myz-vgb.ru A Business Encyclopedia

F-Distribution

Definition: The F-Distribution is also called as Variance Ratio Distribution as it usually defines the ratio of the variances of the two normally distributed populations. The F-distribution got its name after the name of R.A. Fisher, who studied this test for the first time in 1924.

Symbolically, the quantity is distributed as F-distribution with ν1 =n1-1 and ν2 = n2-1 degrees of freedom and is represented as:

F-Distribution-1Where,
S12 is the unbiased estimator of σ12 and is calculated as:

F-Distribution-2S22 is the unbiased estimator of σ22 and is calculated as:

F-Distribution-3The parameters of the F-distribution are degrees of freedom ν1 for the numerator and degrees of freedom ν2 for the denominator. Thus, with the change in the values of these parameters the distribution also changes. The F distribution probability density function is given by:

F-Distribution-4Y0 = constant depending on the values of ν1 and ν2.

For testing the hypothesis of the equality of two population variances, the following statistic is used:

F-Distribution-5Here, the Null hypothesis = σ12 = σ22 which follows the F-distribution with degrees of freedom ν1 and ν2. Often, the larger sample variance is placed in the numerator for the convenient computations. In doing so, we get the ratio of sample variance equals to or greater than one.

If the computed value of F exceeds the table value of F, then the null hypothesis is rejected and the alternative hypothesis gets accepted. On the other hand, if the computed value of F is less than the table value, the null hypothesis is accepted.

Leave a Reply

Your email address will not be published. Required fields are marked *

Shares

Related pages


employees provident fund contribution rateadvertising jargonsadvantages of job enrichmentconvenience sampling meaningdefinition divestblackscholes formularegiocentric orientationdisadvantages of job enlargementdefine classic conditioningcourteous hindi meaningpavlov classical conditioning theorybusiness cycle in managerial economicswhat is the meaning of draweedefinition of pertjob enrichment defined1 black scholesoligopoly marketsdiminishing rate of substitutioncrm advantages and disadvantagesprocess of capital budgeting stepsmoratorium on loanguerrilla meanstaylorism theoryhow to overcome psychological barriers in communicationexample of market skimmingethnocentrism disadvantagesvestibule definitiondefinition of hr scorecardwhat is the purpose of hrmmarketing promotion mixconcentric and conglomerate diversificationqueues meaningfixed asset turnover ratio formulaunderstudy trainingcause of cost push inflationtheory of motivation by herzbergincome tax return tdspromotional pricing meaningbarometric forecastdefinition for guerrilla warfarechit fund company meaningdefine macro environment in marketingmeaning forexsocial loofingwhat is sbi kiosk bankingsimplex algorithprocess of business process reengineeringperfect monopoly definitiondefine provident fundthematic mutual fundsdefine macro environment in marketingvertical marketing system examplesasset turnover ratio definitiondefinition of segmentation in marketingordinal scale examplesjoseph a schumpeterppf public provident funddelfi methoddefinition of suasionvague means in hindiliquidity ratios for banksbusiness turnaround managementwhat is macro environment in marketingentrepreneurial defhow to trade using demat accountwhat is multiplier in economicsexplain foreign exchange ratesstrategic stabilitycyclical unemployment definition and examplesthe laissez faire leadership stylemeaning of subscribed capitalrecurring deposit wikimeaning of loafingmarginal utility of money is constantcamels financial analysismajor factors influencing consumer behaviourrevenue turnover formulapositive valence definition