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Scaled v. ordinal v. nominal data(3)

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Scaled v. ordinal v. nominal data(3)

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Scaled v. ordinal v. nominal data(3)

  1. 1. This presentation will assist you in determining if the data associated with the problem you are working on
  2. 2. This presentation will assist you in determining if the data associated with the problem you are working on Participant Score A 10 B 11 C 12 D 12 E 12 F 13 G 14
  3. 3. This presentation will assist you in determining if the data associated with the problem you are working on Participant Score A 10 B 11 C 12 D 12 E 12 F 13 G 14
  4. 4. This presentation will assist you in determining if the data associated with the problem you are working on is:
  5. 5. This presentation will assist you in determining if the data associated with the problem you are working on is: Scaled
  6. 6. This presentation will assist you in determining if the data associated with the problem you are working on is: Scaled Ordinal
  7. 7. This presentation will assist you in determining if the data associated with the problem you are working on is: Scaled Ordinal Nominal Proportional
  8. 8. Before we begin, it is important to note that with questions of difference, where you are comparing groups, the data you should classify as scaled, ordinal, or nominal proportional are data that represent RESULTS (weight gain, driving speed, IQ, etc.), In this case, you are NOT classifying what are called CATEGORICAL variables like gender, treatment/control group, type of athlete, school type, ethnicity, political or religious affiliation, etc.
  9. 9. What is scaled data?
  10. 10. What is scaled data? Note – scaled data has two subcategories (1) interval data (no zero point but equal intervals) and (2) ratio data (a zero point and equal intervals)
  11. 11. What is scaled data? For the purposes of this presentation we will not discuss these further but just focus on both as scaled data.
  12. 12. Scaled data is data that has a couple of attributes.
  13. 13. We will describe those attributes with illustrations from a scaled variable:
  14. 14. We will describe those attributes with illustrations from a scaled variable: Temperature.
  15. 15. Attribute #1 – scaled data assume a quantity. Meaning that 2 is more than 3 and 4 is more than 3 and 20 is less than 30, etc. For example: 40 degrees is more than 30 degrees. 110 degrees is less than 120 degrees.
  16. 16. Attribute #1 – scaled data assume a quantity. Meaning that 2 is more than 3 and 4 is more than 3 and 20 is less than 30, etc. For example: 40 degrees is more than 30 degrees. 110 degrees is less than 120 degrees.
  17. 17. Attribute #1 – scaled data assume a quantity. Meaning that 3is more than 2and 4 is more than 3 and 20 is less than 30, etc. For example: 40 degrees is more than 30 degrees. 110 degrees is less than 120 degrees.
  18. 18. Attribute #1 – scaled data assume a quantity. Meaning that 3 is more than 2 and 4is more than 3and 20 is less than 30, etc. For example: 40 degrees is more than 30 degrees. 110 degrees is less than 120 degrees.
  19. 19. Attribute #1 – scaled data assume a quantity. Meaning that 3 is more than 2 and 4 is more than 3 and 20is less than 30, etc. For example: 40 degrees is more than 30 degrees. 110 degrees is less than 120 degrees.
  20. 20. Attribute #1 – scaled data assume a quantity. Meaning that 3 is more than 2 and 4 is more than 3 and 20 is less than 30, etc. For example: 40 degrees is more than 30 degrees. 110 degrees is less than 120 degrees.100 degrees is more than 40 degrees
  21. 21. Attribute #1 – scaled data assume a quantity. Meaning that 3 is more than 2 and 4 is more than 3 and 20 is less than 30, etc. For example: 40 degrees is more than 30 degrees. 110 degrees is less than 120 degrees.60 degrees is less than 80 degrees
  22. 22. Attribute #1 – scaled data assume a quantity. Meaning that 3 is more than 2 and 4 is more than 3 and 20 is less than 30, etc. For example: 40 degrees is more than 30 degrees. 110 degrees is less than 120 degrees.60 degrees is less than 80 degrees If the data represents varying amounts then this is the first requirement for data to be considered - scaled.
