RANDOM-SAMPLING-parameter-and-statistic.pptx

Statistics and Probability

1. Illustrating random sampling, distinguishes between parameter and statistics

2. OBJECTIVES: 2 Illustrates the different types random variable; Identify the perimeter and statistic

3. QUESTION: 3 Who is the most attractive person in this class?

4. RANDOM SAMPLING 4 a part of the sampling technique in which each sample has an equal probability of being chosen. A sample chosen randomly is meant to be an unbiased representation of the total population.

5. RANDOM SAMPLING 5 Random Sampling may be taken from: Population – it refers to the entire group that is under study or investigation. Sample – it is a subset taken from a population, either by random or non-random techniques. A representation of the population where one hopes to draw valid conclusion from about the population.

6. RANDOM SAMPLING 6 Random sampling is defined as: • A technique used in selecting people or items for research • A selection of n elements derived from a population N, which is the subject of the investigation or experiment, where each sample point has an equal chance of being selected using the appropriate sampling technique.

7. 7 TYPES OF RANDOM SAMPLING

8. LOTTERY OR SIMPLE RANDOM SAMPLING 8 - a sampling technique where every nth member of the population has an equal chance of being selected. EXAMPLE: When members of the population of students have their names represented into small pieces of paper which are in the box then mixed together and picked out at random.

9. LOTTERY OR SIMPLE RANDOM SAMPLING 9

10. SYSTEMATIC RANDOM SAMPLING 10 - a sampling technique in which members of the population are listed and samples are selected in intervals called sample intervals. Every nth element from the list is selected from a randomly selected starting point.

11. SYSTEMATIC RANDOM SAMPLING 11 EXAMPLE : Imagine that you are all 60 in a class. You really wanted to draw 20 samples out of 60 students. So how are you going to do it?

12. SYSTEMATIC RANDOM SAMPLING 12 FORMULA:   Therefore, the interval is 3. Every 3 rd students are included as samples. 1,2, 3 ,4,5, 6 ,7,8, 9 ,10,11, 12 ,… 60

13. SYSTEMATIC RANDOM SAMPLING 13

14. CONVENIENCE SAMPLING 14 a type of non-probability sampling. Selecting respondents in which the members of the population do not have equal chance of being selected as samples. Selecting samples based on convenience.

15. CONVENIENCE SAMPLING 15 EXAMPLES: 1. Standing outside the mall and giving survey questionnaires to mall goers. 2. Conducting survey to students as they enter the school. 3. Posting a survey on social media like Facebook. 4. Interviewing people in the park.

16. CONVENIENCE SAMPLING 16 ADVANTAGE - This sampling method saves time when gathering data from on-hand population, it involves speed and convenience. DISADVANTAGE - It does not provide a representative result; it cannot offer any information about the entire group of people.

17. CONVENIENCE SAMPLING 17

18. CLUSTER SAMPLING 18 a probability sampling method in which you divide a population into clusters, such as districts or schools, and then randomly select some of these clusters as your sample. The clusters should ideally each be mini-representations of the population as a whole.

19. CLUSTER SAMPLING 19 EXAMPLE: There are 14 clusters. After you choose clusters randomly. You can now choose in each individuals to form your sample.

20. CLUSTER SAMPLING 20

21. STRATIFIED RANDOM SAMPLING 21 A sampling procedure wherein the members of the population are grouped based on their homogeneity. It is used when there are number of distinct subgroups in the population, within each of which is required that there is full representation.

22. STRATIFIED SAMPLING TECHNIQUE 22 A. Equal Allocation This process chooses the same number of individuals or elements from each group or stratum, regardless of their differences in size, to form the sample B. Proportional Allocation This process chooses particular number of individuals or elements proportional to the size of each group or stratum to form the sample.

23. EXAMPLE OF EQUAL ALLOCATION 23 Suppose a population is divided into 4 strata, A, B, C, and D, and you are going to conduct a survey for your research and you need 160 respondents (n). Let say A has a size of 200, B with 300, C with 250, and D with 250 as well. STEP1 : Divide the sample size by the number of strata. 160÷4=40 STEP2 : Select randomly a number of 40 individuals per stratum. STEP3 : Gather all 40 individuals from each stratum to form the sample

24. EXAMPLE OF PROPORTIONAL ALLOCATION 24 Suppose a population is divided into 4 strata, A, B, C, and D, and you are going to conduct a survey for your research and you need 160 respondents (n). Let say A has a size of 200, B with 300, C with 250, and D with 250 as well.

