Dixon Q Test for Outliers
The Dixon Q Test, also known simply as the Q Test, is a statistical test used to identify and reject outliers in a small data set. It’s particularly useful for normally distributed data sets with fewer than 30 observations.
Test Statistic
The test calculates a Q statistic, which is the ratio of the gap between the suspected outlier and the closest data point to the range of the data set.
The test statistic for this procedure is as follows:
\[Q_{TS} = \frac{\mbox{Gap}}{\mbox{Range}}\]
Crtical Values
If the Q statistic exceeds a critical value from a Q table (which varies based on sample size and confidence level), the suspected data point is considered an outlier and can be rejected.
\[\begin{array}{|c|c|c|c|} \hline n & \alpha=0.10 & \alpha=0.05 & \alpha=0.01 \\ \hline 3 & 0.941 & 0.970 & 0.994 \\ \hline 4 & 0.765 & 0.829 & 0.926 \\ \hline 5 & 0.642 & 0.710 & 0.821 \\ \hline 6 & 0.560 & 0.625 & 0.740 \\ \hline 7 & 0.507 & 0.568 & 0.680 \\ \hline 8 & 0.468 & 0.526 & 0.634 \\ \hline 9 & 0.437 & 0.493 & 0.598 \\ \hline 10 & 0.412 & 0.466 & 0.568 \\ \hline 11 & 0.392 & 0.444 & 0.542 \\ \hline 12 & 0.376 & 0.426 & 0.522 \\ \hline 13 & 0.361 & 0.410 & 0.503 \\ \hline 14 & 0.349 & 0.396 & 0.488 \\ \hline 15 & 0.338 & 0.384 & 0.475 \\ \hline \end{array}\]
If the Test Statistic is greater than the Critical value, reject the null hypothesis \[Q_{TS} > Q_{CV}\]