Question

Describe in your own words why it is “better”, statistically speaking, to have a large random sample when you are doing a study. Please be specific and use an example if it helps you explain your thinking.

Answer 1

When we are doing a study , we have to improve the power of a test

Power of a test is rejecting the null hypothesis , when it is false

Now power of the test increases as sample size increases

Increasing sample size makes the hypothesis test more sensitive - more likely to reject the null hypothesis when it is, in fact, false.

As n increases, so does the power of the significance test. This is because a larger sample size narrows the distribution of the test statistic. The hypothesized distribution of the test statistic and the true distribution of the test statistic (should the null hypothesis in fact be false) become more distinct from one another as they become narrower, so it becomes easier to tell whether the observed statistic comes from one distribution or the other. The price paid for this increase in power is the higher cost in time and resources required for collecting more data. There is usually a sort of “point of diminishing returns” up to which it is worth the cost of the data to gain more power, but beyond which the extra power is not worth the price.