Today i will teach you types of sampling methods

## Random Sampling

A **random sample** is a sample in which all members of the population have an equal chance of being selected.

Random samples are selected by using chance methods or random numbers. One such method is to number each subject in the population. Then place numbered cards in a bowl, mix them thoroughly, and select as many cards as needed. The subjects whose numbers are selected constitute the sample. Since it is difficult to mix the cards thoroughly, there is a chance of obtaining a biased sample. For this reason, statisticians use another method of obtaining numbers. They generate random numbers with a computer or calculator. Before the invention of computers, random numbers were obtained from tables.

Some five-digit random numbers are shown in Table D in Appendix A. A section of Table D is shown on page 13. To select a random sample of, say, 15 subjects out of 85 subjects, it is necessary to number each subject from 01 to 85. Then select a starting number by closing your eyes and placing your finger on a number in the table. (Although this may sound somewhat unusual, it enables us to find a starting number at random.) In this case, suppose your finger landed on the number 88948 in the fourth column, the fifth number down from the top. Since you only need two-digit numbers, you can use the last two digits of each of these numbers. The first random number then is 48. Then proceed down until you have selected 15 different numbers between and including 01 and 85. When you reach the bottom of the column, go to the top of the next column. If you select a number 00 or a number greater than 85 or a duplicate number, just omit it.

In our example, we use the numbers (which correspond to the subjects) 48, 43, 44, 19, 07, 27, 57, 24, 68, and so on. Use Table D in the Appendix to get all the random numbers.

## Systematic Sampling

A **systematic sample** is a sample obtained by selecting every k^{th} member of the population where k is a counting number.

Researchers obtain systematic samples by numbering each subject of the population and then selecting every *k*th subject. For example, suppose there were 2000 subjects in the population and a sample of 50 subjects was needed. Since 2000 ÷ 50 = 40, then *k* = 40, and every 40th subject would be selected; however, the first subject (numbered between 1 and 40) would be selected at random. Suppose subject 12 were the first subject selected; then the sample would consist of the subjects whose numbers were 12, 52, 92, etc., until 50 subjects were obtained. When using systematic sampling, you must be careful about how the subjects in the population are numbered. If subjects were arranged in a manner such as wife, husband, wife, husband, and every 40th subject were selected, the sample would consist of all husbands. Numbering is not always necessary. For example, a researcher may select every 10th item from an assembly line to test for defects.Page 13** SPEAKING OF STATISTICS**The Worst Day for Weight Loss

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Many overweight people have difficulty losing weight. *Prevention* magazine reported that researchers from Washington University School of Medicine studied the diets of 48 adult weight loss participants. They used food diaries, exercise monitors, and weigh-ins. They found that the participants ate an average of 236 more calories on Saturdays than they did on the other weekdays. This would amount to a weight gain of 9 pounds per year. So if you are watching your diet, be careful on Saturdays.

Are the statistics reported in this study descriptive or inferential in nature? What type of variables are used here?TABLE DRandom Numbers

51455 | 02154 | 06955 | 88858 | 02158 | 76904 | 28864 | 95504 | 68047 | 41196 | 88582 | 99062 | 21984 | 67932 |

06512 | 07836 | 88456 | 36313 | 30879 | 51323 | 76451 | 25578 | 15986 | 50845 | 57015 | 53684 | 57054 | 93261 |

71308 | 35028 | 28065 | 74995 | 03251 | 27050 | 31692 | 12910 | 14886 | 85820 | 42664 | 68830 | 57939 | 34421 |

60035 | 97320 | 62543 | 61404 | 94367 | 07080 | 66112 | 56180 | 15813 | 15978 | 63578 | 13365 | 60115 | 99411 |

64072 | 76075 | 91393 | 88948 | 99244 | 60809 | 10784 | 36380 | 5721 | 24481 | 86978 | 74102 | 49979 | 28572 |

14914 | 85608 | 96871 | 74743 | 73692 | 53664 | 67727 | 21440 | 13326 | 98590 | 93405 | 63839 | 65974 | 05294 |

93723 | 60571 | 17559 | 96844 | 88678 | 89256 | 75120 | 62384 | 77414 | 24023 | 82121 | 01796 | 03907 | 35061 |

86656 | 43736 | 62752 | 53819 | 81674 | 43490 | 07850 | 61439 | 52300 | 55063 | 50728 | 54652 | 63307 | 83597 |

31286 | 27544 | 44129 | 51107 | 53727 | 65479 | 09688 | 57355 | 20426 | 44527 | 36896 | 09654 | 63066 | 92393 |

