For tind, is obtained by. $\eta ^ { 2 }$
A) $\frac { t ^ { 2 } } { t ^ { 2 } + d f }$
B) $\quad \frac { t ^ { 2 } + d f } { t ^ { 2 } }$
C) $\frac { t } { t ^ { 2 } + d f }$
D) $\underline { t } ^ { 2 } \frac { + d f } { t }$

Question

For tind, is obtained by. $\eta ^ { 2 }$ 
A) $\frac { t ^ { 2 } } { t ^ { 2 } + d f }$
B) $\quad \frac { t ^ { 2 } + d f } { t ^ { 2 } }$
C) $\frac { t } { t ^ { 2 } + d f }$
D) $\underline { t } ^ { 2 } \frac { + d f } { t }$

Quizplus · Accepted Answer

The formula for tind is given as: $\eta ^ { 2 }=\frac { t ^ { 2 } } { t ^ { 2 } + d f }$. Solving for $\eta ^ 2$ we get: $\eta ^ { 2 }=\frac { t ^ { 2 } } { t ^ { 2 } + d f }\times \frac { t ^ { 2 } } { t ^ { 2 } }$. Simplifying we get: $\eta ^ { 2 }=\frac { t ^ { 4 } } { (t ^ { 2 } + d f) t ^ { 2 } }$. Taking the square root we get: $\eta =\frac { t ^ { 2 } } { \sqrt { (t ^ { 2 } + d f) t ^ { 2 } } }$. Simplifying we get: $\eta =\frac { t ^ { 2 } } { \sqrt { t ^ { 4 } + d f t ^ { 2 } } }$. Taking the square again we get: $\eta ^ { 2 }=\frac { t ^ { 4 } } { t ^ { 4 } + d f t ^ { 2 } }$. Therefore, the answer is A.

For Tind, Is Obtained By η2\eta ^ { 2 }η2 A) t2t2+df\frac { t ^ { 2 } } { t ^ { 2 } + d f }t2+dft2​

For Tind, Is Obtained By $\eta ^ { 2 }$ A) $\frac { t ^ { 2 } } { t ^ { 2 } + d f }$