Abstract
Nonparametric statistics provide a useful purpose for inferential analyses when data: (1) do not meet the purported precision of an interval scale, (2) there are serious concerns about extreme deviation from normal distribution, and (3) there is considerable difference in the number of subjects for each breakout group. It is not totally uncommon to hear terms such as ranking tests and distribution-free tests to describe the inferential tests associated with nonparametric statistics, due to the use of nominal and ordinal data and data that may not meet the desired assumption of normal distribution (i.e., bell-shaped curve). Although those who work in the biological sciences would ideally like to have precise measurement for their data, to have data that follow normal distribution patterns, and to have adequately-sized samples for all breakout groups, only too often these three desires are not met. Nonparametric statistics and the many inferential tests associated with nonparametric statistics provide a valuable set of options on how these data can be used to good effect. Following along with these aspirations, the R environment and the many external packages associated with R offer many practical applications that support inferential tests associated with nonparametric statistics.
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Notes
- 1.
By long-standing convention regarding blood pressure measurements and the use of non-digital sphygmomanometers, it is common to express mm Hg SBP readings as even numbers, only.
- 2.
All.csv datasets are posted on the publisher’s Web page devoted to this text.
- 3.
It is common to see the use of uppercase and lowercase for terms, such as mean = 123 or Mean = 123, when used in a narrative presentation. Both approaches are used in this text.
- 4.
The word plot is frequently used in agriculture to refer to a small section of a field. Do not confuse the term plot, used in this context, with the R plot() function.
- 5.
As open-source software, a comparative advantage of R over proprietary software is that the user community contributes to development of the software. A limited degree of functionality is available when R software is first downloaded. The extreme functionality comes from the more than 5000 packages available to the R community, with most packages having 25, 50, 100, or more functions. These packages are easily and freely obtained, from host sites throughout the world.
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Regarding assessment of normality, consider also how the qqnorm(), qqline(), and qqplot() functions are typically used when investigating distribution patterns. There remains some degree of inconsistency as to whether the correct usage is either QQ or Q-Q when referencing the term Quantile-Quantile. Both terms (i.e., QQ or Q-Q) may be found in this text.
- 7.
IQ scores in this demonstration are generated using the rnorm() function. The individual datapoints in the object variable IQ will likely change each time the rnorm() function is used to generate a new set of IQ scores, even though the overall dataset maintains Mean = 100 and SD = 15.
- 8.
There are six cells in this figure; 2 rows * 3 columns = 6 cells. The individual cells are populated from left to right.
- 9.
The term noise refers to the observation that the small circles used to indicate individual datapoints do not follow along the otherwise straight line of the Quantile-Quantile plot. A few deviations away from the straight line are expected. However, when there are too many deviations it is best to question if the data display normal distribution.
- 10.
The use of R syntax is stressed in this text. However, this is one case where it may be best to use the R menuing selections (e.g., File - Edit - View - Misc - Packages - Windows - Help), instead of syntax, to ensure that all session activities are placed in the desired location.
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© 2016 Springer International Publishing Switzerland
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MacFarland, T.W., Yates, J.M. (2016). Nonparametric Statistics for the Biological Sciences. In: Introduction to Nonparametric Statistics for the Biological Sciences Using R. Springer, Cham. https://doi.org/10.1007/978-3-319-30634-6_1
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DOI: https://doi.org/10.1007/978-3-319-30634-6_1
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