9.8: Hypothesis: Accept or Fail to Reject?

The outcome of any hypothesis testing leads to rejecting or not rejecting the null hypothesis. This decision is taken based on the analysis of the data, an appropriate test statistic, an appropriate confidence level, the critical values, and P-values. However, when the evidence suggests that the null hypothesis cannot be rejected, is it right to say, 'Accept' the null hypothesis?

There are two ways to indicate that the null hypothesis is not rejected. 'Accept' the null hypothesis and 'fail to reject' the null hypothesis. Superficially, both these phrases mean the same, but in statistics, the meanings are somewhat different. The phrase 'accept the null hypothesis' implies that the null hypothesis is by nature true, and it is proved. But a hypothesis test simply provides information that there is no sufficient evidence in support of the alternative hypothesis, and therefore the null hypothesis cannot be rejected. The null hypothesis cannot be proven, although the hypothesis test begins with an assumption that the hypothesis is true, and the final result indicates the failure of the rejection of the null hypothesis. Thus, it is always advisable to state 'fail to reject the null hypothesis' instead of 'accept the null hypothesis.'

'Accepting' a hypothesis may also imply that the given hypothesis is now proven, so there is no need to study it further. Nevertheless, that is never the case, as newer scientific evidence often challenges the existing studies. Discovery of viruses and fossils, rediscovery of presumed extinct species, criminal trials, and novel drug tests follow the same principles of testing hypotheses. In those cases, 'accepting' a hypothesis may lead to severe consequences.

In an experiment, a farm with infected plants is subjected to a widely applicable insecticide.

This insecticide is expected to increase the number of healthy plants after its application. However, at the end of the experiment, the proportion of healthy and infected plants remained the same.

Here, the null hypothesis that the insecticide has no effect seems to hold, but should one accept the hypothesis or fail to reject it?

Accepting this hypothesis would mean that the insecticide is ineffective and cannot improve the plants' health.

This decision actually overlooks the other plausible explanations for the observed results.

In this case, using an unprescribed amount or concentration of insecticide might have resulted in no effect.

There is a possibility of plants being infected by something that the insecticide cannot target.

Failing to reject a null hypothesis means there is no sufficient evidence for the expected or the observed effect.

Today, if scientists had accepted null hypotheses, the discovery of plant viruses or the rediscovery of many extinct species would not have been possible.