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

@article{Shapiro1965AnAO, title={An Analysis of Variance Test for Normality (Complete Samples)}, author={Samuel S. Shapiro and M. B. Wilk}, journal={Biometrika}, year={1965}, volume={52}, pages={591-611} }

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 combination of the sample order statistics by the usual symmetric estimate of variance. This ratio is both scale and origin invariant and hence the statistic is appropriate for a test of the composite hypothesis of normality. Testing for distributional assumptions in general and for normality in…

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## References

SHOWING 1-10 OF 19 REFERENCES

THE DISTRIBUTION OF THE RATIO, IN A SINGLE NORMAL SAMPLE, OF RANGE TO STANDARD DEVIATION

- Mathematics
- 1954

vations. While the first ratio can play a useful part in providing certain rapid tests in the analysis of variance, the second, whose value depends only on the configuration of a particular sample,…

THE RATIO OF THE MEAN DEVIATION TO THE STANDARD DEVIATION AS A TEST OF NORMALITY

- Mathematics
- 1935

The usual method of dealing with this problem, and that which in principle is adopted here, is that of devising a function, or functions, of the sample variables XI, X2, ... ccX', which assume…

Use of Half-Normal Plots in Interpreting Factorial Two-Level Experiments

- Geology
- 1959

Plotting the empirical cumulative distribution of the usual set of orthogonal contrasts computed from a 2 p experiment on a special grid may aid in its criticism and interpretation. Bad values,…

A Test of Goodness of Fit

- Mathematics
- 1954

Some (large sample) significance points are tabulated for a distribution-free test of goodness of fit which was introduced earlier by the authors. The test, which uses the actual observations without…

Design and analysis of industrial experiments

- Computer Science
- 1954

This paper is based on a lecture on the “Design and Analysis of Industrial Experiments” given by Dr O. L. Davies on the 8th of May 1954 and the recent designs developed by Box for the exploration of response surfaces are briefly considered.

IV.—On Least Squares and Linear Combination of Observations

- Mathematics
- 1936

In a series of papers W. F. Sheppard (1912, 1914) has considered the approximate representation of equidistant, equally weighted, and uncorrelated observations under the following assumptions:–
(i)…

The advanced theory of statistics

- Mathematics
- 1945

A method for continuously effecting reactions in a liquid phase in the presence of a gas and of a finely divided solid catalyst in a bubble column-cascade reactor with little or no liquid…