Final answer:
A small treatment effect can be statistically significant if the p-value is below the threshold indicating that the effect is unlikely to be due to chance, especially in studies with large sample sizes and low variance.
Step-by-step explanation:
True, it is possible for a very small treatment effect to be a statistically significant treatment effect. The significance of an effect in statistics is determined by the p-value, which is a measure of the probability that an observed difference could have occurred by random chance alone. If the p-value is below a predetermined threshold (often 0.05 or 5 percent), the result is considered statistically significant, regardless of the size of the effect. This can occur even if the actual difference in outcomes is very small, as long as the data show that such a small effect is unlikely to have occurred due to randomness and the sample size is sufficiently large to give the test enough power.
For example, consider a medical trial testing whether a new medicine reduces cholesterol by 25 percent. The null hypothesis might be that the medicine has no effect, and the alternative hypothesis is that the medicine reduces cholesterol levels. Even if the medicine only reduces cholesterol by a small amount, if the sample size is large and the variance is low, the study could still find a statistically significant effect.
Therefore, it's essential for researchers to consider not just the significance but also the effect size and real-world relevance of the findings when interpreting their results. A statistically significant result with a very small effect might not be practically important, especially in fields like medicine where the implications of the findings can have a substantial impact on health decisions.