When there are no outliers

Firstly mention that all residuals do not have the same standard deviation — their standard deviation is highest for points whose x-value is near the mean x-value of the data. Standardised residuals divide each residual by an estimate of its standard deviation. Standardised residuals far from zero are often used to indicate outliers.

  • Only about 5% will be outside ±2
  • Hardly any will be outside ±3

Click Another Data Set a few times. Then repeat with larger sample sizes.

  • Standardised residuals are occasionally outside ±2, especially when the sample size is increased
  • Standardised residuals outside ±3 are rare when the sample size is small, but are not uncommon when the sample size is very large.

In large data sets, do not assume that standardised residuals outside ±3 must be outliers — values a little outside can occur by chance.