SS300
Research Methods in the Social Sciences
Exercise 2: Random and Systematic Sampling
In this exercise you will scientifically sample countries using two methods: simple random sampling
and systematic random sampling. These two methods are different from the non-probability sampling
methods discussed in class because each sampling element (“case”) has an equal chance of being
picked for study.
There are two variables in this analysis, country name and female literacy in percent. The unit of
analysis is the country. The concept “female literacy” was measured as the percent of the female
population enrolled in secondary school in 1996. The data for this exercise were taken from the 1996
World Data Table published by the Population Reference Bureau.
Simple random samples (30%). You will take three simple random samples, one of ten cases, one of
30 cases, and one of 50. You will enter the results into Table 1.
How to take a simple random sample (SRS) with SPSS (PASW).
1. Get the data in Excel format. There is a link on the SS300 web page on the same line as the
text for this exercise.
2. Open the data in SPSS. Make sure “List Files of Type” says Excel xls. Don’t forget to check the
“Read variable names” box so that the program takes the column headings as the names of
the variables.
3. Go to the SPSS menu bar and open the Data menu. Click “Select,” “Random” and fill in the
blanks with the appropriate information to take the 10 and 30 simple random samples.
4. Once the sample has been selected subsequent operations will be conducted only on the
sample.
5. The statistics can be calculated by going to the menu bar and selecting Analysis | Descriptive
Statistics then identifying the test variable for the analysis. Be careful that you select the
correct one here.
6. Calculate confidence intervals at the 95% level for the means you calculated from the
systematic sample.
7. Now do the 30 country sampling.
Table 1. Simple random sampling statistics for three sample sizes.
Sample statistic
Simple random sample
10
30
50
samples
samples
samples
Mean
Standard deviation
Minimum
Maximum
+ - 95% confidence interval
Systematic sample (30%). The systematic sample involves merely selecting every nth case from the
sampling frame. You will take three systematic random samples, one of ten cases, one of 30 cases,
and one of 50. You will enter the data into Table 2.
How to take a systematic sample (SS) in SPSS.
1. First calculate the sampling interval (also called the sampling fraction, the skip interval, or
“system”) by using the formula, N/n. This means divide the population (N) by the required
sample size (n). That means for the first sampling you do, divide the number of countries in
the study “population” by 10.
2. Second, select the random start by telling SPSS to randomly select 1 case.
3. Select the remaining cases by counting down from the random start by the appropriate
sampling interval and changing the 0 (unselected) value of the filter variable to 1 (selected).
4. Calculate the statistics in the same way you did for the SRS.
5. Calculate confidence intervals at the 95% level for the means you calculated from the
systematic sample.
6. Enter the sample statistics called for in the appropriate places in Table 2 below.
7. Now do the 30 country sampling.
Table 2. Systematic random sampling statistics for three sample sizes.
Sample statistic
Systematic random sample
10
30
50
samples
samples
samples
Random start
Sampling interval
Mean
Standard deviation
Minimum
Maximum
+ - 95% confidence interval
Questions.
1. Of the simple random sample sizes, which ones estimated the population parameter well and
which ones estimated the population parameter poorly? Explain how you know this. (20%)
2. Of the systematic sample sizes, which one(s) estimated the population parameter well and
which one(s) estimated the population parameter poorly? Explain how you know this. (20%)
Remember that you must attach all of the print-outs that you generate for this exercise to this file.
Failure to do so will result in no credit.