Biological hypotheses, like the one on the previous page (Biological vs. statistical hypotheses) that suggests atrazine will result in lower abundance of amphibians, have specific associated predictions.  Furaha predicted that survival would be lower for leopard frogs living in a particular habitat that contained atrazine than a habitat that did not.  Another student, Diego, suggests that there may be reproductive abnormalities associated with the exposure to atrazine that could lead to fewer numbers of offspring being produced.  He predicts that, for frogs raised in the lab, there will be more abnormalities in the gonads of male frogs raised in tanks with atrazine than those raised in tanks without atrazine.

As mentioned above, a statistical test will have an associated null (H₀) and alternative hypothesis (H_A).

Typically, the null hypothesis indicates that there was no difference or no effect.  This is the “status quo” position. Bear in mind that this hypothesis is usually not what the researcher is trying to demonstrate. We stick with this hypothesis when we find the variation from what is expected is considered plausible due to random chance.

• In the example above, Diego’s null hypothesis would be that there was no difference in the mean number of abnormalities by treatment (atrazine vs. no atrazine).
  • Mean number of abnormalities _atrazine = Mean number of abnormalities _{no atrazine}

The alternative hypothesis indicates that there is a difference or effect. This is usually what the researcher is trying to demonstrate.

• In the example above, there is a difference in the mean number of abnormalities by treatment (atrazine vs. no atrazine).
  • Mean number of abnormalities _atrazine ≠ Mean number of abnormalities _{no atrazine}

When we run a statistical test, we start with the premise that the null hypothesis is true and seek to determine whether the data allow us to reject the null hypothesis, in favor of our alternative.

For example, imagine you are trying to figure out if a coin is fair (null hypothesis) or biased in favor of tails (alternative hypothesis) when flipping it, and your data is that 8 out of 11 coin flips have resulted in a tails. We assess how unusual results like our 8 out of 11 coin flips being tails are under the premise that the coin is fair. If we find that our observations are unusual, we would reject the null hypothesis and conclude that the evidence suggests the coin is biased. This assessment is done using probability theory, but we won’t be adventuring into those details. Instead, we’ll learn about some summary measures (test statistics and P-values) that will help us determine if we reject the null hypothesis or not, while our software does the heavy computational lifting for us.