# 17.1.12 Dixon's Q-Test

## Supporting Information

To open the Dixon's Q-test dialog box from the menu:

1. Click Statistics: Descriptive Statistics: Dixon's Q-test (Open Dialog...)

## Dialog Box Controls

Results Log Output Select to output results to the Results Log. Controls recalculation of analysis results: None Auto Manual For more information, see: Recalculating Analysis Results Number of (replicate) observations must be between 3 and 10 (inclusive) and contained in one column. For help with range controls, see: Specifying Your Input Data Option list: 0.1 0.05 0.01 Select to generate an outlier plot. Scatter plot with upper and lower confidence limits and dataset mean as line plots. Worksheet range to output the outlier plot data (available if Outlier Plot is selected). For help with the range controls, see: Output Results The worksheet range to output the report table.

## Algorithm

For a series of results from repeated measurements:

1. Rank $n$ results in ascending order, assigning them values of $x_{1}$ to $x_{n}$.
2. Calculate the test statistic $Q$, as: $Q=\frac{ x_{2}-x_{1} }{x_{n}-x_{1} }$ (for testing if smallest observation is an outlier),
or $Q=\frac{ x_{n}-x_{n-1} }{x_{n}-x_{1} }$ (for testing if highest observation is an outlier).
3. Compare the calculated $Q$ value with $Q$critical (critical value is obtained from a table of $Q$ values, using sample size $n$ and significance level).

## Handling Missing Values

The missing values in the data range will be excluded in the analysis

## References

Stephen L R. Ellison, Vicki J. Barwick and Trevor J Duguid. Farrant. 2009. Practical Statistics for the Analytical Scientist. The Royal Society of Chemistry, Cambridge, UK.