SAMPLING-TECHNIQUES-AND-SAMPLING-DISTRIBUTION.pptx

Sampling Techniques

1. Random sampling, Parameter, Statistics, and Sampling Distribution

2. Objectives 2 At the end of the class session, you will be able to do the following: 1. illustrate random sampling; 2.distinguish between parameter and statistic; and 3.identifies sampling distributions of statistics (sample mean).

3. Population and Sample

4. Population 4 the entirety of the group including all the members that forms a set of data.

5. Sample 5 contains a few members of the population. they were taken to represent the characteristics or traits of the whole population.

6. Population vs Sample 6

7. Random Sampling

8. R a ndom Sampling 8 A part of sampling method or technique in which each sample has an equal probability of being chosen. A sample chosen randomly ismeant to be unbiased representation of the total population. An unbiased randomsample is important for drawing conclusions.

9. Probability and Non-Probability Sampling

10. Probability Sampling 10 Every member of the population has the chance of being selected. It involves principle or randomization or chance.

11. Simple Random Sampling 11 one of the simplest forms of collecting data from the total population. In this method, every element of the population has the same probability of being selected for inclusion in the sample. One way to do simple random sampling is using Table of Random Numbers . This contain rows and columns of mechanically generated digits. Another way of doing this is by using Lottery Method . Under this, there are two methods

12. Example 12 A researcher wants to study the effects of social media on 1000 Senior High School students of Zamboanga Sibugay NHS. He wishes to use the simple random sampling (without replacement) and to determine how many students should be in the sample.

13. Systematic Random Sampling 13 a random sampling method in which every kth element on the population is selected until the desired number of elements in the sample is obtained. The value of is the sampling interval which can be obtained using the formula below.  

14. Example 14 Suppose in a 250 students, you can only choose 71 students to be part of your sample. How are you going to choose your sample?

15. Stratified Random Sampling 15 A sampling method in which the population is first divided into subpopulation called strata and then samples are randomly selected separately from each stratum. In Stratified Sampling, the several subgroups or strata is based on characteristics. The most common strata used are year level, gender, age, ethnicity, religion, educational attainment, etc.

16. Example 16 Suppose you want to know the opinion of 200 students in a certain school which has a total population of 6,000. If there are 1,200 grades 7; 1,100 grade 8; 1,050 grade 9; 940 grade 10; 900 grade 11 and 810 grade 12 students, how are you going to choose your sample using stratified sampling?

17. Cluster Random Sampling 17 Area Sampling is a sampling technique in which the entire population is broken into small groups called clusters and then some of the clusters are randomly selected. The data from the randomly selected clusters are the one that is analyzed. It means that all elements from the sampled clusters will make up the sample.

18. Cluster Random Sampling 18 If the clusters are too large, then we need for a second set of smaller clusters. Like for example, divide the Province into towns, then towns into barrios, then a sample of barrios will be selected at random. Cluster Sampling is good for dealing large and dispersed populations. It uses one of other sampling techniques to get sample within each cluster. This method requires more cost and time compare to other methods.

19. Cluster Random Sampling 19

20. Non-Probability Sampling 20 Not every member of the population has the equal chance of being selected. It can rely on the subjective judgement of the researcher.

21. Convenience Sampling 21 Selecting a sample based on the availability of the member and/or proximity to the researcher. Also known as accidental, opportunity or grab sampling

22. Convenience Sampling 22

23. Purposive Sampling 23 Samples are chosen based on the goals of the study. They may be chosen based on their knowledge of the study being conducted or if they satisfy the traits or conditions set by the researcher.

24. Purposive Sampling 24

25. Quota Sampling 25 Proportion of the groups in the population were considered in the number and selection of the respondents.

26. Quota Sampling 26

27. Snowball Sampling 27 Participants in the study were tasked to recruit other members for the study.

28. Snowball Sampling 28

29. Parameter and Statistic

30. Parameter 30 It is a measure that describes an entire population based on all of the elements within that population. The value of a Parameter is fixed and unknown and usually denoted by a Greek letter. Population mean , population standard deviation and population variance , are examples of parameter  

31. Statistic 31 It is a measure that describes a fraction of the population under study or the sample. Statistic is a known number and a variable which depends on the portion of the population. It usually denoted by a Roman letter. Sample mean ( bar), sample standard deviation and sample variance , are examples of statistic.  

32. SAMPLING DISTRIBUTION OF THE SAMPLE MEANS FROM AN INFINITE POPULATION

33. Infinite population 33 A population in which there is no limit to the number of elements. Examples: the stars in the sky, dots in a line.

34. Finite population 34 Consists of a finite or fixed number of elements, measurements, or observation.

35. Notes 35 The mean of the sampling distribution of the sample means is equal to the population mean . That is,  

36. Notes 36 The variance of the sampling distribution of the sample means is given by: for finite population; and for infinite population.  

37. Notes 37 The standard deviation of the sampling distribution of the sample means is given by: for finite population where is the finite population correction factor for infinite population.  

38. Example 38 A certain population has a mean of 50 and a standard deviation of 4. If 15 random samples are drawn from this population, how will you describe the sampling distribution of the sample means?

39. THE CENTRAL LIMIT THEOREM

40. The Central Limit Theorem 40 If random samples of size are drawn from a population with mean and variance , the sampling distribution of the mean approaches normal distribution with mean and variance as , the same size, gets larger regardless of the shape of the original population distribution.  

41. Defining the Sampling Distribution of the Sample Mean using the Central Limit Theorem

42. Example 1 42 A certain population has a mean of 50 and a standard deviation of 5. If random sample of 15 measurements is drawn from this population, how will you describe the sampling distribution of the sample means?

43. Example 2 43 The heights of male OSHS students are normally distributed with mean of 70 inches and standard deviation of 2 inches. If 90 samples consisting of 30 students each are drawn from the population, what would be the mean and standard deviation of the computed sampling distribution of the means?