  23. 23. Attribute #2
  24. 24. Attribute #2 – scaled data has equal intervals or each unit has the same value.
  25. 25. Attribute #2 – scaled data has equal intervals or each unit has the same value. Meaning the distance between 1and 2is the same as the distance between 14 and 15 or 1,123 and 1,124.
  26. 26. Attribute #2 – scaled data has equal intervals or each unit has the same value. Meaning the distance between 1and 2is the same as the distance between 14 and 15 or 1,123 and 1,124. They all have a unit value of 1 between them.
  27. 27. In our temperature example:
  28. 28. 40o - 41o 100o - 101o 70o – 71o Each set of readings are the same distance apart: 1o
  29. 29. 40o - 41o 100o - 101o 70o – 71o Each set of readings are the same distance apart: 1o The point here is that each unit value is the same across the entire scale of numbers
  30. 30. 40o - 41o 100o - 101o 70o – 71o Each set of readings are the same distance apart: 1o Note, this is not the case with ordinal numbers where 1st place in a marathon might be 2:03 hours, 2nd place 2:05 and 3rd place 2:43. They are not equally spaced!
  31. 31. What does a scaled data set look like?
  32. 32. Here are some examples:
  33. 33. Height
  34. 34. Height Persons Height Carly 5’ 3” Celeste 5’ 6” Donald 6’ 3” Dunbar 6’ 1” Ernesta 5’ 4”
  35. 35. Height Attribute #1: We are dealing with amounts Persons Height Carly 5’ 3” Celeste 5’ 6” Donald 6’ 3” Dunbar 6’ 1” Ernesta 5’ 4”
  36. 36. Height Persons Height Carly 5’ 3” Celeste 5’ 6” Donald 6’ 3” Dunbar 6’ 1” Ernesta 5’ 4” Attribute #2: There are equal intervals across the scale. One inch is the same value regardless of where you are on the scale.
  37. 37. Intelligence Quotient (IQ)
  38. 38. Intelligence Quotient (IQ) Persons Height IQ Carly 5’ 3” 120 Celeste 5’ 6” 100 Donald 6’ 3” 95 Dunbar 6’ 1” 121 Ernesta 5’ 4” 103
  39. 39. Intelligence Quotient (IQ) Persons Height IQ Carly 5’ 3” 120 Celeste 5’ 6” 100 Donald 6’ 3” 95 Dunbar 6’ 1” 121 Ernesta 5’ 4” 103 Attribute #1: We are dealing with amounts
  40. 40. Intelligence Quotient (IQ) Persons Height IQ Carly 5’ 3” 120 Celeste 5’ 6” 100 Donald 6’ 3” 95 Dunbar 6’ 1” 121 Ernesta 5’ 4” 103 Attribute #2: Supposedly there are equal intervals across this scale. A little harder to prove but most researchers go with it.
  41. 41. Pole Vaulting Placement
  42. 42. Pole Vaulting Placement Persons Height IQ PVP Carly 5’ 3” 120 3rd Celeste 5’ 6” 100 5th Donald 6’ 3” 95 1st Dunbar 6’ 1” 121 4th Ernesta 5’ 4” 103 2nd
  43. 43. Pole Vaulting Placement Persons Height IQ PVP Carly 5’ 3” 120 3rd Celeste 5’ 6” 100 5th Donald 6’ 3” 95 1st Dunbar 6’ 1” 121 4th Ernesta 5’ 4” 103 2nd Attribute #1: We are dealing with amounts
  44. 44. Pole Vaulting Placement Persons Height IQ PVP Carly 5’ 3” 120 3rd Celeste 5’ 6” 100 5th Donald 6’ 3” 95 1st Dunbar 6’ 1” 121 4th Ernesta 5’ 4” 103 2nd Attribute #2: We are NOT dealing with equal intervals. 1st place (16’0”) and 2nd place (15’8”) are not the same distance from one another as 2nd Place and 3rd place (12’2”).
  45. 45. Based on this explanation is your data scaled?
