# Cochran Q test

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In statistics, the ** Q test** is used for identification and rejection of outliers. This test should be used sparingly and never more than once in a data set. To apply a

*Q*test for bad data, arrange the data in order of increasing values and calculate

*Q*as defined:

Q = Q_{gap}/Q_{range}

Where *Q*_{gap} is the absolute difference between the outlier in question and the closest number to it. If *Q*_{calculated} > *Q*_{table} then reject the questionable point.

## Table

Number of values: | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |

Q_{90%}: | 0.941 | 0.765 | 0.642 | 0.560 | 0.507 | 0.468 | 0.437 | 0.412 |

Q_{95%}: | 0.970 | 0.829 | 0.710 | 0.625 | 0.568 | 0.526 | 0.493 | 0.466 |

## Example

For the data:

Arranged in increasing order:

Outlier is 0.169. Calculate *Q*:

With 10 observations at 90% confidence, Q_{calculated} < Q_{table}. Therefore keep 0.169 at 90% confidence.

## References

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