I need two comments, each part is around 100 words.
Nonparametric data is distinguished from its parametric counterpart depending on distribution. Samples of continuous data where the distribution is known or can easily be identified are considered parametric. Nonparametric refers to data in which the distribution is unknown. Brownlee at Machine Learning Mastery (2018) notes that nonparametric datasets can be identified by characteristics such as:
- The data is not real-valued (ordinal, intervals, etc.)
- The data does not fit a well understood shape.
- The data contains outliers, multiple peaks, or shifts.
- The data is too small to meet parametric standards.
This means that nonparametric statistical methods are required to be more flexible in order to fit the unique dataset. There are fewer assumptions about the sample data and analysis can be conducted without the mean, standard deviation, or other related parameters when they are unknown (Grant, 2020). Instead, nonparametric analysis revolves around the median as the measure for central tendency rather than the mean. While they can be used more broadly for unique sets of data, nonparametric statistical methods also run the risk of being less precise as they become more generalized. It is important to understand the applications and limitations of the types of statistical tests because parametric and nonparametric analysis might produce different conclusions when applied to the same dataset. Typically, parametric tests are considered to be more powerful and accurate, if an effect actually exists then a parametric test is more likely to pinpoint it than nonparametric methods (Frost, 2017). However, parametric tests may provide inaccurate results when applied to a dataset with a strong skew, multiple peaks, or non-extraneous outliers.
Typically, parametric statistical methods are preferred when the data analyzed can be categorized by a distribution (usually the normal distribution). These tests include any t, z, and F tests. Nonparametric statistical methods then are used for those datasets that cannot be categorized by any distribution. There are six advantages considered and three disadvantages. Even though there are more advantages than disadvantages, the disadvantages have a bigger impact on the results of the test than the advantages combined do. Nonparametric tests can be less sensitive – which means they cannot as easily detect differences of the analyses from their null hypothesis. Thus, it can be harder to reject and accept on smaller margins. Less information is needed to be fed into the model. This can decrease accuracy of results for nonparametric tests. An example of this may be found with the sign tests – they only need a directional vector of the data points but don’t need to know the magnitude from the metric used. Finally, these tests are simply less efficient than the parametric tests. Since there is less information used to test hypotheses, more data needs to be fed into the models in order to somewhat compensate.
Advantages to using these tests though include that they can be used to test population parameters without needing to normally distributed; data can be nominal or ordinal; datasets that don’t have population parameters may be tested; the tests are easier to calculate and understand; and less assumptions need to be met – which makes the test faster to use.
If the assumptions can be met, it is much preferred for the tester to use parametric tests when analyzing datasets. However, if the assumptions cannot be met, the nonparametric tests are a valid, although somewhat lacking choice. Assumptions for a nonparametric statistical test include that the samples are randomly selected and that if there are more than one sample used, they be independent (unless a test specifically provides a provision otherwise).
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