What does it mean if the chance of observed results is high?

When the chance of observing the results is high, it indicates that the data collected is consistent with the null hypothesis, which proposes that there is no effect or no difference in the population being studied. This situation suggests that the observed results could likely occur under the conditions stipulated by the null hypothesis.

Therefore, in hypothesis testing, when the probability of obtaining results as extreme as, or more extreme than, the observed results (given that the null hypothesis is true) is high, there is insufficient evidence to reject the null hypothesis. Hence, the conclusion is to accept the null hypothesis, suggesting that any observed differences may be due to random chance rather than a significant effect. This conceptual framework reinforces the link between statistical significance and the likelihood of observing particular results under the null hypothesis.

In contrast, rejecting the null hypothesis would be appropriate if the chance of observing the results is low, while increasing the sample size or conducting a power analysis are strategies more relevant to study design and assessing the ability to detect effects rather than directly interpreting the results of an experiment.