# Power comparisons of Shapiro-Wilk , Kolmogorov-Smirnov , Lilliefors and Anderson-Darling tests

@inproceedings{Razali2011PowerCO, title={Power comparisons of Shapiro-Wilk , Kolmogorov-Smirnov , Lilliefors and Anderson-Darling tests}, author={Nornadiah Mohd Razali and Yap Bee Wah}, year={2011} }

The importance of normal distribution is undeniable since it is an underlying assumption of many statistical procedures such as t-tests, linear regression analysis, discriminant analysis and Analysis of Variance (ANOVA). When the normality assumption is violated, interpretation and inferences may not be reliable or valid. The three common procedures in assessing whether a random sample of independent observations of size n come from a population with a normal distribution are: graphical methods…

## 2,690 Citations

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## References

SHOWING 1-10 OF 25 REFERENCES

### Investigation of Four Different Normality Tests in Terms of Type 1 Error Rate and Power under Different Distributions

- Mathematics
- 2006

The Jarqua-Bera test was superior for normal and standard normal distributions and for nonnormal distributions, achieving sufficient power at smaller sample sizes, the Shapiro-Wilk was the most powerful.

### Detecting Departures from Normality: A Monte Carlo Simulation of a New Omnibus Test Based on Moments.

- Mathematics
- 1998

The assumption of normality underlies much of the standard statistical methodology. Knowing how to determine whether a sample of measurements is from a normally distributed population is crucial both…

### Comprehensive study of tests for normality and symmetry: extending the Spiegelhalter test

- Mathematics
- 2006

Statistical inference in the form of hypothesis tests and confidence intervals often assumes that the distribution(s) being sampled are normal or symmetric. As a result, numerous tests have been…

### An Analysis of Variance Test for Normality (Complete Samples)

- Mathematics
- 1965

The main intent of this paper is to introduce a new statistical procedure for testing a complete sample for normality. The test statistic is obtained by dividing the square of an appropriate linear…

### A comparison of various tests of normality

- Mathematics
- 2007

This article studies twelve different normality tests that are used for assessing the assumption that a sample was drawn from a normally distributed population and compares their powers. The tests in…

### Type I Error Rate and Power of Three Normality Tests

- Mathematics
- 2003

Shapiro-Wilks, Lilliefors and Kolmogorov-Smirnov test results were the weakest among all three tests, but all three test were most powerful when ran on data with exponential distribution.

### On the Kolmogorov-Smirnov Test for Normality with Mean and Variance Unknown

- Mathematics
- 1967

Abstract The standard tables used for the Kolmogorov-Smirnov test are valid when testing whether a set of observations are from a completely-specified continuous distribution. If one or more…

### Goodness-of-Fit-Techniques

- Mathematics
- 1986

"Overview, Ralph B. D'Agostino and Michael A. Stephens Graphical Analysis, Ralph B. D'Agostino Tests of Chi-Squared Type, David S. Moore Tests Based on EDF Statistics, Michael A. Stephens Tests Based…

### Algorithm AS 181: The W Test for Normality

- Computer Science
- 1982

The purpose of the present algorithm is to enable the calculation of the Shapiro and Wilk Wstatistic and its significance level for any sample size between 3 and 2000.

### An Extension of Shapiro and Wilk's W Test for Normality to Large Samples

- Mathematics
- 1982

Shapiro and Wilk's (1965) W statistic arguably provides the best omnibus test of normality, but is currently limited to sample sizes between 3 and 50. W is extended up to n = 2000 and an approximate…