Example 2: Drawing Students from a Registrar's List

A university librarian wants to find out how much students know about the reference services offered by the library. She wants to study all students rather than library users, so she decides to draw her sample from the registrar's list of enrolled students rather than sample library users.

She knows that she will have time available to interview only 100 to 150 students and settles on a sample size of 124 since it represents 1.5% of the student body. (The fact that the sample is 1.5% of the population has nothing to do with sample size or accuracy, but it does make the sample somewhat easier to explain.) She will use the program to calculate the precision range that goes with this sample size. She is wiling to accept a confidence of 90% and because she expects a great diversity of knowledge of services, she adopts the conservative value of 50% for estimating variability. In the sample size menu she enters a value of zero for the precision. This tells the program that it should ask the user for a sample size and calculate the precision from this. The information for this example has been entered in the sample size menu below. When a value of zero is entered for precision a new option, sample size appears. The librarian has entered 124, the size that she wants to use.

                             SAMPLE SIZE
Type the letter to set or change the values used in calculating a sample size

p -- Precision--how close the sample value should be to the true value
                you have chosen plus or minus 7.4%
c -- Confidence--how certain that the observation is within the
                given precision.
                you have chosen 90%
v -- Variability--what percent of the sample will be in the most
                important category?
                you have chosen 50%
e -- Explain -- To explain the sample size based on the values above.

                  CALCULATED size is 124

When e for explain is selected the response is:
for a confidence level of 90%
and a precision of plus or minus 7.4 % 
the sample size is 124
This means that if in your study you observe a characteristic in
50% of the sample you will know that there is
only one chance in 10 that the value for
the population is outside the range of 
43% to 57%

The report is in the form that we saw above but in this case it is the precision value that the machine has calculated. The last line of the report rounds the precision up to the next whole number to make it easier to read.

At this point she could generate random numbers and draw names from the registrar's list, but she suspects that knowledge of library services varies for students in different programs. A stratified sample is a useful device in such circumstances. It allows you to study the behavior of your population and of the sub-groups that comprise it. This is accomplished by taking not one big random sample, but a random sample of each of the sub-groups that you are sampling. The size of the random sample for each sub-group is proportional to its participation in the population.

The university librarian decides to take a stratified sample to be sure that each program is appropriately represented. To do this, she apportions the total sample size according to the number of students in each program and then draws a separate set of random numbers for each group. For example, there are 846 business students, 10.7% of the university total. She thus wants to sample 13 business students, 10.7% of the sample of 124.

She draws a sample size of thirteen random numbers from 1 to 846 and then counts through the business students on the registrar's list marking those whose number was selected in the random draw. This process of apportioning the sample, drawing random numbers in the appropriate range, and marking student names continues for each of the programs of the university.

Counting through a printed list of students and marking the selected names by hand may seem archaic in the computer information age. In the sense that, given enough effort, you could get a computer to do the job, it is archaic. But it is important to keep a sense of proportion. Counting through a list, even a list of thousands of students, doesn't take all that much time. And chances are that you aren't doing a whole lot of sampling studies. Many times simple manual methods are the easiest and most direct way of solving a problem.


this page is at http://testbed.cis.drexel.edu/sample/example2.html