Question

Three Discussion Questions Each response must have a minimum of 150 words MUST have references for each response! Quality work!

1. what is the overall real world application of F-Testing? How would this be used in modern business systems to help management make more sound choices on the impacts that their data has on the business overall?   
2. So far these is an obvious show of understanding of the ANOVA process for both one factor and two factor versions. But remember the Ho for ANOVA is that all of the means are the same. If we reject Ho and see that one or more of the means is different, how do we find which ones are the different ones? Thoughts on the subject?   
3. if ANOVA is testing if means are the same or different, why do we use the F-Test which measures how variances differ? Any thoughts?

Answer 1

it is now wise to see F- distribution as just the ratio of two random variables the applications of this distribution is pretty interesting, such as the testing of regression parameters in multiple linear regression which has a huge importance in financial market and modelling of say exchange rates and derivatives, where we try to see if the exchange rate really depends on the explanatory variables which are considered in the modelling, Another application is in the testing of mean vector where the student T-sq statistic is seen to be following an F-distribution and the testing is done to check if the mean vector the application of this can be seen in checking if the prices of a basket of goods has changed or not. A very well known application of F-distribution is testing the ratio of variances of two test statistic which are testing the same hypothesis but we know a test statistic with a lower variance is better the application of this method in real world is seen more in quantitative research while checking for a a easier way to estimate or test an important parameter such as consumption ratio of GDP.

ANOVA is a very similar way for checking regression parameters but its application are limited to just that, here we see the difference in SSR sum of squared regression has significantly changed or not, or how much more variance is explained by the new variable.