Shapiro-Wilk Test

Shapiro-Wilk Test

Shapiro-Wilk Test

Description

The Shapiro-Wilk test is a normality test in probability determination statistics. It is used to determine whether a simple random sample of a variable’s values has been derived from a normal distribution.

Why to use

For normality test

When to use

To find out whether a random sample has been derived from a normal distribution.

When not to use

On data other than numerical data.

Prerequisites

  • The input variable should be of numerical type.
  • Shapiro-Wilk normality test generates a significant result if the sample size is sufficiently large.

Input

Any dataset that contains numerical data.

 

Output

  • W Statistic
  • p-Value
  • alpha (α)

Statistical Methods used

NA

Limitations

  • It can be used only on numerical data.
  • The data is inferred to be normally distributed depending upon the user’s assessment or requirements.
  • For sample size > 5000, the normality test result can be inferred only from the W Statistic value.

The p-value is the probability of attaining observed results of a statistical hypothesis test, assuming that the null hypothesis is true.

The null hypothesis of the Shapiro-Wilk test is – Input data comes from a normal distribution, while the alternative hypothesis is – Input data does not come from a normal distribution.

The Shapiro-Wilk test rejects the null hypothesis of normality when the p-value is less than or equal to 0.05. Failing the normality test allows you to state with 95% confidence that the data does not fit the normal distribution. Passing the normality test enables you to declare that no significant departure from normality was found.

The test generates a W Statistic value which depends on the ordered random sample values and the constants generated by covariances, variances, and means of a normally distributed random sample. If the W Statistic value is small, the null hypothesis is rejected, and it can be concluded that the random sample is not normally distributed.

Shapiro-Wilk normality test generates a significant result if the sample size is sufficiently large.

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