If there is a relationship between two variables in a popula

If there is a relationship between two variables in a population, which is more likely to result in a statistically significant relationship in a sample (meaning you reject the null hypothesis) -- a small sample, a large sample, or are they equivalent? Explain.

Solution

Statistical significance means that there is a good chance that we are right in finding that a relationship exists between two variables. But statistical significance is not the same as practical significance. We can have a statistically significant finding, but the implications of that finding may have no practical application. The researcher must always examine both the statistical and the practical significance of any research finding.

    For example, we may find that there is a statistically significant relationship between a citizen\'s age and satisfaction with city recreation services. It may be that older citizens are 5% less satisfied than younger citizens with city recreation services. But is 5% a large enough difference to be concerned about?

    Often times, when differences are small but statistically significant, it is due to a very large sample size; in a sample of a smaller size, the differences would not be enough to be statistically significant.

it depends on the sample size; a minor relationship observed in a sample based on a large enough number of observations can easily achieve statistical SIGNIFICANCE.