SAMPLING SURVEY TECHNIQUE

1. SAMPLING SURVEY TECHNIQUE

2. POPULATIONS and SAMPLES THE POPULATION is the set of all the individuals of interest in particular study The sample is selected from the population The result from the sample are generalized from the population THE SAMPLE is a set of individuals selected from a population, usually intended to represent the population in a research study

3. Teknik pengumpulan data Pengumpulan Data Sensus (populasi) Sampling (sampel) Probabilita Non-Probabilita

4. PARAMETER and STATISTIC • A parameter is a value, usually a numerical value, that describes a population. A parameter may be obtained from a single measurement, or it may be derived from a set of measurements from the population • A statistic is a value, usually a numerical value, that describes a sample. A statistic may be obtained from a single measurement, or it may be derived from a set of measurement from sample

5. SAMPLING ERROR • Although samples are generally representative of their population, a sample is not expected to give a perfectly accurate picture of the whole population • There usually is some discrepancy between sample statistic and the corresponding population parameter called sampling error

6. TWO KINDS OF NUMERICAL DATA Generally fall into two major categories: • Counted frequencies  enumeration data • Measured  metric or scale values  measurement or metric data Statistical procedures deal with both kinds of data

7. DATUM and DATA • The measurement or observation obtain for each individual is called a datumor, more commonly a score or raw score • The complete set of score or measurement is called the data set or simply the data • After data are obtained, statistical methods are used to organize and interpret the data

8. VARIABLE • A variable is a characteristic or condition that changes or has different values for different individual • A constantis a characteristic or condition that does not vary but is the same for every individual • A research study comparing vocabulary skills for 12-year-old boys

9. QUALITATIVE and QUANTITATIVECategories • Qualitative: the classes of objects are different in kind. There is no reason for saying that one is greater or less, higher or lower, better or worse than another. • Quantitative: the groups can be ordered according to quantity or amount It may be the cases vary continuously along a continuum which we recognized.

10. DISCRETE and CONTINUOUS Variables • A discrete variable. No values can exist between two neighboring categories. • A continuousvariable is divisible into an infinite number or fractional parts • It should be very rare to obtain identical measurements for two different individual • Each measurement category is actually an interval that must be define by boundaries called real limits

11. CONTINUOUS Variables • Most interval-scale measurement are taken to the nearest unit (foot, inch, cm, mm) depending upon the fineness of the measuring instrument and the accuracy we demand for the purposes at hand. • And so it is with most psychological and educational measurement. A score of 48 means from 47.5 to 48.5 • We assume that a score is never a point on the scale, but occupies an interval from a half unit below to a half unit above the given number.

12. FREQUENCIES, PERCENTAGES, PROPORTIONS, and RATIOS • Frequency defined as the number of objects or event in category. • Percentages (P) defined as the number of objects or event in category divided by 100. • Proportions (p). Whereas with percentage the base 100, with proportions the base or total is 1.0 • Ratio is a fraction. The ratio of a to b is the fraction a/b. A proportion is a special ratio, the ratio of a part to a total.

13. MEASUREMENTS and SCALES (Stevens, 1946) Ratio Interval Ordinal Nominal

14. FREQUENCY DISTRIBUTION, GRAPH, and PERCENTILE

15. A class of 40 students has just returned the Perceptual Speed test score. Aside from the primary question about your grade, you’d like to know more about how you stand in the class • How does your score compare with other in the class? What was the range of performance • What more can you learn by studying the scores?

16. Score of PERCEPTUAL SPEED Test Taken from Guilford p.55

17. OVERVIEW • When a researcher finished the data collect phase of an experiment, the result usually consist pages of numbers • The immediate problem for the researcher is to organize the scores into some comprehensible form so that any trend in the data can be seen easily and communicated to others • This is the jobs of descriptive statistics; to simplify the organization and presentation of data • One of the most common procedures for organizing a set of data is to place the scores in a FREQUENCY DISTRIBUTION

18. GROUPED SCORES • After we obtain a set of measurement (data), a common next step is to put them in a systematic order by grouping them in classes • With numerical data, combining individual scores often makes it easier to display the data and to grasp their meaning. This is especially true when there is a wide range of values.

19. TWO GENERAL CUSTOMS IN THE SIZE OF CLASS INTERVAL • We should prefer not fewer than 10 and more than 20 class interval. • More commonly, the number class interval used is 10 to 15. • An advantage of a small number class interval is that we have fewer frequencies which to deal with • An advantage of larger number class interval is higher accuracy of computation

20. TWO GENERAL CUSTOMS IN THE SIZE OF CLASS INTERVAL 2. Determining the choice of class interval is that certain ranges of units (scores) are preferred. Those ranges are 2, 3, 5, 10, and 20. These five interval sizes will take care of almost all sets of data

21. Score of PERCEPTUAL SPEED Test Taken from Guilford p.55

22. HOW TO CONSTRUCT A GROUPED FREQUENCY DISTRIBUTION Step 1 : find the lowest score and the highest score Step 2 : find the range by subtracting the lowest score from the highest Step 3 : divide the range by 10 and by 20 to determine the largest and the smallest acceptable interval widths. Choose a convenient width (i) within these limits

23. Score of PERCEPTUAL SPEED Test Range = 42  42 : 10 = 4,2 and42 : 20 = 2,1

24. WHERE TO START CLASS INTERVAL • It’s natural to start the interval with their lowest scores at multiples of the size of the interval. • When the interval is 3, to start with 24, 27, 30, 33, etc.; when the interval is 4, to start with 24, 28, 32, 36, etc.

