Final answer:
D) The result is unlikely to occur by random variation.
A statistically significant result means that it is unlikely to occur by random variation, suggesting that the result is not due to chance. This is determined by comparing the p-value to a preset significance level, with α = 0.05 being commonly used. It is essential to distinguish between achieving statistical significance and practical importance while also being aware of the potential for Type I and Type II errors.
Step-by-step explanation:
When determining statistical significance, the option that best describes reaching a significant result is D) The result is unlikely to occur by random variation. This means that when we conduct a hypothesis test, we are comparing the observed data to what would be expected under the null hypothesis—usually that there is no effect or difference. A statistically significant result suggests that the observed data are not likely to have occurred if the null hypothesis were true.
To make a decision in hypothesis testing, we compare the p-value to a predetermined significance level, typically α = 0.05 (5%). If the p-value is less than α, we reject the null hypothesis, indicating that our result is statistically significant and not due to chance. However, achieving statistical significance does not necessarily mean the result is practically important or meaningful; it simply indicates a low probability of the observed result occurring if the null hypothesis is true.
In the context of hypothesis testing, a Type I error occurs when the null hypothesis is true, but we mistakenly reject it. A Type II error happens when the null hypothesis is false, but we fail to reject it. The significance level (α) is set to control the probability of making a Type I error, while the power of a test (which is related to the probability of making a Type II error) is a function of the sample size and the effect size.
In conclusion, a statistically significant result suggests that the research findings are not likely to have happened by chance, but it is important to also consider practical significance and the possibility of errors when interpreting the results.