Data considerations for One-Way ANOVA

To ensure that your results are valid, consider the following guidelines when you collect data, perform the analysis, and interpret your results.

The data should include only one categorical factor
  • If you have one continuous predictor, use Simple Regression.
  • If you have two categorical predictors and no continuous predictors, use Two-way ANOVA.
  • If you have more than one continuous predictor, use Multiple Regression.
  • If you have one or more categorical predictors and continuous predictors, convert the categorical predictors to Make Indicator Variables before you perform multiple regression.

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.
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.
The groups should not have substantially different standard deviations

ANOVA assumes that all of the groups have the same standard deviation. If the standard deviations are substantially different, the results can be misleading. In the one-way ANOVA output, use the group standard deviations to assess the variability across groups. If you cannot assume equal variances, use Welch's ANOVA, which is an option for one-way ANOVA that is available in Minitab Statistical Software.

Sample data should be from a normal population, or each sample should be > 15 or 20

If the sample size is greater than 15 or 20, and you can assume equal variances, the test performs very well with skewed and nonnormal distributions. If the sample size is less than 15 or 20, the results may be misleading with nonnormal distributions.

The actual sample size that you need depends on the number of groups in your data, as follows:
  • If you have 2-9 groups, the sample size for each group should be at least 15.
  • If you have 10-12 groups, the sample size for each group should be at least 20.
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.
The model should provide a good fit to the data

If the model does not fit the data, then the results can be misleading. In the output, use residual plots, diagnostic statistics for unusual observations, and model summary statistics to determine how well the model fits the data.

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