null.norm: Normality test for null values

In iCAMP: Infer Community Assembly Mechanisms by Phylogenetic-Bin-Based Null Model Analysis

Normality test for null values

Description

To test whether the null values of each turnover of each bin follow normal distribution.

Usage

null.norm(icamp.output = NULL, rand.list = NULL, index.name = "Test.Index",
          p.norm.cut = 0.05, detail.out = FALSE)

Arguments

icamp.output	list, the exact output of the function icamp.big in which detail.null must be TRUE, to save all null values.
rand.list	list, the null values of a certain dissimilarity index. Each eletment is a matrix that represents a bin. In each eletment matrix, the first two columns indicate sample IDs of the pairwise comparison (turnover), and each of the other columns shows the null values from one time of randomization.
index.name	character, when rand.list is given, to specify the name of the dissimilarity index.
p.norm.cut	numeric, the threshold of significant P value. A p value lower than this indicates significant difference from normal distribution.
detail.out	logic, if TRUE, the detailed statistics and P values for each turnover of each bin will be output; otherwise, only output a summary on non-normal percentage for each bin.

Details

Normal distribution of null values is basic assumption when using Standard Effect Size (SES, e.g. betaNRI, betaNTI) to identify significant difference between null and observed values. This function uses five different methods to perform normality test, including Anderson-Darling test (Anderson), Cramer-von Mises test (Cramer), Kolmogorov-Smirnov test (Kolmogorov, also known as Lilliefors test), Shapiro-Francia test (ShapiroF), and Shapiro-Wilk test (Shapiro). The function 'shapiro.test' in package 'stats', and various functions in package 'nortest' are used.

Value

Output is a list object.

summary	data.frame, each row represents a bin and a dissimilarity index. Seven columns. The first column indicates the dissimilarity index; the second column indicate Bin ID; each of the other columns indicate non-normal ratio based on a method. The non-normal raio is calculated as percentage of turnovers where null value distribution is significantly different from normal distribution.
P.value.cut	the value of p.norm.cut
detail	list, each first-level element represents a dissimilarity index; each second-level element is a matrix represents a bin; and the matrix has 14 columns, including the dissimilarity index (Index), bin ID (BinID), sample IDs (name1 and name2), and the statistics and P value based on different methods.

Note

Version 2: 2020.8.19, update help document, add example Version 1: 2020.8.1

Author(s)

Daliang Ning

References

Stephens, M.A. (1986): Tests based on EDF statistics. In: D'Agostino, R.B. and Stephens, M.A., eds.: Goodness-of-Fit Techniques. Marcel Dekker, New York.

Dallal, G.E. and Wilkinson, L. (1986): An analytic approximation to the distribution of Lilliefors' test for normality. The American Statistician, 40, 294-296.

Stephens, M.A. (1974): EDF statistics for goodness of fit and some comparisons. Journal of the American Statistical Association, 69, 730-737.

Royston, P. (1993): A pocket-calculator algorithm for the Shapiro-Francia test for non-normality: an application to medicine. Statistics in Medicine, 12, 181-184.

Thode Jr., H.C. (2002): Testing for Normality. Marcel Dekker, New York

Patrick Royston (1982). An extension of Shapiro and Wilk's W test for normality to large samples. Applied Statistics, 31, 115-124. doi: 10.2307/2347973.

Patrick Royston (1982). Algorithm AS 181: The W test for Normality. Applied Statistics, 31, 176-180. doi: 10.2307/2347986.

Patrick Royston (1995). Remark AS R94: A remark on Algorithm AS 181: The W test for normality. Applied Statistics, 44, 547-551. doi: 10.2307/2986146.

Juergen Gross and Uwe Ligges (2015). nortest: Tests for Normality. R package version 1.0-4. https://CRAN.R-project.org/package=nortest

See Also

icamp.big, change.sigindex

Examples

data("icamp.out")
nntest=null.norm(icamp.output = icamp.out, detail.out = TRUE)

iCAMP documentation built on June 1, 2022, 9:08 a.m.