\(\bullet\) State the null hypothesis

The null hypothesis is what is being tested

In the following example we are testing to see if all the population means are equal

\(H_0 = \mu_1 > \mu_2\)

\(H_0 =\) The null hypothesis
\(\mu_n =\) The population mean

\(\bullet\) State the alternate hypothesis

The alternate hypothesis is what makes the null hypothesis false

With the same example the alternate hypothesis would be

\(H_1 = \mu_1 < \mu_2\)

\(H_1 =\) The alternate hypothesis

\(\mu_n =\) the population mean

\(\bullet\) Set the \(\alpha\) value

The \(\alpha\) value is the confidence level

The standard is a confidence level of 95% or \(\alpha = 0.05\)

With this we can create a table of all possible outcomes

A visual interpretation of 95% confidence level. The area is probability that event in wrong while the green is correct

\(\bullet\) Collect the data

Some useful tools is plotly’s interactive box plot to examine the data prior to preforming F-test

\(\bullet\) Calculate the needed F statistic

To find your f statitic use this R code

qf(p,df1,df2,lower.tail=FALSE)****

p is the significance level for this case 0.05

df1 is the numerator degrees of freedom

df2 is the denominator degrees of freedom

This code returns the f statistic from the F table

Like below with input qf(0.05, 2, 20,lower.tail=FALSE) outputs

## [1] 3.492828

\(\bullet\) Establish acceptance zones for null hypothesis
The green is the probability the null hypothesis is accepted, red being rejected

\(\bullet\) Make conclusions

If your calculated F statistic from your one way ANOVA test is higher than the F value from the table then you must reject the null hypothesis

If your calculated F statistic is less than the F table result then you fail to reject the null hypothesis