Review:
Lilliefors Test
overall review score: 4
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score is between 0 and 5
The Lilliefors test is a statistical goodness-of-fit test used to determine whether a sample data set follows a normal distribution. It is a modification of the Kolmogorov-Smirnov test, adjusted for cases where the population mean and variance are unknown and must be estimated from the sample. The test provides a way to assess normality without requiring these parameters to be specified beforehand, making it useful in practical data analysis scenarios.
Key Features
- Non-parametric test for normality
- Adjusts the Kolmogorov-Smirnov test for parameter estimation from data
- Applicable to small to moderate sample sizes
- Provides p-values indicating the likelihood that the data comes from a normal distribution
- Widely implemented in statistical software packages
Pros
- Effective for testing normality when population parameters are unknown
- Does not require specifying distribution parameters in advance
- Suitable for small sample sizes compared to some other tests
- Widely recognized and supported in statistical tools
Cons
- Less powerful than some alternative normality tests like the Shapiro-Wilk test in certain situations
- Assumes continuous data; may not perform well with discrete variables
- Can sometimes produce conservative results, leading to false negatives