Under conditions where a large sample is used in experimental research, and "power" of a statistical test is maximized, it is possible to have statistically significant results, yet a fairly small...?

A. Ethical concern
B. Effect size
C. Set of assumptions
D. Standard Deviation

Ethical

Under conditions where a large sample is used in experimental research and the "power" of a statistical test is maximized, it is possible to have statistically significant results, yet a fairly small effect size. The effect size refers to the magnitude or strength of the relationship or difference being examined.

To understand this, we need to break it down into three key components:

1. Sample Size: When conducting experimental research, the sample size refers to the number of participants or observations included in the study. Generally, larger sample sizes provide more accurate and precise estimates of population parameters. Having a large sample size reduces the likelihood of random variability influencing the results.

2. Power of a Statistical Test: Power is the probability of correctly rejecting a false null hypothesis. It represents the ability of a statistical test to detect a true effect when it exists. In other words, it measures the likelihood of finding a statistically significant result if the alternative hypothesis is true.

3. Effect Size: Effect size quantifies the magnitude or strength of the relationship or difference between variables being studied. It tells us the practical significance or real-world impact of the observed effect. Effect sizes are measured differently depending on the statistical test and type of data, but common measures include Cohen's d, r-squared, and odds ratios.

Now, coming back to the question, when a large sample is used and the statistical test has high power, it means that the study has a high chance of detecting even small effects. In such cases, statistically significant results may be obtained, indicating that the observed effect is unlikely to have arisen due to chance. However, the effect size may still be small, meaning that the practical significance of the observed effect might be limited.

Therefore, the correct answer to your question is B. Effect size.