Independent T-test & Standard Deviation calculator
Independent T - test is also known as unpaired t test. It is used to measure the significant difference between two different groups (Not related). Example: Physiotherapist wants to check grade I mobilization on Group A and he can set the Group B as a control group to check for the placebo effects. Or We can also compare the two experiment groups.
Sample standard deviation\[S = \sqrt{\frac{\sum_{}^{}\left ( x_{i} - \mu \right )^{2}}{n-1}}\]
Population standard deviation\[\sigma = \sqrt{\frac{\sum_{}^{}\left ( x_{i} - \mu \right )^{2}}{n}}\]
Welch t-test\[t=\frac{\mu A - \mu B}{\sqrt{\frac{S{DA}^{2}}{n{A}}+\frac{S{DB}^{2}}{n{B}}}}\]
Welch test: Degrees of freedom (Satterthaite-Welch adjustment)\[df= \frac{\left ( \frac{S{DA}^{2}}{n{A}}+ \frac{S{DB}^{2}}{n{B}} \right )^2}{\frac{\left ( \frac{S{DA}^{2}}{n{A}} \right )^2}{nA-1}+\frac{\left ( \frac{S{DB}^{2}}{nB} \right )}{nB-1}}\]
Student's T-test (Unpaired)\[t= \frac{\left(\mu A - \mu B\right)}{\sqrt{\left(\frac{S{p}^2}{n{A}}\right)+\left(\frac{S{p}^2}{n{B}}\right)}}\]
Where\[S{p}^2= \frac{\left (n{A}-1\right)SA^2 + \left(n{B}-1 \right)SB^2}{n{A}+n{B}-1}\]
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