# Generalized approach for using unbiased symmetric metrics with negative values: normalized mean bias factor and normalized mean absolute error factor

## Abstract

Unbiased symmetric metrics provide a useful measure to quickly compare two datasets, with similar interpretations for both under and overestimations. Two examples include the normalized mean bias factor and normalized mean absolute error factor. However, the original formulations of these metrics are only valid for datasets with positive means. This paper presents a methodology to use and interpret the metrics with datasets that have negative means. The updated formulations give identical results compared to the original formulations for the case of positive means, so researchers are encouraged to use the updated formulations going forward without introducing ambiguity.

- Authors:

- Publication Date:

- Research Org.:
- Pacific Northwest National Lab. (PNNL), Richland, WA (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1054039

- Report Number(s):
- PNNL-SA-88316

KP1501021

- DOE Contract Number:
- AC05-76RL01830

- Resource Type:
- Journal Article

- Journal Name:
- Atmospheric Science Letters, 13(4):262-267

- Additional Journal Information:
- Journal Name: Atmospheric Science Letters, 13(4):262-267

- Country of Publication:
- United States

- Language:
- English

### Citation Formats

```
Gustafson, William I., and Yu, Shaocai.
```*Generalized approach for using unbiased symmetric metrics with negative values: normalized mean bias factor and normalized mean absolute error factor*. United States: N. p., 2012.
Web. doi:10.1002/asl.393.

```
Gustafson, William I., & Yu, Shaocai.
```*Generalized approach for using unbiased symmetric metrics with negative values: normalized mean bias factor and normalized mean absolute error factor*. United States. doi:10.1002/asl.393.

```
Gustafson, William I., and Yu, Shaocai. Tue .
"Generalized approach for using unbiased symmetric metrics with negative values: normalized mean bias factor and normalized mean absolute error factor". United States. doi:10.1002/asl.393.
```

```
@article{osti_1054039,
```

title = {Generalized approach for using unbiased symmetric metrics with negative values: normalized mean bias factor and normalized mean absolute error factor},

author = {Gustafson, William I. and Yu, Shaocai},

abstractNote = {Unbiased symmetric metrics provide a useful measure to quickly compare two datasets, with similar interpretations for both under and overestimations. Two examples include the normalized mean bias factor and normalized mean absolute error factor. However, the original formulations of these metrics are only valid for datasets with positive means. This paper presents a methodology to use and interpret the metrics with datasets that have negative means. The updated formulations give identical results compared to the original formulations for the case of positive means, so researchers are encouraged to use the updated formulations going forward without introducing ambiguity.},

doi = {10.1002/asl.393},

journal = {Atmospheric Science Letters, 13(4):262-267},

number = ,

volume = ,

place = {United States},

year = {2012},

month = {10}

}

DOI: 10.1002/asl.393

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