# Interpret the key results for P 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 binomial 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 binomial 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 P chart to show an increased number of points outside the control limits. Underdispersion can cause a traditional P chart to show too few points outside of the control limits. The Laney P' chart adjusts for these conditions.

## Example of overdispersion

The ratio of observed variation to expected variation is 175.7%. This value indicates overdispersion because it is greater than the upper confidence limit of 136.6%. Overdispersion can cause points on a traditional P chart to appear to be out of control when they are not. To adjust for overdispersion, use a Laney P' chart.

## Example of underdispersion

The ratio of observed variation to expected variation is 46%. This value indicates underdispersion because it is less than the lower confidence limit of 60%. Underdispersion can cause the control limits on a traditional P 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 P' chart.