Random Sampling

• When it is impractical to observe an entire population, statisticians usually depend on studying its subsets to make inferences about the whole population. If the researcher wants the inference or the study to be valid, the sample should be unbiased representative of the entire population. Hence, the researcher should take random samples from the whole set. This is called random sampling.
• Types of Random Sampling

  • Simple Random Sampling (SRS)
  • Systematic Random Sampling
  • Stratified Random Sampling
  • Cluster or Area Random Sampling
• Simple Random Sampling (SRS) - a sampling technique in which every element of the population has the same probability of being selected for inclusion in the sample.
• Each element of the population is assigned a unique number. The numbers are written on pieces of paper with identical size and shape. These pieces of paper are then folded and placed in a bowl or box where they are thoroughly mixed. Without looking or eyes closed, the

  researcher picks the required number of folded pieces of paper. All elements bearing the numbers picked by the researcher become elements of the sample. The selection of elements depends entirely on chance. This is also called Simple Random Sampling without Replacement (SRSWOR).
• Simple Random Sampling with Replacement (SRSWR) gives an element of the population more than one chance to be chosen as part of the sample. In fishbowl sampling, the selected piece of paper was returned to the box or bowl after it was noted, and the next sample

  is drawn again from the same number of population.
• The margin of error or the confidence interval is a measurement of error in the results of a survey, specifically one that relies on the random sampling method. It is usually a small amount that is allowed for in case of miscalculation.
• A random number table is a list of numbers, composed of digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Numbers, typically five-digit numbers in the list are arranged so that each digit has no predictable relationship to the digits that preceded it or to the digits that followed it. In short,

  the digits are arranged randomly.
• Systematic Random Sampling - a random sampling technique in which a list of elements of the population is used as a sampling frame and the elements to be included in the desired sample are selected by skipping through the list at regular intervals. If the kth member is selected in the first group, then all the kth members of the succeeding groups will also be included in the sample.
• Stratified Random Sampling - a random sampling technique in which the population is first divided into strata so that each group will have common characteristic, such as age, gender, or grade level and then samples are randomly selected separately from each stratum.
• Cluster or Area Random Sampling - a random sampling technique in which the entire population is broken into small groups, or clusters, and then, some of the clusters are randomly selected. The data from the randomly selected clusters are the ones that are analyzed.
• Types of Simple Random Sampling (SRS)

  • lottery method (SRSWOR & SRSWR)
  • Table of Random Numbers
  • Random Number Generators.
• Slovin's Formula


  Used to calculate the sample size (n) given the population size (N) and a margin of error (e).