Table 3.

Formulae in Various Types of Comparison for Comparing Two Group Means

Type of comparison	H1	H0	Sample size for control group	Sample size for test group
Test for Equality	μt – μc ≠ δ	μt – μc = δ	$n_c=\frac{(1+1⁄k){\sigma }^2(Z_{(\alpha ⁄2)}+Z_{\beta }{)}^2}{({\mu }_t–{\mu }_c–\delta {)}^2}$	nt = knc
Test for Superiority	μt – μc > δ (> 0)	μt – μc ≤ δ	$$\begin{gathered} n_c=\frac{(1+1⁄k){\sigma }^2(Z_{\alpha }+Z_{\beta }{)}^2}{\left(\right({\mu }_t–{\mu }_c)–\delta {)}^2} \\ \delta > 0:\mathrm{Superiority}, \\ \delta < 0:\mathrm{Non}–\mathrm{inferiority} \end{gathered}$$	nt = knc
Test for Non-inferiority	μt – μc > δ (< 0)	μt – μc ≤ δ		nt = knc
Test for Equivalence	|μt – μc| < δ	|μt – μc| ≥ δ	$n_{\mathit{c}}\mathit{=}\frac{\mathit{(}1+1\mathit{⁄}\mathit{k}\mathit{)}{\mathit{\sigma }}^{\mathit{2}}\mathit{ }\mathit{(}{\mathit{Z}}_{\mathit{\alpha }}\mathit{+}{\mathit{Z}}_{\mathit{\beta }\mathit{⁄}\mathit{2}}{\mathit{)}}^{\mathit{2}}}{{\mathit{(}\mathit{\delta }\mathit{–}\mathit{|}{\mathit{\mu }}_{\mathit{t}}\mathit{–}{\mathit{\mu }}_{\mathit{c}}\mathit{\left|}\mathit{\right)}}^{\mathit{2}}}$	nt = knc