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.
Important Questions from Probability and Statistics
In a frequency curve, what is plotted on the vertical axis?
If the probability of a bad reaction from a certain injection is 0.001, the chance that out of 2000 individuals, more than two will suffer of a bad reaction is
If x and y are deviation from mean x̅ and y̅ respectively and if r = 0.5, ∑xy = 120, σy = 8 and ∑x 2= 90, what is the value of 'n' ?
In an examination involving multiple choice questions, a student works out the solution in 50% of the questions. In the remaining questions the student guesses the answer. However, when the answer is guessed the probability that it is correct is 0.30. When the student works out the solutions it may be wrong with probability 0.10.
If the answer to a particular question is correct, what is the probability that the student guessed the answer?
The lengths of a large stock of titanium rods follow a normal distribution with a mean (μ) of 440 mm and a standard deviation (σ) of 1 mm. What is the percentage of rods whose lengths lie between 438 mm and 441 mm?