25. EXAMPLE OF PROPORTIONAL ALLOCATION 25 STEP1: Add all the individuals per stratum to determine the population 200+300+250+250=1000 STEP2: Divide the size of each stratum with the population to determine their proportions. A=200÷1000=0.2 C=250÷1000=0.25 B=300÷1000=0.3 D=250÷1000=0.25

26. EXAMPLE OF PROPORTIONAL ALLOCATION 26 STEP3: Multiply each proportion obtained from step 2 to the sample size A=0.2 ×160= 32 B=0.3 ×160= 48 C=0.25 ×160= 40 D=0.2 5×160= 40

27. STRATIFIED SAMPLING TECHNIQUE 27 Solve the sample size. GROUP A -500 GROUP B – 1300 GROUP C – 1600 GROUP D - 600 e = 5% or 0.05 Using Slovin’s Formula: w here: n = sample size N = population size e = margin error  

28. EXAMPLE OF PROPORTIONAL ALLOCATION 28

29. STRATIFIED SAMPLING TECHNIQUE 29 RESPONDENTS POPULATION SIZE SAMPLE SIZE GROUP A 500 GROUP B 1300 GROUP C 1600 GROUP D 600 TOTAL

30. STRATIFIED SAMPLING TECHNIQUE 30 RESPONDENTS POPULATION SIZE SAMPLE SIZE GROUP A 500 46 GROUP B 1300 118 GROUP C 1600 146 GROUP D 600 55 TOTAL N=4000 n=364

31. 31 Population vs Sample Parameter vs Statistic

32. POPULATION VS SAMPLE 32 A population data set contains all members of a specified group (the entire list of all possible data values). A sample data set contains a part, or a subset, of a population

33. POPULATION VS SAMPLE 33 Illustrative example: Grade 10 completers – 1,000 students (population) Random sample – 100 students

34. POPULATION VS SAMPLE 34 EXAMPLES: A. Identify whether the following refer to population or sample. The total number of students in a school. A group of 30 patients in a hospital undergoing treatment for COVID. The ages of all vendors in a public market. The top 50 top-earning Filipinos. The list of all countries in the world.

35. PARAMETER VS STATISTIC 35 Parameter (Population data) – are numbers that summarize data for an entire population. Statistic (Sample data) – are number that summarize data from a sample.

36. PARAMETER VS STATISTIC 36 STATISTIC PARAMETER MEAN s STANDARD DEVIATION VARIANCE PROPORTION P n SIZE N STATISTIC PARAMETER MEAN s STANDARD DEVIATION VARIANCE PROPORTION P n SIZE N

37. STRATIFIED SAMPLING TECHNIQUE 37 EXAMPLES: B. Tell whether the given example is a parameter or statistic. The average weight of all males in the Philippines. The average height of 100 cats in Pasig. The average test score of 20 students in a class of 500. The average daily allowance of all students in a class. Based on a sample of 900 elementary students, it was found out that 30% of them could not do long division.

38. ACTIVITY 38 1. Using proportional allocation. Determine the sample size of each department. DEPARTMENT POPULATION SAMPLE A 200 B 100 C 120 D 150 E 230 TOTAL N = n =

39. GENERALIZATION 39 Based on your understanding to the lesson, when will we use random sampling?

40. CHECK IT OUT 40 Direction: Determine the given situation whether it is Parameter or Statistic 1. The list of all students in Immaculate Conception College. 2. The top 10 students in a classroom 3. The total of officials in barangay. 4. A group of 32 senior citizens who gets their insurance. 5. The total number of pigs in a farm.

41. EVALUATION 41 Direction: Write it down what you’ve learned today. 1. Parameter 2. Statistic 3. Lottery or Simple Random Sampling 4. Systematic Random Sampling 5. Stratified Random Sampling

42. ASSIGNMENT 42 Direction: Compute the sample size of each team using equal allocation and proportional allocation TEAM POPULATION SAMPLE 1 18 2 14 3 17 4 13 5 21 TOTAL N =

43. 43 “YOU DIDN’T COME THIS FAR JUST TO COME THIS FAR”