1. Psychology 101

2. Statistics THE DESCRIPTION, ORGANIZATION AND INTERPRATATION OF DATA

3. DESCRIBING DATA

4. SCALING The method by which one puts numbers to variables.

5. 1. NOMINAL The most Primitive of all scales and is included by definition in all other scales.

6. Criteria 1. NAMING OR POINTATABLE VARIABLE

7. Criteria 2. NO NUMERICAL ANALYSIS POSSIBLE

8. EXAMPLES: Drivers License

9. Examp. Social Security Number

10. Examp. Numbers On The Backs of Football Players

11. Scale 2 ORDINAL

12. The objects of a variable set can be rank ordered on some operationally defined characteristic.

13. Ordinal Scale Rank order in terms of the magnitude of the variables i.e.

14. More of, or less of, one variable with respect to another variable.

15. Requires the use of the nominal scale.

16. Examples Positions in a race; 1 st, 2 nd etc.

17. The Scale You Are Most Familiar With GRADES A > B > C > D > F

18. Problems With Ordinal Scales 1. No Zero point

19. 2. What is the magnitude of the distance between units of the scale

20. Example Grades A > B > C > D > F What is the last upper number What is the last lower number How much less is a B from an A. How much less is a C from a B etc.

21. High Ordered Metric Scale Tries to measure the distance between two ordinal variables

22. Ideally, grades are equal distance from one another

23. A > B > C > D > F You can take the test and get one of two grades, A or C.

24. You don‘t have to take the test and get a B.

25. If One Takes The Test The subjective gain of getting a B is so small relative to getting a C that one would gamble for the A.

26. Subjective loss less than the subjective gain

27. If One Takes the Assured B The subjective loss of the B by taking the test is too large relative to the gain of getting an A. One would not gamble for the A. The distance AB is shorter than the distance BC.

28. Choose B for sure

29. One Can Make The Same Comparisons Between Grades BC and CD.

30. When One Makes All Of The Possible Choices, One Sees That The Distances Do Not Rank Order Themselves In Terms Of Magnitude.

31. Scale 3 INTERVAL SCALE

32. 1. Possesses all of the characteristics of the Nominal and Ordinal scale especially rank-order

33. 2. Numerically equal distance on the an interval scale means equal distance on the property being measured

34. There Must Be An Arbitrary Zero.

35. Examples Centigrade and Fahrenheit temperature scale. Both based on the Freezing And boiling point of water.

36. The underling concept is mean molecular motion. Centigrade scale starts at zero and has 100 equal intervals. Fahrenheit scale starts at 32 and ends at 212 with 180 equal appearing intervals

37. The Distances Between Rank Orders Is Equal The distance from 20 degrees to 30 degrees is the same as the distance between 75 degrees and 85 degrees, or -75 degrees and -85 degrees. There Are Ten Degrees Of Difference

38. One Can Use Most Of The Mathematical Operations With Interval Scales ADD, Subtract, Multiply, Divide, Square, and Take Square Root. Will be used in most of the statistical methods covered below.

39. Ratio Scale The most powerful of the scale. An Absolute Zero. Includes Nominal, Ordinal and Interval Scales Equal Intervals. The Ratio Between Intervals Are Equal

40. Example Kelvin or Absolute Zero Temperature scale. Defined as that point where all molecular motion (Brownian movement) stops. There is no true Ratio scale in Psychology

41. ORGANIZING DATA

42. DATA ORGANIZATION Frequency Distribution A distribution that counts the number of individuals obtaining a given score and arranges those counts in a rank order from high to low or low to high (ordinal scale).

43. Histogram

44. Frequency Polygon

45. Measures of Central Tendency How common are you

46. MODE Pie Ala Mode, the hump of ice cream on the pie! The most frequently measured score! Distribution of scores can have more than one hump!

47. Median

48. Where is the word Median Used in Common Parlance?

49. Keep Off The Median – used in Highway Driving

50. Mean Average

51. Positively Skewed Distribution

52. Note how the positive numbers pull the mean to the right.

53. Measures of Variability How unique are you------How scores differ one from another.

54. Range Lowest to highest

55. Deviation The difference between a score and some constant measure

56. The constant can be any measure, but that which makes most sense is one of the measures of central tendency

57. The Mean is the best measure to subtract from each score

58. Deviation score X - MEAN = DEVIATION

59. Σ = sum of

60. SUM OF MEANS Σ (X – MEAN) = 0

61. How do I get rid of negative deviation scores SQUARE THE DEVIATION SCORES

63. VARIANCE Σ (X – MEAN) 2 N

64. Standard Deviation Square Root of Variance

65. Intrinsic Rational for the Value of a Standard Deviation

66. 1) The standard deviation reflects dispersion of scores so that the variability of different distributions may be compared in terms of the standard deviation.

