Lets calculate one way ANOVA with the below dataset.
Assumptions:
Null Hypothesis = H0: µ1=µ2=µ3
Alternative Hypothesis= Ha: µ1!=µ2!=µ3
Calculate the Mean:
Grand Mean: Mean of all sample means or mean for all observation from all samples
Between Group Variability:
When you see below image the two different samples is overlapped, which means means for two samples, so even in grand mean there won’t help much
Fig 1
In the below image two different sample is has no overlap, so obviously there mean will also differ
Fig 2
The above two scenarios we will called Between Group Variability
Within Group Variability 
Between Group vs Within Group Variability:
Lets calculate Between groups:
We need to find the difference between from each data point to the mean and there individual sum.
Lets calculate Within the groups :
F-Statistic
The statistic which measures if the means of different samples are significantly different or not is called the F-Ratio. Lower the F-Ratio, more similar are the sample means. In that case, we cannot reject the null hypothesis.
F =
Our F-stats < F critical value, So we can reject null hypothesis
Data and Machine by viswateja 