In order to determine the sample size of a research, it is needed to determine the permissible scope of sampling error, confidence level and the expected variance. The values of these parameters will depend on the trade-off between the value of more accurate information and the cost of increasing the sample size.
A confidence level is the degree of certainty that the observed value of the element falls within a given range of the confidence interval. Generally, the most widely used is 95% confidence level. To obtain more accurate data confidence level may be increased to 99%, but this entails a significant increase in the sample size. In case if accuracy is not very important for the given research, the confidence level is reduced to 90%, which leads to a reduction of the sample size.
The confidence interval (tolerable error) is the tolerable deviation of the observed values from the true population values. The level of this tolerance is determined by the researcher based on the requirements for the accuracy of information. If permissible error increases, the sample size is reduced, even if the confidence level will be 95%.
Consider the fictitious example. Assume, a researcher studies the reaction of the customers on a new product. Let’s say, a sample of size 1000 was collected. 60% of individuals reported that they like a new product, 40% reported that they don’t like it. What is 95% confidence level for the population proportion of those who like it? This interval can be calculated in the following way:
p±z0.95p1-pn,
where p is a sample proportion, n is a sample size and z is the critical z-value for 95% confidence level. Substitute the given values:
0.6±1.960.61-0.610000.6±0.096
The 95% CI is (0.504, 0.696). We are 95% confident that the population proportion of those who like a new product is between 50.4% and 69.6%
Now let’s lower the sample size to 50 and look how the confidence interval will change:
0.6±1.960.61-0.6500.6±0.136
Now, the 95% CI is (0.464, 0.736). We are 95% confident that based on the new sample the population proportion of those who like a new product is between 46.4% and 73.6%. As it was expected, for the smaller sample, the confidence interval is wider (because the accuracy of the study was decreased).
