Outlier Identification validation

Free statistical outlier screening for environmental datasets using the Dixon, Rosner and Grubbs tests with automatic test selection by sample size.

Scenarios: 4
Values agreeing: 18
Values differing: 6
Validated against: USEPA ProUCL, R EnvStats / nortest

Open Outlier Identification

Rosner's test agrees with R EnvStats to fourteen decimal places, including the masked-outlier scenario. Dixon's test agrees with ProUCL exactly. The automatic switch from Dixon to Rosner is fixed at the sample size stated in the help text. ProUCL's Rosner statistic standardises by the population standard deviation and its critical values are read from a table printed to two decimal places; this toolkit and R use the sample standard deviation and compute the critical value in closed form.

Scenarios

Rosner's test on 30 results with two planted high outliersTypical use
Twenty-six results on automatic selection - the first n that picks RosnerBoundary case
Two nearly equal extremes - the masking case sequential tests are built forBoundary case
Twenty-five results on automatic selection - the last n that picks DixonBoundary case

Rosner's test on 30 results with two planted high outliers

Typical use

Input

30 values

value
10.2
11.4
9.8
10.7
12.1
9.4
11
10.5
9.9
10.8
11.7
10.1
9.6
10.4
11.2
10.9
9.7
10.6
11.5
10.3
9.5
11.1
10
11.8
9.3
10.75
11.35
9.85
48.6
52.3

Settings: test = rosner, significance = 0.05, maxOutliers = 5

Against R EnvStats / nortest (EnvStats 3.1.0, nortest 1.0-4, R 4.6.1)

Value	R EnvStats / nortest	EnviroAutomate	Difference	Agreement band	Verdict
Outliers found outlierCount	2	2	0	exact match	Agree
Outlier values outlierValues	52.3,48.6	52.3,48.6	-	exact match	Agree
Test statistic testStatistic	3.846428303673836	3.846428303673835	8.88e-16	within 0.000001 relative	Agree
Critical value criticalValue	2.908473059740961	2.908473059740994	3.29e-14	within 0.000001 relative	Agree

Against USEPA ProUCL (ProUCL 5.2.0)

Value	USEPA ProUCL	EnviroAutomate	Difference	Agreement band	Verdict
Test used testUsed	rosner	rosner	-	exact match	Agree
Test statistic testStatistic	3.9121839780229974	3.846428303673835	0.0658	within 0.000001 relative	Differs
Why these differ: Rosner's statistic is the largest standardised deviation from the mean, and the two tools standardise by different spreads. ProUCL divides by the population standard deviation; this toolkit divides by the sample standard deviation, the n-1 form. That is the whole of the difference - recomputing this scenario with the population divisor reproduces ProUCL's number to fifteen decimal places. Rosner (1983) and Gilbert (1987) both define the statistic with the sample standard deviation, and R's EnvStats rosnerTest agrees with this toolkit to fourteen decimal places, so the toolkit's value is kept.
Critical value criticalValue	2.91	2.908473059740994	0.00153	within 0.000001 relative	Differs
Why these differ: ProUCL reads its Rosner critical values out of Gilbert's published table, which is printed to two decimal places; this toolkit computes the same quantity in closed form from the Student's t distribution. R's EnvStats computes it the same way and agrees with this toolkit to fourteen decimal places. The difference is the rounding in the printed table, not a disagreement about the method, and it never changes which results are flagged in these scenarios.

Twenty-six results on automatic selection - the first n that picks Rosner

Boundary case

Input

26 values

value
10.2
11.4
9.8
10.7
12.1
9.4
11
10.5
9.9
10.8
11.7
10.1
9.6
10.4
11.2
10.9
9.7
10.6
11.5
10.3
9.5
11.1
10
48.6
10.35
10.45

Settings: test = auto, significance = 0.05, maxOutliers = 5

Against R EnvStats / nortest (EnvStats 3.1.0, nortest 1.0-4, R 4.6.1)

Value	R EnvStats / nortest	EnviroAutomate	Difference	Agreement band	Verdict
Outliers found outlierCount	1	1	0	exact match	Agree
Outlier values outlierValues	48.6	48.6	-	exact match	Agree
Test statistic testStatistic	4.881453558821862	4.881453558821862	0	within 0.000001 relative	Agree
Critical value criticalValue	2.840774076470642	2.8407740764706393	2.66e-15	within 0.000001 relative	Agree

Against USEPA ProUCL (ProUCL 5.2.0)

