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SS
Research Methods in the Social Sciences
Exercise 2: Random and Systematic Sampling
I
n 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.
There are two variables in this analysis, country and female literacy. 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. This variable is a good proxy (or “stand-in”) measure for the female literacy rate. The country is also the sampling element.
The data for this exercise were taken from the 1996 World Data Table published by the Population Reference Bureau.
- Simple random samples ( 25% ). You will take two simple random samples, one of ten cases and one of 30.
How to take a simple random sample (SRS) with SPSS.
a. 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. b. Open the data in SPSS. Don’t forget to check the “Read variable names” box so that the program takes the column headings as the names of the variables. c. Go to the SPSS menu bar and open the Data menu. Click “Select,” “Random” and fill in the blanks with the appropriate data for the 10 and 30 simple random samples. d. Once the sample has been selected subsequent operations will be conducted only on the sample. e. 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. f. Calculate confidence intervals at the 95% level for the means you
calculated from the systematic sample.
- Systematic sample ( 25% ). The systematic sample involves merely selecting every n thcase from the sampling frame. You must do two samples, one of ten cases and one of 30 cases.
How to take a systematic sample (SS) in SPSS.
a. First calculate the sampling interval (also called the sampling fraction, the skip interval, or “system”) by using the formula, N/n (population/required sample size). b. Second, select the random start by telling SPSS to randomly select 1 case. c. 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). d. Calculate the statistics in the same way you did for the SRS. e. Calculate confidence intervals at the 95% level for the means you calculated from the systematic sample. f. Enter the sample statistics called for in the appropriate places in Table 1 below.
- Population parameter (10%). Calculate the population parameter (true value) for the entire 142 countries.
Table 1. Simple random and systematic sampling statistics for two sample sizes.
Sample statistic Simple random sample
Systematic sample Population parameter 10 samples
30 samples
10 samples
30 samples Random start Sampling interval Mean Standard deviation Minimum Maximum
Calculating Confidence Intervals
Confidence intervals are used in social science research to determine whether differences between means of two different samples are so large that you must consider the two samples as being from two different populations - at least regarding the variable under investigation. If you don't get my terminology read ahead in your text to the section on sampling, dust off a stats book, or bring your questions to class. You should have a vague recollection of confidence intervals from your experience with STA 215 (or MTH 215 for old timers). Confidence intervals delimit an area, above and below a mean for a statistic in which the true mean for the population from which the sample was taken lies. In other words, if I were interested in the average age of GVSU students I could take a sample of 1,000 students (I'll ask you later how to do it) and ask each sampled student his or her age. The mean age of my sample is called a statistic. It is different from what I would get if I asked all GVSU students their age. That total mean is called a parameter , or population parameter, and it represents the true mean age of GVSU students. To summarize, a confidence interval is a margin of error. It represents a range of values around a specific point. A range is used because the statistics of random processes do not let a researcher predict an exact point, however, they let him/her say with a high level of confidence (e.g. 95%) that the true population parameter lies within a certain range. The formula to calculate confidence intervals around a mean is as follows:
Where;
Symbol Meaning The sample mean
The sample size
The z score, 1.96, which represents the alpha level, 0.05, the 95% confidence level.
The standard deviation of a sample
The standard deviation of the sampling distribution
A worked example of calculating confidence intervals
As an example, take the recent sample survey of I.Q. in Allendale. Two hundred people were sampled. The mean I.Q. for the sample was 105 points. the standard deviation was 15 points. Knowing the standard deviation and mean enables you to first estimate the standard error (S.E.) as depicted in the steps below.
Conclusion: the mean I.Q. for population in question (the parameter for the population of Allendale) is somewhere between 102.92 (105-2.08) and 107. (105+2.08) at the 95% confidence level.
