1. What is ANOVA and Why do we use it?

2. ANOVA-stands for “Analysis Of Variance”
It’s purpose is to detect statistical DIFFERENCE of mean values.
Used specifically when comparing the mean values of 3 OR MORE GROUPS.
You should have at least 5!! (age categories, religions, income levels, etc.)
When raw data is entered it will provide you with a P VALUE
You always begin assuming the NULL HYPOTHESIS which is that there IS NO DIFFERENCE between the groups.

3. What is a P Value?
The P value gives you the probability that the difference in averages/means between groups is due to randomness.
For example:
If you flip 2 different coins 10 times and get 7 heads/3 tails on one coin and 4 heads/6 tails on the other, would you conclude that those two coins are ACTUALLY DIFFERENT?
Or were the different measurements likely just due to randomness?
The threshold at which you determine statistical significance is arbitrarily set.
Ex. 1 A marketing firm testing a new product may set P = .05
Ex. 2 A pharmaceutical co. Testing a new drug may set their P at .01
**For IB ESS IA Surveys, P = 0.10
This means that we require there to be a less than 10% chance that the differences are due to randomness.

4. What Next?
If your P value is above 0.10, we conclude that there is no significant difference between the groups and we ACCEPT the null hypothesis.
If the P value is below 0.10, we conclude that there is significant difference and we REJECT the null hypothesis.
BUT... It does not tell us which two groups the difference is between. It just tells us that there is a difference SOMEWHERE.
Now we need to do PAIRWISE COMPARISONS to figure out which two populations are actually different from one and other.

5. If you reject the null hypothesis...
You need to perform the Bonferroni Correction, which means you are simply changing your P Threshold
Your Bonferroni Value will be your original P value (0.10) divided by the total number of pairs.
If you have 5 Levels of Independent Variables your total number of pairs is 10 ( )
This makes your new P Value 0.01 (0.1/10)
If any of your pairwise comparison p values are BELOW this threshold, you reject the null hypothesis and conclude that those two groups are SIGNIFICANTLY DIFFERENT

6. One-Way ANOVA Analysis Tutorial for Google Sheets