Design of Experiments > Balanced and Unbalanced Designs

## What are Balanced and Unbalanced Designs?

In ANOVA and Design of Experiments, a

**balanced design**has an equal number of observations for all possible level combinations. This is compared to an

**unbalanced design**, which has an

*unequal*number of observations. Levels (sometimes called

*groups*) are different groups of observations for the same independent variable. For example, let’s say you’re taste-testing various cereals. Your levels for “brand of cereal” might be: Lucky Charms, Raisin Bran, or Kellogg’s Cornflakes:

- A balanced design might have 30 boxes of each brand.
- An unbalanced design might have 29 boxes of Lucky Charms, 21 boxes of Raisin Bran, and 30 boxes of Kellogg’s Cornflakes.

In factorial design, a balanced experiment could also mean that the same factor is being run the same number of times for all levels. For example, factors A and B might be run 10 times for two levels.

## Balanced vs. Unbalanced Designs in Testing

When performing statistical tests, **balanced designs are usually preferred **for several reasons, including:

- The test will have larger statistical power,
- The test statistic is less susceptible to small departures from the assumption of equal variances (homoscedasticity).

However, for single factor ANOVA, a lack of balance doesn’t usually affect the results (Milliken and Johnson, 1984).

**Even the most carefully planned balanced design could end up being unbalanced.** For example:

- Your shipment of Lucky Charms might be delayed.
- A couple of boxes of cereal might be stale and unusable.
- Some of your test subjects might not show up.

If this happens, you should try to turn your design into a nearly-balanced design. There are several ways to do this, including:

- Estimating the missing data. For example, you could use the mean of the observations you do have to “fill in the blank.”
- Adjusting weights. For example, to compensate for a missing box of cereal, you could adjust the weight upwards for the boxes you have left.

**References**:

Milhken. G. A.. and D. E. Johnson. (1984). Analysis of messy data. Volume 1: designed experiments. Van Nostrand Reinhold. New York, New York. USA. P. 127.

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