The ANOVA test is a statistical test that can be done in place of multiple T-tests when comparing the means of more than two groups at a time.
The t-test tells us if the variation between two groups is "significant". If you have 5 five levels of a manipulated variable in an experiment, you would need to compare the mean of each level of the MV to the mean of each other level of the MV. That’s 10 T-tests! Not only would 10 T-tests be a pain to calculate, but multiple t-tests are not the answer because with each T-test, the likelihood of drawing an incorrect conclusion increases. If we did 10 t-tests, we should not be surprised to observe things that happen only 5% of the time (p=0.05).
Just like the T-test, the ANOVA tests the null and alternative hypothesis:
Null Hypothesis:
"There is not a significant difference between the groups; any observed differences may be due to chance and sampling error.
For example:
There is no significant difference between the number of birds at the different locations; the differences we see in the means of the groups may be due to chance and sampling error.
Alternative Hypothesis:
"There is a significant difference between the groups; the observed differences are most likely not due to chance or sampling error."
For example:
There is a significant difference between the number of birds at the different locations; the difference we see in the means of the groups is mostly likely not due to chance or sampling error.