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Table 3 Statistical power of the between-group within-group test T BW (25): σ μ  = 1

From: Statistical power as a function of Cronbach alpha of instrument questionnaire items

    k = 5 k = 10
N per group Δ BW C α φ BW \({\tilde{\varphi}}_{\mathit{\mathsf{B}}\mathit{\mathsf{W}}}\) φ BW \({\tilde{\varphi}}_{\mathit{\mathsf{B}}\mathit{\mathsf{W}}}\)
30 0.4 0.5 0.194 0.179 0.183 0.194
   0.6 0.268 0.264 0.254 0.268
   0.7 0.387 0.375 0.359 0.387
   0.8 0.591 0.618 0.594 0.591
   0.9 0.908 0.884 0.901 0.908
50 0.3 0.5 0.164 0.184 0.214 0.184
   0.6 0.242 0.254 0.261 0.254
   0.7 0.387 0.367 0.365 0.367
   0.8 0.511 0.564 0.591 0.564
   0.9 0.893 0.889 0.893 0.889
  1. Note: N per group: number of subjects per group; k: number of items; \({\varDelta}_{\mathit{\mathsf{B}}\mathit{\mathsf{W}}}={\delta}_{\mathit{\mathsf{B}}\mathit{\mathsf{W}}}/{\sigma}_{\mu }\); C α : Cronbach alpha; φ BW : theoretical power (27); \({\tilde{\varphi}}_{\mathit{\mathsf{B}}\mathit{\mathsf{W}}}\): simulation-based empirical power