1.5 Sampling
Sampling
Gathering information about an entire population is often virtually impossible due to costs or other factors. Instead, we typically use a sample of the population which should have the same characteristics as the population it is representing. Statisticians use various methods of random sampling in an attempt to achieve this goal. This section will describe a few of the most common methods.
There are several different methods of random sampling. In each form, each member of a population initially has an equal chance of being selected for the sample. There are advantages and disadvantages to each sampling method.
Simple Random Sampling
The gold standard and maybe easiest method to describe is called a simple random sample (SRS). Any group of n individuals is equally likely to be chosen as any other group of n individuals if the simple random sampling technique is used. In other words, each sample of the same size has an equal chance of being selected.
For example, suppose Lisa wants to form a four-person study group (herself and three other people) from her pre-calculus class, which has 31 members not including Lisa. To choose a simple random sample of size three from the other members of her class, Lisa could put all 31 names in a hat, shake the hat, close her eyes, and pick out three names.
A more technological approach is for Lisa to pair the last name of each class member with a two-digit number, as in the table below:
| ID | Name | ID | Name | ID | Name |
|---|---|---|---|---|---|
| 00 | Anselmo | 11 | King | 21 | Roquero |
| 01 | Bautista | 12 | Legeny | 22 | Roth |
| 02 | Bayani | 13 | Lundquist | 23 | Rowell |
| 03 | Cheng | 14 | Macierz | 24 | Salangsang |
| 04 | Cuarismo | 15 | Motogawa | 25 | Slade |
| 05 | Cuningham | 16 | Okimoto | 26 | Stratcher |
| 06 | Fontecha | 17 | Patel | 27 | Tallai |
| 07 | Hong | 18 | Price | 28 | Tran |
| 08 | Hoobler | 19 | Quizon | 29 | Wai |
| 09 | Jiao | 20 | Reyes | 30 | Wood |
| 10 | Khan |
Figure 1.8: Lisa’s class roster
Lisa can use a table of random numbers (found in many statistics books and mathematical handbooks), a calculator, or a computer to generate random numbers. For this example, suppose Lisa uses a calculator to generate the following random numbers:
0.94360, 0.99832, 0.14669, 0.51470, 0.40581, 0.73381, 0.04399
Lisa identifies multiple two-digit numbers in each of these random numbers (i.e., 0.94360 becomes 94, 43, 36, and 60). If any of these two-digit numbers corresponds with a name on her list, that student is chosen. She can generate more random numbers if necessary.
The random numbers 0.94360 and 0.99832 do not contain appropriate two-digit numbers. However, the third random number, 0.14669, contains 14, the fifth random number contains 05, and the seventh random number contains 04. The two-digit number 14 corresponds to Macierz, 05 corresponds to Cuningham, and 04 corresponds to Cuarismo. Besides herself, Lisa’s group will consist of Marcierz, Cuningham, and C