# 2.13.1.10 lillietest

## Brief Information

Lilliefors normality test

## Command Line Usage

 

1. lillietest irng:=col(b) 

2. lillietest irng:=col(b) df:=mydf stat:=s prob:=p 

## Variables

Display
Name
Variable
Name
I/O
and
Type
Default
Value
Description
Input irng

Input

Range

<active>

Specify the input data range

Statistics stat

Output

double

<unassigned>

The computed statistic of the test

Degrees of Freedom df

Output

double

<unassigned>

Degrees of freedom of the test

P-value prob

Output

double

<unassigned>

The probability that the null hypothesis is rejected

## Description

The function performs Lilliefors modification of the Kolmogorov-Smirnov test to determine if the null hypothesis of composite normality is a reasonable assumption regarding the population distribution of a random sample X. The Lilliefors test is based on simulation, so the significance level is restricted to (the region tabularized by Lilliefors).

## Examples

1. lillietest irng:=col(a)

This command will perform Lilliefors test on the first column, then you can type:

lillietest.=

to list the results.

2. lillietest irng:=col(b) stat:=s

This command will do lilliefors test on Col(b) and assign the test statistic value to variable.

## Algorithm

Lilliefors test is adapted from the Kolmogorov-Smirnov test, and the statistics is computed in the same way as that of Kolmogorov-Smirnov test. However, the p-value is estimated by linear interpolation of the Lilliefors's table, and is different from that of Kolmogorov-Smirnov test.

## Related X-Functions

Keywords:degrees of freedom