The relation between 't' ratio and 'F' ratio is :
t=Square root of F
F Ratio and t Ratio Statistical Link
The relationship between the t ratio (t-statistic) and the F ratio (F-statistic) is a key concept in statistical hypothesis testing. This connection is particularly evident when the F-test is used in contexts where the numerator has only one degree of freedom.
In such specific statistical situations, the F-statistic is precisely the square of the corresponding t-statistic. Mathematically, this is expressed as:
$F = t^2$
To find the relationship for the t-statistic itself, we take the positive square root of both sides of this equation. This yields:
$t = \sqrt{F}$
This inverse relationship highlights that the t-statistic is effectively the square root of the F-statistic under these conditions, frequently observed in simple regression or when comparing two variances.
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