Which of these statements is correct about the F-distribution?
The correct statement about F-distribution is: -> It cannot be negative. Because, the minimum value of F-statistic is 0 i.e, it is the distribution of positive values.
One characteristic of the F distribution is that F cannot be negative. One characteristic of the F distribution is that the computed F can only range between -1 and +1. The shape of the F distribution is determined by the degrees of freedom for the F-statistic, one for the numerator and one for the denominator.
What is the F Distribution. The F-distribution, also known Fisher-Snedecor distribution is extensively used to test for equality of variances from two normal populations. F-distribution got its name after R.A. Fisher who initially developed this concept in 1920s. It is a probability distribution of an F-statistic.
The F-distribution is positively skewed and with the increase in the degrees of freedom ν1 and ν2, its skewness decreases. The value of the F-distribution is always positive, or zero since the variances are the square of the deviations and hence cannot assume negative values. Its value lies between 0 and ∞.
The graph of the F distribution is always positive and skewed right, though the shape can be mounded or exponential depending on the combination of numerator and denominator degrees of freedom.
Definition of F distribution
: a probability density function that is used especially in analysis of variance and is a function of the ratio of two independent random variables each of which has a chi-square distribution and is divided by its number of degrees of freedom.
Question: Which of the following is not a characteristic of the F distribution? Answer It is a continuous distribution.
As the number of DFs increases in both the numerator and denominator, the distribution approaches a normal distribution. *It is Asymptotic.
The exact shape of the F distribution depends on the two different degrees of freedom.
The distribution used for the hypothesis test is a new one. It is called the F distribution, named after Sir Ronald Fisher, an English statistician. The F statistic is a ratio (a fraction).
Is an F distribution normally distributed?
Normal distributions are only one type of distribution. One very useful probability distribution for studying population variances is called the F-distribution. We will examine several of the properties of this type of distribution.
The F Distribution
The distribution of all possible values of the f statistic is called an F distribution, with v1 = n1 - 1 and v2 = n2 - 1 degrees of freedom. The curve of the F distribution depends on the degrees of freedom, v1 and v2.
An F-test assumes that data are normally distributed and that samples are independent from one another. Data that differs from the normal distribution could be due to a few reasons. The data could be skewed or the sample size could be too small to reach a normal distribution.
Probability density functions of the F-distribution. To find Fa (n1,n2) such that P(F > Fa (n1,n2)) = α (shaded area in Fig. 4.6), we use the F table. For example, if F has 3 numerator and 6 denominator degrees of freedom, then F0.01 (3, 6) = 9.78.
