
The actual definition of the F Ratio is as follows:
This is sometimes shortened to:
The larger the value of the F Ratio (sometimes called the F Statistic), the greater the likelihood that the difference between groups is due to Real Differences and not just due to chance (Random Differences). The required degree of certainty (for example, we want to be at least 95% that the groups are different) determines how large the F Ratio has to be for us to be able to state that the groups are different. The distribution of the F Ratio is called the F Distribution. The F Distribution is a family of distributions, each described by the following two parameters: ѵ1 = Degrees of Freedom Between Groups ѵ2 = Degrees of Freedom Within Groups Critical F Values have been calculated for various degrees of certainty (99% certainty, 95% certainty, etc.) for each of the basic F Distributions. The general rule use to state whether real differences exists between groups for a given level of certainty is as follows:
General Rule:
If F Statistic (ѵ1 , ѵ2) > F Critical
(ѵ1 , ѵ2)> The different treatments affected the output
The F Statistic and F Critical are calculated using the same ѵ1 and ѵ2. If
the F Statistic is greater than the F Critical that is calculated for a
specific degree of certainty, we can state that groups are statistically
different.
ANOVA Tests the Null Hypothesis 
1) Normality  Each of the groups should be
Normally distributed.
Homoscedasticity can be confirmed by a test called Levene's Test.
The hand calculations for ANOVA are very tedious. Excel has a builtin ANOVA
function that does a great job. The problem below is completed using
handcalculation but could much quicker using
Excel's builtin ANOVA function. The completed problem below is the simplest
type of ANOVA, known as Single Factor ANOVA. 1) Single Factor ANOVA
Each ANOVA test type is explained below:
Problem: Three Sales Closing Methods Tested With Single Factor ANOVA Three different sale closing methods were used. Three groups of
four salespeople were randomly chosen. Each group was instructed to use only
one of the closing methods for all of their sales. Sales totals of each
salesperson over the next two weeks were collected. Determine with a 95%
level of certainty whether there is a difference in the effectiveness of the
closing methods. Following are
Problem Solving Steps
If F Statistic (ѵ1 , ѵ2) > F Critical
(ѵ1 , ѵ2)> The different treatments affected the output Arrange the data as below to facilitate calculations:
Square Each
Sum of Squares Within Treatments = 34 + 2 + 10 = 46
F Criticalα=0.05(ѵ1=2,ѵ2=9) = 4.265
The calculated F Statistic(ѵ1 = 2, ѵ2 = 9) = 7.04. This is greater than F Criticalα=0.05 (ѵ1 = 2, ѵ2 = 9) = 4.265. This indicates that there is less than a 5% chance that this result could have occurred if there was no difference in the effectiveness between the closing methods. Therefore, there is at least a 95% certainty that there is a real difference in effectiveness of the closing methods. The Null Hypothesis, which was therefore rejected, states that choice of closing methods does not affect sales.
Statistics in Excel Home Normal Distribution t Distribution Binomial Distribution Regression Confidence Intervals Combinations and Permutations Correlation and Covariance ANOVA Other Useful Distributions
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