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S _ { tilde { f } _ { 1 } - overline { Y } _ { 2 } } = sqrt { frac
S _ { \tilde { f } _ { 1 } - \overline { Y } _ { 2 } } = \sqrt { \frac { ( N _ { 1 } - 1 ) s _ { 1 } ^ { 2 } + ( N _ { 2 } - 1 ) s _ { 2 } ^ { 2 } } { ( N _ { 1 } + N _ { 2 } ) - 2 } } \sqrt { \frac { N _ { 1 } + N _ { 2 } } { N _ { 1 } N _ { 2 } } }
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