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tem.Rmd
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tem.Rmd
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---
title: "Technical Error of Measurement"
author: "Ernest Guevarra"
date: "`r Sys.Date()`"
output: rmarkdown::html_vignette
vignette: >
%\VignetteIndexEntry{Technical Error of Measurement}
%\VignetteEngine{knitr::rmarkdown}
%\VignetteEncoding{UTF-8}
---
```{r setup, include = FALSE}
knitr::opts_chunk$set(
collapse = TRUE,
comment = "#>"
)
```
## Intra-observer TEM for two measurements, and inter-observer TEM involving two measurers
$$ TEM ~ = ~ \sqrt{\frac{\sum D ^ 2}{2N}} $$
where
$D ~ = ~ \text{The difference between measurements}$
$N ~ = ~ \text{The number of individuals measured}$
## Inter-observer TEM with more than two observers
$$ TEM ~ = ~ \sqrt{\sum\nolimits_1 ^ N \left (\sum\nolimits_1 ^ K M ^ 2 ~ - ~ \frac{\left (\sum\nolimits_1 ^ K M \right ) ^ 2 / K}{N(K ~ - ~ 1)} \right )} $$
where
$N ~ = ~ \text{Number of subjects}$
$K ~ = ~ \text{Number of observers}$
$M ~ = ~ \text{Measurement}$
## Relative TEM
$$ \% ~ TEM ~ = ~ \frac{TEM}{mean} ~ \times ~ 100 $$
## Total TEM for two observers and two measurements per observer
$$ \text{Total TEM} ~ = ~ \sqrt{\frac{TEM ~ \times ~ (intra_1) ^ 2 ~ + ~ TEM ~ \times ~ (intra_2) ^ 2}{2} ~ + ~ TEM \times (inter) ^ 2} $$
## Total TEM for three observers and two measurements per observer
$$ \text{Total TEM} ~ = ~ \sqrt{\frac{TEM ~ \times ~ (intra_1) ^ 2 ~ + ~ TEM ~ \times ~ (intra_2) ^ 2 ~ + ~ TEM ~ \times ~ (intra_3) ^ 2}{3} ~ + ~ TEM ~ \times ~ inter ^ 2} $$
## Relative total TEM
$$ \% ~ \text{Total TEM} ~ = ~ \frac{\text{Total TEM}}{mean} ~ \times ~ 100 $$
## Coefficient of Reliability (R)
$$ R ~ = ~ 1 ~ - ~ \frac{\text{Total TEM} ^ 2}{SD ^ 2} $$