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Introduction to Biological Sciences lab, first semester

A *t*-test of means is actually a special case of a broader type of analysis called **analysis of variance** (or **ANOVA**). A regular *t*-test of means produces exactly the same results as a single-factor ANOVA. The advantage of an ANOVA over a *t*-test is that in a more complicated design, ANOVA can be used to simultaneously assess the significance of more than one factor, as well as interactions among factors.

In a two-factor ANOVA, one of the factors can be a random effect which contributes to the variability in the measurements, but which is not manipulated nor can be controlled by the experimenter. The "block" group is a group of samples that are likely to have experienced the same uncontrollable conditions. **Blocking** is a technique used in experimental design when it is not possible to control some sources of variation. A properly blocked experiment can make the effects of a treatment detectable statistically when it is clear that an uncontrollable factor is present in the experiment. In the example of Section 8.1, the "student group" is the block effect. Other examples of block effects might be samples growing in the same flower pot, trials conducted on the same day, etc.

Rather than using a paired *t*-test to analyze the malonate/no-malonate data of Section 8.1, we could perform a two-factor ANOVA, with presence or absence of malonate as one factor, and student group as another factor. The analysis of variance produces *P*-values for each of the two factors with the malonate effect significant at *P*=0.0453 (the same result as in the paired *t*-test) and the effect of the student group highly significant with *P*<0.001 . Although we will not be learning how to conduct an ANOVA until next semester, it is worthwhile to be aware of it because it is one of the most commonly performed statistical tests.

Another useful characteristic of ANOVA is that it can also be used to assess what fraction of the variance in the data is due to each factor. The effect of malonate explains 1.9% of the variance while the effect of student group is responsible for a whopping 93.1% of the total variance in the data. This illustrates that uncontrolled variability can be a very important factor in an experiment and can swamp out the effect of the factor that we actually want to investigate. Although we were able to compensate for unwanted variability in the experiment by appropriate statistical analysis, it would have been better to have reduced the student group effect by better controlling the conditions of the test, using the same sample extract for all trials, and reducing the number of different experimenters conducting the test. This would have the effect of reducing the size of the error bars in Fig. 17 of section 8.1.

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