Table 3 Comparison of common Level 2 BCI-Based AAC performance metrics

Written symbol rate (WSR)

$\mathit{WSR}=\left\{\begin{array}{c}\hfill \frac{\left(2\mathit{SR}-1\right)}{c}\hfill \\ \hfill 0\hfill \end{array}\right.\begin{array}{c}\hfill ,\mathit{SR}>0.5\hfill \\ \hfill ,\mathit{else}\hfill \end{array}$

where SR = ITR × c/log₂(N)

Practical bit rate (PBR)

$\mathit{PBR}=\left\{\begin{array}{c}\hfill \frac{\left(2P-1\right)}{c}\hfill \\ \hfill 0\hfill \end{array}\right.\times {log}_2\left(N\right)\begin{array}{c}\hfill ,P>0.5\hfill \\ \hfill ,\mathit{else}\hfill \end{array}$

The original reference did not report a formula, this was back-calculated from the results

Extended confusion matrix (ECM)

Confusion matrix, as in Table 2, extended to allow for an extra detected class, “abstention.”

Eff_SYS

$\mathit{Ef}{f}_{\mathit{SYS}}=\frac{1}{\overline{L_{\mathit{CW}}}\times \overline{\mathit{ESC}}}$

Where$\overline{\mathit{ESC}}={\displaystyle \sum _{i=1}^{N_{\mathit{LA}}}\frac{\widehat{p}\left(i\right)}{2p\left(i\right)-1}}$

Where L_CW is the mean codeword length, N_LA is the number of symbols in the logical alphabet,$\widehat{p}$ is the probability of a logical output appearing, and p(i) is the probability of identifying output i.

This equation is simplified from equation (20) of[17], assuming that all errors require two selections to correct. Interested readers are referred to[17] for alternative methods of error correction.

Eff_SYS’

$\mathit{Ef}{f}_{\mathit{SYS}}\text{'}=\frac{1}{\overline{L_{\mathit{CW}}}\times \overline{\mathit{ESC}}}$

Where$\mathit{ESC}={\displaystyle \sum _{i=1}^{N_{\mathit{LA}}}\widehat{p}\times \left(\frac{1}{p\left(i\right)}+\left(\frac{1}{p\left(i\right)}-1\right)\left(\frac{1}{2*p_B-1}\right)\right)}$

Where L_CW is the mean codeword length, N_LA is the number of symbols in the logical alphabet, and$\widehat{p}$ is the probability of a logical output appearing, as per[6]. The symbols p(i) and p_b are the probabilities of correctly identifying output i and the backspace option, respectively.

Output characters per minute (OCM)

$\mathit{OCM}=\frac{\mathit{Correct}\mathit{Characters}}{\mathit{Time}\mathit{Taken}}$

BCI-Utility metric

$U=\frac{E\left(\mathit{benefit}/\mathit{selection}\right)}{E\left(\mathit{time}/\mathit{selection}\right)}$

U must be derived for particular problems and can take different forms, several of which are presented in[16]. Several of these forms are redundant with other level 2 metrics, for example, in the experiment presented in[16], this metric becomes identical to practical bit rate.