The document discusses common sampling techniques used in statistics, defining sampling as the process of selecting units from a population to generalize results. It covers various methods including probability and non-probability sampling, along with strategies like simple random, systematic, stratified, and cluster sampling, highlighting their advantages and procedures. Additionally, it explains sample size determination using Slovin's formula and provides examples to illustrate the concepts, emphasizing the importance of selecting representative samples for accurate research outcomes.

1. Nueva Ecija University of Science and Technology Sumacab Campus, Cabanatuan City COLLEGE OF EDUCATION Elementary Statistics Prepared By: Krizza Joy M. Dela Cruz

2. Common sampling techniques

3. Sampling Sampling is the process of selecting units from a population of interest in order to study and fairly generalize the results back to the population from which the sample was chosen. (Reyes, Saren, 2004)

5. Example “ Generalizing urban homeless males between ages 30 and 50 in the Philippines” Theoretical population? Accessible Population? Sampling frame? Sample?

6. “ Effect of Technology on Enthusiasm for Learning Science of in-school youths in the different colleges and universities in the Philippines” Theoretical population? Accessible Population? Sampling frame? Sample?

7. “ Speed and Accuracy of High School Students in solving mathematical problems involving fundamental operations on fractions” Theoretical population? Accessible Population? Sampling frame? Sample?

8. Note: Sample is the group of people who you select to be in your study. The group that actually COMPLETES your study is a sub-sample of the sample – it doesn’t include the non-respondents or dropouts.

9. SLOVIN’S FORMULA n = where n is the sample size N is the population size e is the margin of error

10. Margin of error is a value which quantifies possible sampling error. Sampling error means that the results in the sample differ from those of the target population because of the “luck of draw”

11. It is an example of pre-election survey of presidential voting preferences of Filipinos in 2004. The survey, commissioned by Polistrat International Consulting firm was conducted through personal interviews of a national sample of 1,200 adult respondents and had a margin of error of 3% done on June 28, 2003.

12. Determining sample size Find n if N = 10,000 and e = 1% N = 10,000 and e = 3% N = 10,000 and e = 5% N = 10,000 and e = 8% N = 10,000 and e = 10%

13. A group of students want to know the age of students in a high school but do not have the resources to survey an entire population of 2,500. If they want to use a sample with a 5% margin of error, what should their sample size be? What should be the representative sample size if the population from which the sample will be taken is 15,000 and the desired margin of error is 10%? At present, Brgy. San Isidro has about 1,800 registered household members and the Brgy. Captain is planning to conduct a survey that would determine the members’ opinion on the issue of responsible parenthood. How many respondents he must consider if the desired margin of error is 1%?

14. Advantages of Sampling Reduced Cost Greater Speed Greater Scope Greater Accuracy

15. Sampling Techniques Types of Sampling Techniques Non-probability Sampling Probability Sampling Convenience Quota Systematic Simple Cluster Stratified Purposive

16. Probability Sampling Probability sampling is any method of sampling that utilizes some form of random selection . Samples are chosen in such a way that each member of the population has a known though not necessarily equal chance of being included in the samples.

17. Advantages of Probability Sampling it avoids biases that might arise if samples were selected based on the whims of the researcher. it provides the basis for calculating the margin of error.

18. Non-probability Sampling Non-probability sampling is a method in which each member of the population does not have a known chance of being included in the sample. Instead, personal judgment plays important role in the selection.

19. SIMPLE RANDOM SAMPLING It is the basic random sampling technique where a group of subjects (a sample) is selected for study from a larger group (a population). Every experimental unit is chosen entirely by chance and each member of the population has an equal chance of being included in the sample. E.g Lottery, generation of random numbers/digits. sampling frame random subsample

20. Lottery Sampling Procedures: Write down the name of each member of the population on pieces of paper. Place these papers in a box or a container drum. The box or lottery drum must be shaken thoroughly to prevent some pieces of paper from sinking at the bottom. Picked the required number of sample units from the lottery drum.

21. Generating Random Numbers This is a better and perhaps more efficient for selecting a simple random sample. Computers and even your calculators can be used to generate random digits. The randomly produced digits can be used to pick your samples. However, a complete listing of the members of the population is needed in this type of random selection.

22. Direct Selection Method Generating random numbers between 0 and 1 using scientific calculator or computer.

23. Through Calculator Press or 2nd · RAN# SHIFT

24. Though Computer Excel: Enter the function = RND () on any blank cell

25. SYSTEMATIC RANDOM SAMPLING Samples are randomly chosen following certain rules set by the researchers. Each unit in the population is identified, and each unit has an equal chance of being in the sample. This involves choosing the kth member of the population with k = N/n but there should be a random start.

26. Procedures: Determine the k (period) Choose a random start List all the samples chosen in the random sampling

27. Example: Choosing a sample of size 84 from 500. k = N/n where N = 500 and n = 84 k = 500/84 k = 5.95 k 6

28. STRATIFIED RANDOM SAMPLING It is used when the population is too big to handle, thus dividing population (N) into homogeneous subgroups, called strata, is necessary. Samples per stratum are then randomly selected, but considerations must be given to the sizes of the random samples to be selected from the subgroups. Sampling Frame strata Random Subsamples

29. Procedures for SRS Equal allocation – the sample sizes from different strata are equal. Proportional allocation – the sample sizes from the different strata are proportional to the sizes of the strata .

30. Example: A survey to find out if families living in a certain municipality are in favor of Charter change will be conducted. To ensure that all income groups are represented, respondents will be divided into high-income (class A), middle-income (class B) and low-income (class C). N=5,000 1,500 Low-income (class C) 2,500 Middle-income (class B) 1,000 High-income (class A) # of families Strata

31. Using a 5% margin of error, how many families should be include in the sample? Using proportional allocation, how many from each group should be taken as samples? Using equal allocation, how many from each group should be taken as samples?

32. N=5,000 1,500 Class C 2,500 Class B 1,000 Class A Equal Allocation Proportional Allocation Number of Families Strata

33. CLUSTER RANDOM SAMPLING It is sometimes called area sampling because this is usually applied when the population is large. In this technique, groups or clusters instead of individuals are randomly chosen.

34. Procedures Divide population into clusters (usually along geographic boundaries) Randomly Sample clusters Measure all units within sample clusters

35. Example: You want to determine the average expenses of families living barangays in cities of Nueva Ecija. In sum, there are 208 barangays in the 5 cities of Nueva Ecija.

36. CONVENIENCE SAMPLING It allows researcher to select those elements that are readily available (accidental sample) or those that happen to be in the place at a certain time (man-on-the-streets) in order to obtain quick results.

37. QUOTA SAMPLING It is very similar to the stratified random sampling but, with quota sampling, samples are selected non-randomly according to some fixed quota. Samples are chosen based on the judgment or prior knowledge of the researcher with the objective of reaching a certain target quota.

38. Types of Quota Sampling Proportional quota sampling – representing the major characteristics of the population by sampling a proportional amount of each. Non-proportional quota sampling is a bit less restrictive. In this method, you specify the minimum number of sampled units you want in each category. Here, you're not concerned with having numbers that match the proportions in the population. Instead, you simply want to have enough to assure that you will be able to talk about even small groups in the population.

39. PURPOSIVE SAMPLING It is done through choosing the samples on the basis of the predetermined criteria set by the researchers.