  46. 46. If your data is scaled as shown in these examples, select
  47. 47. If your data is scaled as shown in these examples, select Scaled Ordinal Nominal Proportional
  48. 48. We have now demonstrated scaled data and given you a brief introduction to ordinal data.
  49. 49. Once again, ordinal data is data that is ranked:
  50. 50. Once again, ordinal data is data that is ranked:
  51. 51. In other words,
  52. 52. Ordinal scales use numbers to represent relative amounts of an attribute.
  53. 53. Ordinal scales use numbers to represent relative amounts of an attribute. 1st Place 16’ 3”
  54. 54. Ordinal scales use numbers to represent relative amounts of an attribute. 1st Place 16’ 3” 2nd Place 16’ 1”
  55. 55. Ordinal scales use numbers to represent relative amounts of an attribute. 1st Place 16’ 3” 2nd Place 16’ 1” 3rd Place 15’ 2”
  56. 56. Ordinal scales use numbers to represent relative amounts of an attribute. 3rd Place 15’ 2” 2nd Place 16’ 1” 1st Place 16’ 3” Relative Amounts of Bar Height
  57. 57. Example of relative amounts of authority
  58. 58. Corporal 2 Sargent 3 Lieutenant 4 Major 5 Colonel 6 General 7 Private 1 Example of relative amounts of authority
  59. 59. Corporal 2 Sargent 3 Lieutenant 4 Major 5 Colonel 6 General 7 Private 1 Notice how we are dealing with amounts of authority Example of relative amounts of authority
  60. 60. Corporal 2 Sargent 3 Lieutenant 4 Major 5 Colonel 6 General 7 Private 1 But, Example of relative amounts of authority
  61. 61. Corporal 2 Sargent 3 Lieutenant 4 Major 5 Colonel 6 General 7 Private 1 But, they may not be equally spaced. Example of relative amounts of authority
  62. 62. Corporal 2 Sargent 3 Lieutenant 4 Major 5 Colonel 6 General 7 Private 1 But, they may not be equally spaced. Example of relative amounts of authority
  63. 63. Corporal 2 Sargent 3 Lieutenant 4 Major 5 Colonel 6 General 7 Private 1 But, they may not be equally spaced. Example of relative amounts of authority
  64. 64. You can tell if you have an ordinal data set when the data is described as ranks.
  65. 65. You can tell if you have an ordinal data set when the data is described as ranks. Persons Pole Vault Placement Carly 3rd Celeste 5th Donald 1st Dunbar 4th Ernesta 2nd
  66. 66. Or in percentiles
  67. 67. Or in percentiles Persons ACT Percentile Rank Carly 55% Celeste 23% Donald 97% Dunbar 37% Ernesta 78%
  68. 68. If your data is ranked as shown in these examples, select
  69. 69. If your data is ranked as shown in these examples, select Scaled Ordinal Nominal Proportional
  70. 70. Finally, let’s see what data looks like when it is nominal proportional:
  71. 71. Nominal data is different from scaled or ordinal,
  72. 72. Nominal data is different from scaled or ordinal, because they do not deal with amounts
  73. 73. Nominal data is different from scaled or ordinal, because they do not deal with amounts nor equal intervals.
  74. 74. For example,
  75. 75. Nationality is a variable that does not have amounts nor equal intervals.
  76. 76. 1 = Canadian 2 = American
  77. 77. 1 = Canadian 2 = American Being Canadian is not numerically or quantitatively more than being American
  78. 78. 1 = Canadian 2 = American The numbers 1 and 2 do not represent amounts. They are just a way to distinguish the two groups numerically.
  79. 79. We could have just as easily used 1s for Americans and 2s for Canadians
  80. 80. We could have just as easily used 1s for Americans and 2s for Canadians 1 = Canadian 2 = American
  81. 81. We could have just as easily used 1s for Americans and 2s for Canadians 1 = American 2 = Canadian
  82. 82. Other examples:
  83. 83. Religious Affiliation
  84. 84. Religious Affiliation 1 - Buddhist 2 - Catholic 3 - Jew 4 - Mormon 5 - Muslim 6 - Protestant
  85. 85. Gender
  86. 86. Gender 1 - Male 2 - Female
  87. 87. Preference
  88. 88. Preference: 1. People who prefer chocolate ice-cream
  89. 89. Preference: 1. People who prefer chocolate ice-cream 2. People who dislike chocolate ice-cream
  90. 90. Pass/Fail
  91. 91. Pass/Fail 1. Those who passed the test
  92. 92. Pass/Fail 1. Those who passed the test 2. Those who failed the test
  93. 93. The word “Nom” in “nominal” means “name”.
