# Interpret the key results for U Chart Diagnostic

The ratio of observed variation to expected variation compares the variation in your data to the variation that you would expect based on a Poisson distribution. The ratio is expressed as a percentage.

A ratio that is close to 100% indicates that your data exhibit the expected amount of variation for a Poisson distribution. Compare the ratio to the 95% upper confidence limit or the 95% lower confidence limit to determine whether your data exhibit significant overdispersion or significant underdispersion:
• If the ratio is greater than the upper confidence limit, then your data exhibit significant overdispersion.
• If the ratio is less than the lower confidence limit, then your data exhibit significant underdispersion.

Overdispersion can cause a traditional U chart to show an increased number of points outside the control limits. Underdispersion can cause a traditional U chart to show too few points outside of the control limits. The Laney U' chart adjusts for these conditions.

## Example of overdispersion

The ratio of observed variation to expected variation is 553.4%. This value indicates overdispersion because it is greater than the upper confidence limit of 147.8%. Overdispersion can cause points on a traditional U chart to appear to be out of control when they are not. To adjust for overdispersion, use a Laney U' chart.

## Example of underdispersion

The ratio of observed variation to expected variation is 54%. This value indicates underdispersion because it is less than the lower confidence limit of 60%. Underdispersion can cause the control limits on a traditional U chart to be too wide. If the control limits are too wide, you can overlook special-cause variation and mistake it for common-cause variation. To adjust for underdispersion, use a Laney U' chart.