# What Does F To F Mean

By | 22/11/2022

A one-manner ANOVA is used to determine whether or not the means of three or more than independent groups are equal.

A one-fashion ANOVA uses the following null and culling hypotheses:

• H0:
All group means are equal.

• HA:
At least one grouping mean is different from the residual.

Whenever you perform a ane-fashion 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

P-value

Treatment
192.2 2 96.one two.358 0.1138

Error
1100.6 27 xl.8

Total
1292.8 29

The
F-value
in the table is calculated as:

• F-value = Hateful Squares Handling / Mean Squares Error

Some other style to write this is as follows:

• F-value = 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 F-value will exist big.

For example, the F-value in the table in a higher place is calculated as:

• F-value = 96.i / 40.8 = two.358

To find the p-value that corresponds to this F-value, nosotros can utilize an F Distribution Figurer with numerator degrees of freedom = df Treatment and denominator degrees of liberty = df Error.

For example, the p-value that corresponds to an F-value of 2.358, numerator df = 2, and denominator df = 27 is
0.1138.

Since this p-value 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 F-Value of an ANOVA

To gain an intuitive understanding of the F-value in an ANOVA tabular array, consider the following example.

Suppose nosotros’d like to perform a one-style ANOVA to determine if three unlike studying techniques produce different mean examination scores. The post-obit 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 ane-way ANOVA for this dataset, we notice that the F-value is2.358
and the respective p-value is0.1138.

Since this p-value 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

• The F-value in an ANOVA is calculated as: variation between sample means / variation within the samples.
• The higher the F-value in an ANOVA, the higher the variation between sample means relative to the variation within the samples.
• The higher the F-value, the lower the respective p-value.
• If the p-value 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.