A onemanner ANOVA is used to determine whether or not the means of three or more than independent groups are equal.
A onefashion ANOVA uses the following null and culling hypotheses:

H_{0}:
All group means are equal. 
H_{A}:
At least one grouping mean is different from the residual.
Whenever you perform a anefashion ANOVA, you lot will end upwardly with a summary table that looks like the following:
Source 
Sum of Squares (SS) 
df 
Mean Squares (MS) 
F 
Pvalue 

Treatment 
192.2  2  96.one  two.358  0.1138 
Error 
1100.6  27  xl.8  
Total 
1292.8  29 
The
Fvalue
in the table is calculated as:
 Fvalue = Hateful Squares Handling / Mean Squares Error
Some other style to write this is as follows:
 Fvalue = variation between sample ways / variation within the samples
If the variation between the sample means is high relative to the variation within each of the samples, then the Fvalue will exist big.
For example, the Fvalue in the table in a higher place is calculated as:
 Fvalue = 96.i / 40.8 = two.358
To find the pvalue that corresponds to this Fvalue, nosotros can utilize an F Distribution Figurer with numerator degrees of freedom = df Treatment and denominator degrees of liberty = df Error.
For example, the pvalue that corresponds to an Fvalue of 2.358, numerator df = 2, and denominator df = 27 is
0.1138.
Since this pvalue is not less than α = .05, we fail to pass up the zero hypothesis. This ways there is no statistically significant departure between the means of the three groups.
Visualizing the FValue of an ANOVA
To gain an intuitive understanding of the Fvalue in an ANOVA tabular array, consider the following example.
Suppose nosotros’d like to perform a onestyle ANOVA to determine if three unlike studying techniques produce different mean examination scores. The postobit tabular array shows the exam scores of 10 students who used each technique:
Nosotros tin create the following plot to visualize the exam scores past group:
The variation
within
the samples is represented by the spread of the values within each individual sample:
The variation
betwixt
the samples is represented past the differences between the sample means:
Upon performing a aneway ANOVA for this dataset, we notice that the Fvalue is2.358
and the respective pvalue is0.1138.
Since this pvalue is not less than .05, we fail to reject the null hypothesis. This means nosotros don’t have sufficient bear witness to say that the studying technique used causes statistically meaning differences in mean exam scores.
In other words, this tells the states that the variation betwixt the sample means is non high enough relative to the variation within the samples to reject the null hypothesis.
Decision
Hither’s a brief summary of the principal points in this article:
 The Fvalue in an ANOVA is calculated as: variation between sample means / variation within the samples.
 The higher the Fvalue in an ANOVA, the higher the variation between sample means relative to the variation within the samples.
 The higher the Fvalue, the lower the respective pvalue.
 If the pvalue is below a certain threshold (e.g. α = .05), we can reject the null hypothesis of the ANOVA and conclude that there is a statistically significant difference between group ways.
Additional Resource
How to Perform a OneMode ANOVA in Excel
How to Perform a OneWay ANOVA by Mitt
1Way ANOVA Calculator
Source: https://www.statology.org/whatdoesahighfvaluemean/