Under what circumstances can a very small treatment effect be statistically significant? Explain your response. a) if the sample size big and the sample variance is small
b) if the sample size and the sample variance are both big
c) if the sample size is small and the sample variance is big
d) if the sample size and the sample variance are both small

The correct answer is:

if the sample size big and the sample variance is small (a)

Step-by-step explanation:

The sample size of a study is the group of subjects that are selected from the general population and is considered an accurate representation of the population. With a large sample size, the likelihood of type I and type II errors occurring reduces. Increasing sample size allows the researcher to increase the significance level of the finding because it increases accuracy in coverage of the universal set, hence the effect accurately mirrors what goes on in the whole group. However, smaller sample size, on the other hand, does not accurately mirror the whole larger group.

The sample variance is the difference between the observed value and the true(actual). It is a measure of deviation or variability between the results and the true value. A smaller variance means increase closeness to the true value hence increase in accuracy and statistical significance.

Therefore, when the treatment effect is small but the sample size is large and variance is small, then the result is statistically significant.

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step-by-step explanatio89