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Dixon's Q test evaluates whether a suspicious data point is an outlier by comparing the gap between it and the nearest value to the total range of the dataset.
For testing the lowest value ($x_1$):
$$Q_{min} = \frac{x_2 - x_1}{x_n - x_1}$$
For testing the highest value ($x_n$):
$$Q_{max} = \frac{x_n - x_{n-1}}{x_n - x_1}$$
If the calculated $Q$ exceeds the critical table value for your chosen sample size and significance level, the data point is designated as an outlier.
When conducting experimental measurements or gathering analytical datasets, encountering abnormal values or anomalies is a common occurrence. These anomalies, frequently referred to as outliers, can severely distort descriptive statistics like means, standard deviations, and regression models. To uphold rigorous scientific integrity, researchers rely on robust statistical hypothesis testing procedures. Among these, Dixon's Q test stands out as one of the most widely accepted methods for small sample sizes, typically ranging from 3 to 30 observations.
Identifying outliers ensures that conclusions drawn from laboratory assays, industrial quality control checks, or academic studies remain accurate and dependable. Failing to account for contaminated data points or recording errors can lead to erroneous inferences, wasted resources, and flawed theoretical models. Dixon's Q test provides an objective, mathematically sound framework to determine whether an extreme data point belongs to the same statistical population as the rest of the observations or if it should be legitimately discarded.