Statistic Distribution Measures
F-distribution:
A continuous right-skewed statistical distribution also Known as Snedecor’s F distribution or the Fisher - Snedecor distribution ( After R.A. Fisher and George W. Snedecor)(2) which arises in the testing of whether two observed samples have the same variance. (1)
Note that three of the most important distributions (namely the normal distribution, the t distribution, and the chi-square distribution) may be seen as special cases of the F distribution: (3)
Example: We want to measure the monthly sales volume from Microsoft and Apple. We collect data for a year ( 12 months). We calculate the variance for both and define the “degrees of freedom’ (n-1= 11) and then we can build the F-distribution.
F statistic ():
Defined as the ratio of the dispersions of the two distributions, in other words it is the value calculated by the ratio of two sample variances . F always >=1.
The F statistic can test the null hypothesis: (1) that the two sample variances are from normal populations with a common variance; (2) that two population means are equal; (3) that no connection exists between the dependent variable and all or some of the independent variables. |
Where and be independent variates distributed as chi-squared with and degrees of freedom.
Example: We want to measure the monthly sales volume from Microsoft and Apple. We collect data for a year ( 12 months). We calculate the variance for both and define the “degrees of freedom’ (n-1= 11) . Then we calculate F= (V² (M) /m)/ V²(A)/a, where V(M) variance for Microsoft, V(A) variance for Apple and m,a degrees of freedom for Microsoft and Apple respectively.
Chi-square Distribution:
The distribution of the sum of the squares of a set of variables, each of which has a normal distribution and is expressed in standardized units. It consist in a family of curves based on he number of degrees of distribution and is denoted by the symbol , which is pronounced "Ky square".
More precisely,
A continuous right-skewed statistical distribution also Known as Snedecor’s F distribution or the Fisher - Snedecor distribution ( After R.A. Fisher and George W. Snedecor)(2) which arises in the testing of whether two observed samples have the same variance. (1)
Note that three of the most important distributions (namely the normal distribution, the t distribution, and the chi-square distribution) may be seen as special cases of the F distribution: (3)
Example: We want to measure the monthly sales volume from Microsoft and Apple. We collect data for a year ( 12 months). We calculate the variance for both and define the “degrees of freedom’ (n-1= 11) and then we can build the F-distribution.
F statistic ():
Defined as the ratio of the dispersions of the two distributions, in other words it is the value calculated by the ratio of two sample variances . F always >=1.
The F statistic can test the null hypothesis: (1) that the two sample variances are from normal populations with a common variance; (2) that two population means are equal; (3) that no connection exists between the dependent variable and all or some of the independent variables. |
Where and be independent variates distributed as chi-squared with and degrees of freedom.
Example: We want to measure the monthly sales volume from Microsoft and Apple. We collect data for a year ( 12 months). We calculate the variance for both and define the “degrees of freedom’ (n-1= 11) . Then we calculate F= (V² (M) /m)/ V²(A)/a, where V(M) variance for Microsoft, V(A) variance for Apple and m,a degrees of freedom for Microsoft and Apple respectively.
Chi-square Distribution:
The distribution of the sum of the squares of a set of variables, each of which has a normal distribution and is expressed in standardized units. It consist in a family of curves based on he number of degrees of distribution and is denoted by the symbol , which is pronounced "Ky square".
More precisely,