To ensure that your results are valid, consider the following guidelines when you collect data, perform the analysis, and interpret your results.
If you use a parametric analysis as an alternative to the Kruskal-Wallis test, you should verify that your data meets the data requirements of that analysis. The data requirements for parametric analyses are not always compatible with the requirements for nonparametric analyses, such as the Kruskal-Wallis test.
- The data should include only one categorical factor
For more information on factors, go to Factors and factor levels.
- The response variable should be continuous
- If the response variable is categorical, your model is less likely to meet the assumptions of the analysis, to accurately describe your data, or to make useful predictions. If you have a categorical response variable, use Cross Tabulation and Chi-Square.
- The sample data do not need to be normally distributed
The distributions of the groups should have the same shape and spread, and contain no outliers.
- If the distributions of the groups include outliers, use Mood’s Median Test.
- If the distributions of the groups are normally distributed and have similar standard deviations, consider using One-Way ANOVA because it has more power.
- The sample size should be less than 15 or 20 observations or your process should be better represented by the median
Nonparametric tests tend to have less power than parametric tests. Also, parametric tests can perform well with nonnormal data given a sufficiently large sample size. Consider using a parametric test even with nonnormal data unless your sample size is very small or if the median is more meaningful for your study.
If your data meet the following sample size guidelines, consider using One-Way ANOVA
because it will perform very well with skewed and nonnormal distributions, and it has more power.
- The data contain 2–9 groups and the sample size for each group is at least 15.
- The data contain 10–12 groups and the sample size for each group is at least 20.
- The sample size for each group should be at least five
- If a sample has fewer than five observations, the p-value can be inaccurate.
- Each observation should be independent from all other observations
If your observations are dependent, your results might not be valid. Consider the following points to determine whether your observations are independent:
- If an observation provides no information about the value of another observation, the observations are independent.
- If an observation provides information about another observation, the observations are dependent.
- Collect data using best practices
To ensure that your results are valid, consider the following guidelines:
- Make sure the data represent the population of interest.
- Collect enough data to provide the necessary precision.
- Measure variables as accurately and precisely as possible.
- Record the data in the order it is collected.