STATS - MODULE 5

• In statistics, the term population refers to the totality of observations or elements from a set of data.

  On the other hand, a sample refers to one or more elements taken from a population for a specific purpose.

  In most studies, only sample of the population is considered. This saves time, money, and effort on the part of the researcher.
• The chosen people are the Sample

  
• Taro Yamane, a mathematical statistician who developed a statistical formula for calculating or determination of sample size in relation to the population under study so that inferences and conclusions reached after the survey can be generalized to the entire population from which the sample was gotten.
• n = Sample size
• N = Population size
• e = Margin of error
• e = 10% to decimal is 0.10
• e = 15% to decimal is 0.15
• Formula in

  Sample size: The Taro Yamane Method

  
• Example:

  According to 2015 census, Guagua, Pampanga has a total population of 117, 430. Compute the sample size given a margin of error of 10%.

  N=117,430

  e=10% or 0.10

  Answer:

  n=99.91 or 100
• Example:

  Given a total population of 23, 250 with a margin of error of 10%. Compute the sample.

  N=23,250

  e=10% or 0.10

  Answer:

  n=99.57 or 100
• Example:

  Given a total population of 385 with a margin of error of 15%. Compute the sample.

  N=385

  e=15% or 0.15

  Answer:

  n=39.85 or 40
• A numerical measure that describes the whole population is called a parameter. For example, if all the students in a school are surveyed about heights and an average height of 65 inches (in) was determined, then 65 in is called a population parameter. A numerical description of the sample, however, is called a statistic. In the previous example, 65 in will be called a sample statistic when only 50 students out of 230 students are surveyed to determine the average height.
• Sampling Techniques

  When conducting studies where only few members of the population can participate, the selection of a sample is very crucial as wrong sampling can lead to invalid results. Researchers

  need to guarantee that the sample chosen to partake in a study is the representative of the entire population and thus, proper sampling technique

  must be carried out to ensure that the results of the study will not be put to waste.
• Probability Versus Nonprobability Sampling

  A sample is a small, representative part of the population. Samples may be selected from the population using either probability (unbiased) or nonprobability (biased) sampling.

  In probability sampling, each member of the population has a known probability of being selected in the sample, while in nonprobability sampling, there is bias in the selection and there is no recognized probability that one member will be included in the sample.
• Probability Sampling

  • Simple Random Sampling
  • Systematic Sampling
  • Stratified Sampling
  • Cluster Sampling
• Nonprobability Sampling

  • Convenience Sampling
  • Purposive Sampling
  • Snowball Sampling
  • Quota Sampling
• Simple Random Sampling — is the most used sampling technique. In this

  technique, each member of the population has an equal chance to be selected as a participant.
• Systematic Sampling — is a random sampling technique which considers every nth element of the population in the sample with the selected random starting point from the first q members.
• Stratified Sampling — sometimes, a given population is purposively divided into homogeneous partitions (or groups) depending on certain factors that might be affecting the results of the study. These homogeneous partitions are also called strata (singular:stratum)
• Cluster Sampling — like stratified sampling, the population is divided into groups, called clusters, in another probability sampling technique called cluster sampling. However, unlike stratified sampling, the clusters are heterogeneous groups of the population. 
• Convenience Sampling — This sampling technique is also called haphazard sampling. As the name implies, this sampling procedure is carried out on the matter of convenience or ease of implementation on the part of the researcher, that is, the samples taken are readily available to participate in the study.
• Purposive Sampling — This sampling technique is done with a purpose in mind. This technique, also called

  judgmental or selective sampling, focuses on samples which are taken based on the judgment of the researcher.
• Snowball sampling — is sometimes called chain-referral sampling. In this technique, the researcher chooses a possible respondent for the study at hand. Then, each respondent is asked to give recommendations referrals to other possible respondents.
• Quota Sampling — is the equivalent of stratified random sampling in terms of nonprobability sampling. In this technique, the researcher starts by identifying quotas, which are predefined control categories such as age, gender, education, or religion.