t-test Calculator | Formula | p | t value formula
![t-test Calculator | Formula | p](https://i.imgur.com/axBPWDg.jpg)
Aswecommonlyperformapairedt-testwhenwehavedataaboutthesamesubjectsmeasuredtwice(beforeandaftersometreatment),letusadopttheconventionofreferringtothesamplesasthepre-groupandpost-group.Thenullhypothesisisthatthetruedifferencebetweenthemeansofpre-andpost-populationsisequaltosomepre-setvalue,ΔDeltaΔ.Thealternativehypothesisisthattheactualdifferencebetweenthesemeansis:DifferentfromΔDeltaΔ;SmallerthanΔDeltaΔ;orGreaterthanΔDeltaΔ.Typically,thispre-determineddifferenceiszero.Wecanthenreformulatetheh...
![t-test Calculator | Formula | p](https://i.imgur.com/H8YKUrg.jpg)
As we commonly perform a paired t-test when we have data about the same subjects measured twice (before and after some treatment), let us adopt the convention of referring to the samples as the pre-group and post-group.
The null hypothesis is that the true difference between the means of pre- and post-populations is equal to some pre-set value, ΔDeltaΔ.
The alternative hypothesis is that the actual difference between these means is:
Different from ΔDeltaΔ; Smaller than ΔDeltaΔ; or Greater than ΔDeltaΔ.Typically, this pre-determined difference is zero. We can then reformulate the hypotheses as follows:
The null hypothesis is that the pre- and post-means are the same, i.e., the treatment has no impact on the population.
The alternative hypothesis:
The pre- and post-means are different from one another (treatment has some effect); The pre-mean is smaller than the post-mean (treatment increases the result); or The pre-mean is greater th...