1. Educational Research: Data analysis and interpretation – 1 Descriptive statistics EDU 8603 Educational Research Richard M. Jacobs, OSA, Ph.D.

2. Medicine needs data to advance

3. Statistics... A set of mathematical procedures for describing, synthesizing, analyzing, and interpreting quantitative data …the selection of an appropriate statistical technique is determined by the research design, hypothesis, and the data collected

4. Preparing data for analysis... Data must be accurately scored and systematically organized to facilitate data analysis: tabulating tabulating: organizing the data in a systematic manner coding coding: assigning numerals (e.g., ID) to data scoring scoring: assigning a total to each participant’s instrument

5. descriptive statistics... descriptive statistics... …permit the researcher to describe many pieces of data with a few indices

6. statistics... statistics... …indices calculated by the researcher for a sample drawn from a population

7. parameters... parameters... …indices calculated by the researcher for an entire population

8. Types of descriptive statistics… 1. graphs 2. measures of central tendency 3. measures of variability

9. graphs... graphs... …representations of data enabling the researcher to see what the distribution of scores look like

10. 1. Graphs… frequency polygon pie chart boxplot stem-and-leaf chart

12. measures of central tendency... measures of central tendency... …indices enabling the researcher to determine the typical or average score of a group of scores

13. 2. Measures of central tendency… mode median mean

14. mode... mode... …the score attained by more participants than any other score

16. median... median... …the point in a distribution above and below which are 50% of the scores

17. mean... mean... …the arithmetic average of the scores

18. measures of variability... measures of variability... …indices enabling the researcher to indicate how spread out a group of scores are

19. 3. Measures of variability… range quartile deviation variance standard deviation

20. range... range... …the difference between the highest and lowest score in a distribution

21. quartile deviation... quartile deviation... …one half of the difference between the upper quartile (the 75%’ile) and the lower quartile (the 25%’ile) in a distribution

22. variance... variance... …a summary statistic indicating the degree of variability among participants for a given variable

23. standard deviation... standard deviation... …the square root of variance providing an index of variability in the distribution of scores

24. Normal distributions of data (the normal curve)... A bell-shaped distribution of scores having four identifiable properties… …50% of the scores fall above the mean and 50% of the scores fall below the mean …the mean, median, and mode are the same value

25. …most scores are near the mean and, the farther from the mean a score is, the fewer the number of participants who attained that score …the same number, or percentage, of scores is between the mean and plus one standard deviation as is between the mean and minus one standard deviation

26. Non-normal distributions of data (skewed distributions)... A non-bell-shaped distribution of scores where… …mean < median < mode negatively skewed distribution (a “negatively skewed distribution”) …mean > median > mode positively skewed distribution (a “positively skewed distribution”)

28. measures of relative position... measures of relative position... …indices enabling the researcher to describe a participant’s performance compared to the performance of all other participants

29. 4. Measures of relative position… percentile ranks standard scores

30. percentile rank... percentile rank... …indicates the percentage of scores that fall at or below a given score

31. standard score... standard score... …a measure of relative position

32. Types of standard scores... Types of standard scores... …z score …T score …stanines

33. z score... z score... …a statistic expressing how far a score is from the mean in terms of standard deviation units

34. T score... T score... …a transformed z score that voids negative numbers and decimals by multiplying the z score by 10 and adding 50

35. stanines... stanines... …a standard score that divides a distribution into nine parts

36. measures of relationship... measures of relationship... …indices enabling the researcher to indicate the degree to which two sets of scores are related

37. 5. Measures of relationship… Spearman Rho Pearson r

38. correlations correlations variables …determines whether and to what degree a relationship exists between two or more quantifiable variables …the degree of the relationship is expressed as a coefficient of correlation

42. confounding factors …the presence of a correlation does not indicate a cause-effect relationship primarily because of the possibility of multiple confounding factors

43. Correlation coefficient… +1.00 strong negative strong positive 0.00 no relationship

44. Spearman Rho... Spearman Rho... …a measure of correlation used for rank and ordinal data

45. Pearson r... Pearson r... …a measure of correlation used for data of interval or ratio scales …assumes that the relationship between the variables being correlated is linear

