This function detects outliers using the maximum normed residual method described in CMH-17-1G. This method identifies a value as an outlier if the absolute difference between the value and the sample mean divided by the sample standard deviation exceeds a critical value.

`maximum_normed_residual(data = NULL, x, alpha = 0.05)`

- data
a data.frame

- x
the variable in the data.frame for which to find the MNR or a vector if

`data=NULL`

- alpha
the significance level for the test. Defaults to 0.05

an object of class `mnr`

This object has the following fields:

`call`

the expression used to call this function`data`

the original data used to compute the MNR`alpha`

the value of alpha given by the user`mnr`

the computed MNR test statistic`crit`

the critical value given the sample size and the significance level`outliers`

a data.frame containing the`index`

and`value`

of each of the identified outliers`n_outliers`

the number of outliers found

`data`

is an optional argument. If `data`

is given, it
should be a
`data.frame`

(or similar object). When `data`

is specified, the
value of `x`

is expected to be a variable within `data`

. If
`data`

is not specified, `x`

must be a vector.

The maximum normed residual test is a test for outliers. The test statistic is given in CMH-17-1G. Outliers are identified in the returned object.

The maximum normed residual test statistic is defined as:

$$MNR = max \frac{\left| x_i - \bar{x} \right|}{s} $$

When the value of the MNR test statistic exceeds the critical value defined in Section 8.3.3.1 of CMH-17-1G, the corresponding value is identified as an outlier. It is then removed from the sample, and the test statistic is computed again and compared with the critical value corresponding with the new sample. This process is repeated until no values are identified as outliers.

“Composite Materials Handbook, Volume 1. Polymer Matrix Composites Guideline for Characterization of Structural Materials,” SAE International, CMH-17-1G, Mar. 2012.

```
library(dplyr)
carbon.fabric.2 %>%
filter(test=="FC" & condition=="ETW2" & batch=="A") %>%
maximum_normed_residual(strength)
#>
#> Call:
#> maximum_normed_residual(data = ., x = strength)
#>
#> MNR = 1.958797 ( critical value = 1.887145 )
#>
#> Outliers ( alpha = 0.05 ):
#> Index Value
#> 6 44.26
## Call:
## maximum_normed_residual(data = ., x = strength)
##
## MNR = 1.958797 ( critical value = 1.887145 )
##
## Outliers ( alpha = 0.05 ):
## Index Value
## 6 44.26
carbon.fabric.2 %>%
filter(test=="FC" & condition=="ETW2" & batch=="B") %>%
maximum_normed_residual(strength)
#>
#> Call:
#> maximum_normed_residual(data = ., x = strength)
#>
#> MNR = 1.469517 ( critical value = 1.887145 )
#>
#> No outliers detected ( alpha = 0.05 )
#>
## Call:
## maximum_normed_residual(data = ., x = strength)
##
## MNR = 1.469517 ( critical value = 1.887145 )
##
## No outliers detected ( alpha = 0.05 )
```