Value	USEPA ProUCL	EnviroAutomate	Difference	Agreement band	Verdict
Test used testUsed	rosner	rosner	-	exact match	Agree
Test statistic testStatistic	4.978125390225926	4.881453558821862	0.0967	within 0.000001 relative	Differs
Why these differ: Rosner's statistic is the largest standardised deviation from the mean, and the two tools standardise by different spreads. ProUCL divides by the population standard deviation; this toolkit divides by the sample standard deviation, the n-1 form. That is the whole of the difference - recomputing this scenario with the population divisor reproduces ProUCL's number to fifteen decimal places. Rosner (1983) and Gilbert (1987) both define the statistic with the sample standard deviation, and R's EnvStats rosnerTest agrees with this toolkit to fourteen decimal places, so the toolkit's value is kept.
Critical value criticalValue	2.84	2.8407740764706393	0.000774	within 0.000001 relative	Differs
Why these differ: ProUCL reads its Rosner critical values out of Gilbert's published table, which is printed to two decimal places; this toolkit computes the same quantity in closed form from the Student's t distribution. R's EnvStats computes it the same way and agrees with this toolkit to fourteen decimal places. The difference is the rounding in the printed table, not a disagreement about the method, and it never changes which results are flagged in these scenarios.

Two nearly equal extremes - the masking case sequential tests are built for

Boundary case

Input

30 values

value
10.2
11.4
9.8
10.7
12.1
9.4
11
10.5
9.9
10.8
11.7
10.1
9.6
10.4
11.2
10.9
9.7
10.6
11.5
10.3
9.5
11.1
10
11.8
9.3
10.75
11.35
9.85
49.1
50.4

Settings: test = rosner, significance = 0.05, maxOutliers = 5

Against R EnvStats / nortest (EnvStats 3.1.0, nortest 1.0-4, R 4.6.1)

Value	R EnvStats / nortest	EnviroAutomate	Difference	Agreement band	Verdict
Outliers found outlierCount	2	2	0	exact match	Agree
Outlier values outlierValues	50.4,49.1	50.4,49.1	-	exact match	Agree
Test statistic testStatistic	3.732836850520452	3.732836850520452	0	within 0.000001 relative	Agree
Critical value criticalValue	2.908473059740961	2.908473059740994	3.29e-14	within 0.000001 relative	Agree

Against USEPA ProUCL (ProUCL 5.2.0)

Value	USEPA ProUCL	EnviroAutomate	Difference	Agreement band	Verdict
Test used testUsed	rosner	rosner	-	exact match	Agree
Test statistic testStatistic	3.7966506499631545	3.732836850520452	0.0638	within 0.000001 relative	Differs
Why these differ: Rosner's statistic is the largest standardised deviation from the mean, and the two tools standardise by different spreads. ProUCL divides by the population standard deviation; this toolkit divides by the sample standard deviation, the n-1 form. That is the whole of the difference - recomputing this scenario with the population divisor reproduces ProUCL's number to fifteen decimal places. Rosner (1983) and Gilbert (1987) both define the statistic with the sample standard deviation, and R's EnvStats rosnerTest agrees with this toolkit to fourteen decimal places, so the toolkit's value is kept.
Critical value criticalValue	2.91	2.908473059740994	0.00153	within 0.000001 relative	Differs
Why these differ: ProUCL reads its Rosner critical values out of Gilbert's published table, which is printed to two decimal places; this toolkit computes the same quantity in closed form from the Student's t distribution. R's EnvStats computes it the same way and agrees with this toolkit to fourteen decimal places. The difference is the rounding in the printed table, not a disagreement about the method, and it never changes which results are flagged in these scenarios.

Twenty-five results on automatic selection - the last n that picks Dixon

Boundary case

Input

25 values

value
10.2
11.4
9.8
10.7
12.1
9.4
11
10.5
9.9
10.8
11.7
10.1
9.6
10.4
11.2
10.9
9.7
10.6
11.5
10.3
9.5
11.1
10
48.6
10.35

Settings: test = auto, significance = 0.05, maxOutliers = 5

Against USEPA ProUCL (ProUCL 5.2.0)

Value	USEPA ProUCL	EnviroAutomate	Difference	Agreement band	Verdict
Test used testUsed	dixon	dixon	-	exact match	Agree
Test statistic testStatistic	0.9461538461538463	0.9461538461538463	0	within 0.000001 relative	Agree
Critical value criticalValue	0.406	0.406	0	within 0.000001 relative	Agree

Not run for this scenario

R EnvStats / nortest - at this sample size the toolkit uses Dixon's test, which EnvStats does not implement under the same convention

Evidence generated 2026-08-26 from a full comparison run against the versions named above.