## 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)

$R ~ = ~ 1 ~ - ~ \frac{\text{Total TEM} ^ 2}{SD ^ 2}$