95519 | 78485 | 20269 | 64027 | 53229 | 59060 | 99269 | 12140 | 97864 | 31064 | 73933 | 37369 | 94656 | 57645 |

78019 | 75498 | 79017 | 22157 | 22893 | 88109 | 57998 | 02582 | 34259 | 11405 | 97788 | 37718 | 64071 | 66345 |

45487 | 22433 | 62809 | 98924 | 96769 | 24955 | 60283 | 16837 | 02070 | 22051 | 91191 | 40000 | 36480 | 07822 |

64769 | 25684 | 33490 | 25168 | 34405 | 58272 | 90124 | 92954 | 43663 | 39556 | 40269 | 69189 | 68272 | 60753 |

00464 | 62924 | 83514 | 97860 | 98982 | 84484 | 18856 | 35260 | 22370 | 22751 | 89716 | 33377 | 97720 | 78982 |

73714 | 36622 | 04866 | 00885 | 34845 | 26118 | 47003 | 28924 | 98813 | 45981 | 82469 | 84867 | 50443 | 00641 |

84032 | 71228 | 72682 | 40618 | 69303 | 58466 | 03438 | 67873 | 87487 | 33285 | 19463 | 02872 | 36786 | 28418 |

70609 | 51795 | 47988 | 49658 | 29651 | 93852 | 27921 | 16258 | 28666 | 41922 | 33353 | 38131 | 64115 | 39541 |

37209 | 94421 | 49043 | 11876 | 43528 | 93624 | 55263 | 29863 | 67709 | 39952 | 50512 | 93074 | 66938 | 09515 |

80632 | 65999 | 34771 | 06797 | 02318 | 74725 | 10841 | 96571 | 12052 | 41478 | 50020 | 59066 | 30860 | 96357 |

Systematic sampling has the advantage of selecting subjects throughout an ordered population. This sampling method is fast and convenient if the population can be easily numbered.

## Stratified Sampling

A **stratified sample** is a sample obtained by dividing the population into subgroups or strata according to some characteristic relevant to the study. (There can be several subgroups.) Then subjects are selected at random from each subgroup.Page 14

Samples within the strata should be randomly selected. For example, suppose the president of a two-year college wants to learn how students feel about a certain issue. Furthermore, the president wishes to see if the opinions of first-year students differ from those of second-year students. The president will randomly select students from each subgroup to use in the sample.

## Cluster Sampling

A **cluster sample** is obtained by dividing the population into sections or clusters and then selecting one or more clusters at random and using all members in the cluster(s) as the members of the sample.

Here the population is divided into groups or clusters by some means such as geographic area or schools in a large school district. Then the researcher randomly selects some of these clusters and uses all members of the selected clusters as the subjects of the samples. Suppose a researcher wishes to survey apartment dwellers in a large city. If there are 10 apartment buildings in the city, the researcher can select at random 2 buildings from the 10 and interview all the residents of these buildings. Cluster sampling is used when the population is large or when it involves subjects residing in a large geographic area. For example, if one wanted to do a study involving the patients in the hospitals in New York City, it would be very costly and time-consuming to try to obtain a random sample of patients since they would be spread over a large area. Instead, a few hospitals could be selected at random, and the patients in these hospitals would be interviewed in a cluster. See Figure 1–3.FIGURE 1–3Sampling Methods

The main difference between stratified sampling and cluster sampling is that although in both types of sampling the population is divided into groups, the subjects in the groups for stratified sampling are more or less homogeneous, that is, they have similar characteristics, while the subjects in the clusters form “miniature populations.” That is, they vary in characteristics as does the larger population. For example, if a researcher wanted to use the freshman class at a university as the population, he or she might use a class of students in a freshman orientation class as a cluster sample. If the researcher were using a stratified sample, she or he would need to divide the students of the freshman class into groups according to their major field, gender, age, etc., or other samples from each group.

Cluster samples save the researcher time and money, but the researcher must be aware that sometimes a cluster does not represent the population.

The four basic sampling methods are summarized in Table 1–3.TABLE 1–3Summary of Sampling Methods

Random | Subjects are selected by random numbers. |

Systematic | Subjects are selected by using every kth number after the first subject is randomly selected from 1 through k. |

Stratified | Subjects are selected by dividing up the population into subgroups (strata), and subjects are randomly selected within subgroups. |

Cluster | Subjects are selected by using an intact subgroup that is representative of the population. |