates information about the mean and standard deviation, whereas a nonparametric correlation merely uses the ordinal position of pairs of scores. When your data isn’t normal, you’ll need to employ a nonparametric test. As a result, the objective is to determine whether your data is normally distributed. When you take look at the distribution of your data, for example. If your data is roughly normal, parametric statistical tests can be used. According to ByJus (2020) non-parametric tests measures central tendency of median values.

### References:

*Difference between parametric and non-parametric (in statistics)*. (2020, December 17). BYJUS. https://byjus.com/maths/difference-between-parametric-and-nonparametric

### REPLY

Nonparametric tests don’t require that your data follow the normal distribution. They’re also known as distribution-free tests and can provide benefits in certain situations. It’s true that nonparametric tests don’t require data that are normally distributed. However, nonparametric tests have the disadvantage of an additional requirement that can be very hard to satisfy. The groups in a nonparametric analysis typically must all have the same variability (dispersion). Nonparametric analyses might not provide accurate results when variability differs between groups.

Conversely, parametric analyses, like the 2-sample t-test or one-way ANOVA, allow you to analyze groups with unequal variances. For some datasets, nonparametric analyses provide an advantage because they assess the median rather than the mean. The mean is not always the better measure of central tendency for a sample. Even though you *can* perform a valid parametric analysis on skewed data, that doesn’t necessarily equate to being the better method. Parametric tests can analyze only continuous data and the findings can be overly affected by outliers. Conversely, nonparametric tests can also analyze ordinal and ranked data, and not be tripped up by outliers.

### Reference

Frost, J. (2022, June 2). *Nonparametric tests vs. parametric tests*. Statistics By Jim. Retrieved July 13, 2022, from https://statisticsbyjim.com/hypothesis-testing/nonparametric-parametric-tests/

The parametric check is the hypothesis that affords generalizations for making statements approximately the imply of the figure population. The nonparametric test is described because the speculation test which isn’t based totally on underlying assumptions, does not now require the population’s distribution to be denoted by using particular parameters. “A statistic estimates a parameter. Parametric statistical procedures assume that the sample distribution is about the same shape (ie, normally distributed) and has the same parameters (ie, means and standard deviations) as the general population distribution. Nonparametric statistical procedures make no such assumptions about the shape or parameters of the population distribution.”(Hopkins, 2018)

### References:

Hopkins S, Dettori JR, Chapman JR. Parametric and Nonparametric Tests in Spine Research: Why Do They Matter? Global Spine J. 2018 Sep;8(6):652-654. doi: 10.1177/2192568218782679. Epub 2018 Jun 12. PMID: 30202720; PMCID: PMC6125939

Nonparametric tests are sometimes called distribution-free tests because they are based on fewer assumptions (e.g., they do not assume that the outcome is approximately normally distributed). Parametric tests involve specific probability distributions (e.g., the normal distribution) and the tests involve estimation of the key parameters of that distribution (e.g., the mean or difference in means) from the sample data. The cost of fewer assumptions is that nonparametric tests are generally less powerful than their parametric counterparts (i.e., when the alternative is true, they may be less likely to reject H0).

It can sometimes be difficult to assess whether a continuous outcome follows a normal distribution and, thus, whether a parametric or nonparametric test is appropriate. There are several statistical tests that can be used to assess whether data are likely from a normal distribution. The most popular are the Kolmogorov-Smirnov test, the Anderson-Darling test, and the Shapiro-Wilk test1. Each test is essentially a goodness of fit test and compares observed data to quantiles of the normal (or other specified) distribution. The null hypothesis for each test is H0: Data follow a normal distribution versus H1: Data do not follow a normal distribution. If the test is statistically significant (e.g., p<0.05), then data do not follow a normal distribution, and a nonparametric test is warranted. It should be noted that these tests for normality can be subject to low power. Specifically, the tests may fail to reject H0: Data follow a normal distribution when in fact the data do not follow a normal distribution. Low power is a major issue when the sample size is small – which unfortunately is often when we wish to employ these tests. The most practical approach to assessing normality involves investigating the distributional form of the outcome in the sample using a histogram and to augment that with data from other studies, if available, that may indicate the likely distribution of the outcome in the population.

There are some situations when it is clear that the outcome does not follow a normal distribution.

### Reference cited:

How to Choose Between Parametric & Nonparametric Tests | Alchemer