The null hypothesis of the Shapiro-Wilk test is that a given data sample has been generated from a normally distributed population.
Understanding the Shapiro-Wilk Test
The Shapiro-Wilk test is a specific type of hypothesis test used to assess whether a sample of data comes from a normal distribution. It is widely applied in statistics because many statistical methods, such as t-tests and ANOVA, assume that the data they analyze are normally distributed.
In the context of the Shapiro-Wilk test, the hypotheses are formally stated as follows:
Hypothesis | Statement |
---|---|
Null Hypothesis (H₀) | The sample data is drawn from a normally distributed population. |
Alternative Hypothesis (H₁) | The sample data is not drawn from a normally distributed population. |
Interpreting the Results
When you perform a Shapiro-Wilk test, the primary output you look at is the p-value. This p-value helps determine whether there is enough evidence to reject the null hypothesis.
- If the p-value is low (typically less than a predetermined significance level, e.g., 0.05): We reject the null hypothesis. This indicates that there is sufficient evidence to conclude that the sample data does not come from a normal distribution. In simpler terms, the data is likely non-normal.
- If the p-value is high (greater than the significance level): We fail to reject the null hypothesis. This suggests that there is not enough evidence to conclude that the data is non-normal. In other words, the data could reasonably be considered to come from a normal distribution.
Practical Implications
Testing for normality is a crucial preliminary step for many statistical analyses. If your data violates the assumption of normality for a particular test, the results of that test might be unreliable.
- Example: Suppose you want to compare the means of two groups using an independent samples t-test. A common assumption for this test is that the data in both groups are normally distributed. You would run a Shapiro-Wilk test on each group's data.
- If both p-values are high, you can proceed with the standard t-test.
- If one or both p-values are low, suggesting non-normality, you might consider:
- Transforming your data to achieve normality.
- Using a non-parametric alternative test (e.g., the Mann-Whitney U test instead of the independent samples t-test), which does not assume normality.
Understanding the null hypothesis of the Shapiro-Wilk test is fundamental to correctly interpreting its output and making informed decisions about subsequent statistical analyses. For further reading on the Shapiro-Wilk test, you can consult resources like Wikipedia's page on the Shapiro-Wilk test.