2.13.1.22 swtest

1 Brief Information
2 Command Line Usage
3 X-Function Execution Options
4 Variables
5 Description
6 Examples
7 Algorithm
8 References
9 Related X-Functions

Brief Information

Shapiro-Wilk Normality test

Command Line Usage

1. swtest irng:=col(a)

2. swtest irng:=Col(A) stat:=w df:=d prob:=p

X-Function Execution Options

Please refer to the page for additional option switches when accessing the x-function from script

Variables

Display Name	Variable Name	I/O and Type	Default Value	Description
Input	irng	Input Range	<active>	This variable specifies the input data range for test normality. The sample size of data range needs to be between 3 and 5000 for the Shapiro-Wilk test to apply.
Statistics	stat	Output double	<unassigned>	Value of Shapiro-Wilk W statistic. This variable specifies the name of output statistic value.
Degrees of Freedom	df	Output double	<unassigned>	Degrees of freedom of the test. This variable specifies the name of output degrees of freedom value.
P-value	prob	Output double	<unassigned>	Probability that the null hypothesis, i.e. that the data are from normal distribution, will be rejected. This variable specifies the name of output probability value.

Description

The Shapiro-Wilk Normality Test is used to determine whether or not a random sample of values follows a normal distribution. The normality test is useful because other statistical tests (such as the t-test, 1- and 2-way ANOVA) require that data be sampled from a normally distributed population in order to produce statistically significant results. A W statistic and a p value are computed, which can be compared with a chosen level of significance, and used to make a statistical decision.

Examples

1. To list all input and output results of Shapiro-Wilk test on the 1st column of the active worksheet, using default setting, type:

swtest irng:=col(a);

swtest.=

2. To return the Shapiro-Wilk test statistic for the 2nd column of active worksheet, and test to see if these sample data arise from a normal distribution, type:

swtest irng:=col(b) stat:=s;

Algorithm

This routine calculates Shapiro Wilk's W statistic with a given significance level for any sample size between 3 and 5000. Origin calculates the W statistic based on the Applied Statistics Algorithm R94. The full description of the theory behind this algorithm is given in Royston (1995).

Given a set of observations sorted into either ascending or descending order, the Shapiro Wilk W statistic is defined as: