Technical Error of Measurement

Ernest Guevarra

2024-12-18

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)

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