ANOVA (Analysis of Variance)
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).
The ANOVA statistic prevents us from having to do multiple t-tests and puts all the data into one number. The math required of the ANOVA test is beyond the scope of this class. There are excellent on-line ANOVA calculators that will do the math and draw a conclusion for you. In nearly every situation in IB biology, if given a choice, you will want to select "one way ANOVA" (what this actually means is beyond our scope, but I can explain it to you if you are actually curious).
Just like the T-test, the ANOVA tests the null and alternative hypothesis:
The ANOVA statistic prevents us from having to do multiple t-tests and puts all the data into one number. The math required of the ANOVA test is beyond the scope of this class. There are excellent on-line ANOVA calculators that will do the math and draw a conclusion for you. In nearly every situation in IB biology, if given a choice, you will want to select "one way ANOVA" (what this actually means is beyond our scope, but I can explain it to you if you are actually curious).
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:
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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:
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Performing an ANOVA
The test statistic that an ANOVA produces is an F-value. The F-value is a ratio of the sample variances. Variances are a measure of dispersion, or how far the data are scattered from the mean. Larger values represent greater dispersion between sample groups. The larger the F-value, the more likely the 3+ samples are significantly different from each other. Here's a good online ANOVA calculator.
Performing an ANOVA test with Google Sheets
In order to run an ANOVA in Google Sheets, you have to install a statistics add-on. Here's a good video explaining how to do it! The "groups" would be the different levels of your manipulated variable. If the p value is greater than 0.05, then the results are not-significant (there is no significant different between the means of the groups).
Performing an ANOVA test with the TI-83/84

- Hit the STAT button on the calculator
- Select option 4 to clear any past lists of data.
- Select option 1 to EDIT your lists.
- Enter your data for each group as Lists. The data for each level of the MV should be placed in its own list.
- Hit STAT button and use the arrow key to move over to the TESTS option
- Scroll down to option H, the ANOVA and hit ENTER
- Enter the lists you want to include in the ANOVA
- Your results are given. The ANOVA test will result in
a “p-value.” If the p-value you get is less than 0.05, we reject the null hypothesis and conclude that there
is a significant difference between the means being compared. Likewise, if the p-value you get is more than
0.05, you would accept the null hypothesis and conclude that there is no significance difference between the means.