# Statistical tests for anomalies using Grubbs' test and Dixon's test

Source:`R/grubbs.R`

`grubbs_anomalies.Rd`

Grubbs' test (proposed in 1950) identifies possible anomalies in univariate data using z-scores assuming the data come from a normal distribution. Dixon's test (also from 1950) compares the difference in the largest two values to the range of the data. Critical values for Dixon's test have been computed using simulation with interpolation using a quadratic model on logit(alpha) and log(log(n)).

## Details

Grubbs' test is based on z-scores, and a point is identified as an
anomaly when the associated absolute z-score is greater than a threshold value.
A vector of logical values is returned, where `TRUE`

indicates an anomaly.
This version of Grubbs' test looks for outliers anywhere in the sample.
Grubbs' original test came in several variations which looked for one outlier,
or two outliers in one tail, or two outliers on opposite tails. These variations
are implemented in the `grubbs.test`

function.
Dixon's test only considers the maximum (and possibly the minimum) as potential outliers.

## References

Grubbs, F. E. (1950). Sample criteria for testing outlying observations.
*Annals of Mathematical Statistics*, 21(1), 27–58.
Dixon, W. J. (1950). Analysis of extreme values.
*Annals of Mathematical Statistics*, 21(4), 488–506.

## Examples

```
x <- c(rnorm(1000), 5:10)
tibble(x = x) |> filter(grubbs_anomalies(x))
#> # A tibble: 6 × 1
#> x
#> <dbl>
#> 1 5
#> 2 6
#> 3 7
#> 4 8
#> 5 9
#> 6 10
tibble(x = x) |> filter(dixon_anomalies(x))
#> # A tibble: 0 × 1
#> # ℹ 1 variable: x <dbl>
y <- c(rnorm(1000), 5)
tibble(y = y) |> filter(grubbs_anomalies(y))
#> # A tibble: 1 × 1
#> y
#> <dbl>
#> 1 5
tibble(y = y) |> filter(dixon_anomalies(y))
#> # A tibble: 1 × 1
#> y
#> <dbl>
#> 1 5
```