25. HOW TO CONSTRUCT A GROUPED FREQUENCY DISTRIBUTION Step 4 : determine the score at which the lowest interval should begin. It should ordinarily be a multiple of the interval. Step 5 : record the limits of all class interval, placing the interval containing the highest score value at the top. Make the intervals continuous and of the same width Step 6 : using the tally system, enter the raw scores in the appropriate class intervals Step 7 : convert each tally to a frequency

26. FREQUENCY DISTRIBUTION TABLE X max = 67 X min = 25 RANGE = 42 Interval = 3 C.i = 15 Interval = 4 C.i = 11

27. PERCEPTUALSPEED

28. WARNING!! • Although grouped frequency distribution can make easier to interpret data, some information is lost. • In the table, we can see that more people scored in the interval 48 – 51 than in any other interval • However, unless we have all the original scores to look at, we would not know whether the 11 scores in this interval were all 48s, all, 49s, all 50s, or all 51 or were spread throughout the interval in some way • This problem is referred to as GROUPING ERROR • The wider the class interval width, the greater the potential for grouping error

29. STEM and LEAF DISPLAY • In 1977, J.W. Tukey presented a technique for organizing data that provides a simple alternative to a frequency distribution table or graph • This technique called a stem and leaf display, requires that each score be separated into two parts. • The first digit (or digits) is called the stem, and the last digit (or digits) is called the leaf.

30. Data Stem & Leaf Display 83 82 63 • 93 78 71 68 33 76 52 97 85 42 46 32 57 59 56 73 74 74 81 76 3 2 3 4 5 6 7 8 9 2 6 6 2 7 9 2 2 8 3 6 1 4 3 8 4 6 3 5 2 1 3 7

31. GROUPED FREQUENCY DISTRIBUTION HISTOGRAM AND A STEM AND LEAF DISPLAY 2 3 2 6 6 2 7 9 2 8 3 1 6 4 3 8 4 6 3 5 2 1 3 7 7 6 5 4 3 2 1 3 4 5 6 7 8 9 0 30 40 50 60 70 80 90

32. MAKING GRAPH POLIGONand HISTOGRAM

33. MAKING GRAPH POLIGON

34. PERCEPTUALSPEED

35. POLIGON f 12 10 8 6 4 2 Class Interval’s MIDPOINT X 0 21.5 29.5 37.5 45.5 53.5 61.5 69.5 25.5 33.5 41.5 49.5 57.5 65.5

36. PERCEPTUAL SPEED f 12 10 8 6 4 2 X 0 21.5 29.5 37.5 45.5 53.5 61.5 69.5 25.5 33.5 41.5 49.5 57.5 65.5

37. MAKING GRAPH HISTOGRAM

38. PERCEPTUALSPEED

39. HISTOGRAM f 12 10 8 6 4 2 Class Interval’s EXACT LIMIT X 0 27.5 35.5 43.5 51.5 59.5 67.5 23.5 31.5 39.5 47.5 55.5 63.5

40. POLIGON and HISTOGRAM f 12 10 8 6 4 2 X 0 27.5 35.5 43.5 51.5 59.5 67.5 23.5 31.5 39.5 47.5 55.5 63.5

41. THE SHAPE OF A FREQUENCY DISTRIBUTION It is possible to draw a vertical line through the middle so that one side of the distribution is a mirror image of the other Symmetrical Skewed positive negative The scores tend to pile up toward one end of the scale and taper off gradually at the other end

42. LEARNING CHECK • Describe the shape of distribution for the data in the following table X f 5 4 3 2 1 4 6 3 1 1 The distribution is negatively skewed

43. PERCENTILES and PERCENTILE RANKS • The percentile system is widely used in educational measurement to report the standing of an individual relative performance of known group. It is based on cumulative percentage distribution. • A percentile is a point on the measurement scale below which specified percentage of the cases in the distribution falls • The rank or percentile rank of a particular score is defined as the percentage of individuals in the distribution with scores at or below the particular value • When a score is identified by its percentile rank, the score called percentile

44. Percentile Rank refers to a percentagePercentile refers to a score • Suppose, for example that A have a score of X=78 on an exam and we know exactly 60% of the class had score of 78 or lower….… • Then A score X=78 has a percentile of 60%, and A score would be called the 60th percentile

45. CENTRAL TENDENCY Mean, Median, and Mode

46. OVERVIEW • The general purpose of descriptive statistical methods is to organize and summarize a set score • Perhaps the most common method for summarizing and describing a distribution is to find a single value that defines the average score and can serve as a representative for the entire distribution • In statistics, the concept of an average or representative score is called central tendency

47. OVERVIEW • Central tendency has purpose to provide a single summary figure that best describe the central location of an entire distribution of observation • It also help simplify comparison of two or more groups tested under different conditions • There are three most commonly used in education and the behavioral sciences: mode, median, and arithmetic mean

48. The MODE • A common meaning of mode is ‘fashionable’, and it has much the same implication in statistics • In ungrouped distribution, the mode is the score that occurs with the greatest frequency • In grouped data, it is taken as the midpoint of the class interval that contains the greatest numbers of scores • The symbol for the mode is Mo

49. The MEDIAN • The median of a distribution is the point along the scale of possible scores below which 50% of the scores fall and is there another name for P50 • Thus, the median is the value that divides the distribution into halves • It symbols is Mdn

50. The ARITHMETIC MEAN • The arithmetic mean is the sum of all the scores in the distribution divided by the total number of scores • Many people call this measure the average, but we will avoid this term because it is sometimes used indiscriminately for any measure of central tendency • For brevity, the arithmetic mean is usually called the mean