46. Mini-Quiz… True and false… …the analysis of the data is as important as any other component of the research process True

47. True and false… …descriptive statistics are normally computed separately for each group in a research study True

48. True and false… …every instrument administered must always be scored accurately and consistently, using the same procedures and criteria True

49. True and false… …tentative scoring procedures must always be tried out beforehand by administering the instrument to the study participants False

50. True and false… …a computer should not be used to perform an analysis that a researcher has never completed by hand or, at least, studied extensively True

51. True and false… …the first step in data analysis is to describe, or summarize, the data using descriptive statistics True

52. True and false… …the number resulting from the computation of a measure of central tendency represents the typical score attained by a group of participants True

53. True and false… …the mean is the most precise, stable index of typical performance that is especially useful in situations in which there are extreme scores False

54. True and false… …unless a correlation coefficient is used to compute the reliability of an instrument in a causal- comparative or experimental study, a correlation coefficient is only computed in a correlation study True

55. True and false… …plus and/or minus two standard deviations includes more the 99% of the scores False

56. True and false… …standard scores are rarely used in research studies True

57. True and false… …to test a hypothesis adequately, more than descriptive statistics are normally needed True

58. True and false… …if the extreme scores are at the upper, or higher, end of the distribution, it is said to be positively skewed True

59. True and false… …the median of a set of scores corresponds to the 50% percentile True

60. True and false… …a standard score is a measure of relative position that is appropriate when the data represent a nominal scale False

61. True and false… …a z score expresses how far a score is from the mean in terms of standard deviation units True

62. True and false… …the Spearman Rho is the appropriate measure of correlation when the variables are expressed as ranks instead of scores True

63. True and false… …the assumption associated with the application of Pearson r is that the relationship between the variables being correlated is linear True

64. Fill in the blank… …statistics which permit the researcher to describe many scores with a small number of indices descriptive statistics

65. Fill in the blank… …the values calculated for a sample drawn form a population statistics

66. Fill in the blank… …the values calculated for an entire population parameters

67. Fill in the blank… …a convenient way to describe a set of data with a single number measures of central tendency

68. Fill in the blank… …the index of central tendency appropriate for nominal data mode

69. Fill in the blank… …the index of central tendency appropriate for ordinal data median

70. Fill in the blank… …the index of central tendency appropriate for interval or ratio data mean

71. Fill in the blank… …the score attained by more participants than any other score mode

72. Fill in the blank… …the point in a distribution above and below which are 50% of the scores median

73. Fill in the blank… …the arithmetic average of the scores mean

74. Fill in the blank… …the difference between the highest and lowest score in a distribution range

75. Fill in the blank… …the measure of variability identifying one half of the difference between the 75 th percentile and the 25 th percentile quartile deviation

76. Fill in the blank… …the measure of variability used for interval and ratio data standard deviation

77. Fill in the blank… …the only appropriate measure of variability for nominal data range

78. Fill in the blank… …+/- 1.00 standard deviations constitutes ____ % of the sample 68%

79. Fill in the blank… …extreme scores at the lower end of the distribution indicates a ______ skewed distribution positively

80. Fill in the blank… …indices describing where a score is in relation to all other scores measures of relative position

81. Fill in the blank… …indicates the percentage of scores that fall at or below a given score percentile ranks

82. Fill in the blank… …if a set of scores is transformed into a set of z scores, the new distribution has a mean of ____ and a standard deviation of ____ zero; one

83. Fill in the blank… …a set of standard scores that divide a distribution into nine parts stanines

84. Fill in the blank… …the most appropriate measure of correlation when the sets of data to be correlated represent either interval or ratio scales Pearson r

85. This module has focused on... descriptive statistics...the statistical procedures for describing, synthesizing, analyzing, and interpreting quantitative data

86. The next module will focus on......the statistical procedures for generalizing to a population of individuals based on information obtained from a limited number of research participants inferential statistics