67. 2) The standard deviation permits the precise interpretation of scores within a distribution.

68. 3) The standard deviation, like the mean, is a member of a mathematical system which permits its use in more advanced statistical considerations.

69. Is there a way to compare the same individual on two different tests?

70. Standard Scores z scores are called Standard Scores

71. COMPARE THE DEVIATION SCORE OF EACH TEST TO ITS STANDARD DEVIATION

72. Z Score z = (X – MEAN) S.D.

73. Characteristics of a z distribution “z” DISTRIBUTIONS ARE CHARACTERIZED BY THE PARAMETERS OF A NORMAL CURVE

74. THE S.D. OF A z DISTRIBUTION = 1

75. THE MEAN OF A “z” DISTRIBUTION = 0

76. A NORMAL CURVES OF IQ

77. Normal Curves

78. How the mean, median and mode are effected by skewness

79. Three types of normal curves depends on range of x values

80. DESCRIBING THE RELATION BETWEEN TWO VARIABLES

81. Correlation Correlation allows one to compare two different groups using parameters of a normal distribution.

82. Correlation Coefficient Correlation coefficient “r” has a range from -1 to + 1

83. Calculation formula r = Σ(z x z y ) /N

84. Assume the following data

89. Use of correlation Correlation coefficient allows one to account for the variation of trait 1 to the variation of trait 2.

90. Caveat (warning) of correlation data Does not allow for inferring causation

91. INFERRING CAUSE FROMDATA

92. POPULATION A POPULATION CONSITS OF ALL MEMBERS WITHIN IN THE UNIVERSE OF A GIVEN GROUP. SELDOM HAVE ACCES TO A POPULATION.

93. SAMPLE A SAMPLE IS A SMALL SUBSET OF THE POUPLATION.

94. CRITERIA FOR A SAMPLE The members of the sample must an unbiased estimate of the population.

95. Unbiased Estimate An unbiased estimate can be gained by reducing the number of free choices in calculating the standard deviation.

96. Putting on shoes When putting on shoes one has 1 degree of freedom.

97. ∑ ( X – X) 2 N-1

98. Existing Data One has existing data that shows high blood pressure is a consistent problem within class X people.

99. With in the class of X people, high blood pressure has a mean of 50 points higher than A normative group and a S.D. of ±5 points.

100. Causal Interpretation of Data Assert a hypothesis concerning the variable of interest.

101. Hypothesis 0 (null) Drug A does not causes a significant drop in blood pressure for those people who have chronic chronic high blood pressure

102. Hypothesis 1 (experimental hypothesis) Drug A does causes a significant drop in blood pressure for those people who have chronic high blood pressure.

103. Draw a sample of X people with high blood pressure Note here, one already has for their disposition the Mean and S.D. of higher blood pressure for the Population of X people.

104. Random Sample of 25 people from population X given Drug A Measure blood pressure of those 25 selected people.

105. Results Mean drop in blood pressure after being given Drug A is 10 points with a S.D. 2.5.

106. Question is Drug A effective? Test the mean difference between that for the population from that of the sample.

107. Calculate a z score Since one has sampled the population of X, one wants to assure oneself that one has an unbiased estimate of the population that is represented by the sample.

108. What calculating the z score does The calculation of the z score forces the assumption that the mean of the blood drop is 0 and a S.D. of 1.

109. One gains the unbiased estimate by correcting the S.D SE (standard error) = S.D. (N-1) 1/2

110. Critical ratio Critical ratio = obtained mean SE

111. Numerically our example SE = SD/(N-1) -1/2 SE = 2.5/(24) -1/2 = 2.5/4.9 = 0.51

112. Sample – Population mean divided by SE 10 – 0/SE = 10/0.51 = 19.61 From a z distribution if the ratio is larger that 1.96 one calls that change significant.

113. Go back to the two Hypotheses Reject Hypothesis 0 Accept Hypothesis 1

114. Confidence interval A confidence interval is saying that within ±2 SE of the mean difference 95 % of the time one would find the mean of the sample.