  94. 94. The word “Nom” in nominal means “name”. Essentially we are using data to name, identify, distinguish, classify or categorize.
  95. 95. Other names for nominal data are categorical or frequency data.
  96. 96. Here is how the nominal data would look like in a data set:
  97. 97. Here is how the nominal data would look like in a data set: Persons Carly Celeste Donald Dunbar Ernesta
  98. 98. Here is how the nominal data would look like in a data set: Persons Gender Carly Celeste Donald Dunbar Ernesta
  99. 99. Here is how the nominal data would look like in a data set: Persons Gender Carly Celeste Donald Dunbar Ernesta 1 = Male 2 = Female
  100. 100. Here is how the nominal data would look like in a data set: Persons Gender Carly 2 Celeste 2 Donald 1 Dunbar 1 Ernesta 2 1 = Male 2 = Female
  101. 101. Persons Gender Preference Carly 2 Celeste 2 Donald 1 Dunbar 1 Ernesta 2
  102. 102. Persons Gender Preference Carly 2 Celeste 2 Donald 1 Dunbar 1 Ernesta 2 1 = Like ice-cream 2 = Don’t like ice-cream
  103. 103. Persons Gender Preference Carly 2 1 Celeste 2 1 Donald 1 1 Dunbar 1 2 Ernesta 2 2 1 = Like ice-cream 2 = Don’t like ice-cream
  104. 104. Persons Gender Preference Carly 2 1 Celeste 2 1 Donald 1 1 Dunbar 1 2 Ernesta 2 2 Religion
  105. 105. Persons Gender Preference Carly 2 1 Celeste 2 1 Donald 1 1 Dunbar 1 2 Ernesta 2 2 Religion 1 - Buddhist 2 - Catholic 3 - Jew 4 - Mormon 5 - Muslim 6 - Protestant
  106. 106. Persons Gender Preference Carly 2 1 Celeste 2 1 Donald 1 1 Dunbar 1 2 Ernesta 2 2 Religion 4 2 5 6 1 1 - Buddhist 2 - Catholic 3 - Jew 4 - Mormon 5 - Muslim 6 - Protestant
  107. 107. Now that we know what nominal data is,
  108. 108. What is nominal proportional data?
  109. 109. What is nominal proportional data? Scaled Ordinal Nominal Proportional
  110. 110. Nominal proportional data is simply the proportion of individuals who are in one category as opposed to another.
  111. 111. For example,
  112. 112. In the data set below:
  113. 113. In the data set below: Persons Gender Carly 2 Celeste 2 Donald 1 Dunbar 1 Ernesta 2
  114. 114. Persons Gender Carly 2 Celeste 2 Donald 1 Dunbar 1 Ernesta 2 3 out of 5 persons are female
  115. 115. Persons Gender Carly 2 Celeste 2 Donald 1 Dunbar 1 Ernesta 2 Or 60% are female
  116. 116. Persons Gender Carly 2 Celeste 2 Donald 1 Dunbar 1 Ernesta 2 That means 2 out of 5 are male
  117. 117. Persons Gender Carly 2 Celeste 2 Donald 1 Dunbar 1 Ernesta 2 Or 40% are male
  118. 118. In such cases you may not see a data set,
  119. 119. you may just see a question like this:
  120. 120. A claim is made that four out of five veterans (or 80%) are supportive of the current conflict. After you sample five veterans you find that three out of five (or 60%) are supportive. In terms of statistical significance does this result support or invalidate this claim?
  121. 121. If you were to put these results in a data set it would look like this:
  122. 122. Veterans A B C D E
  123. 123. Veterans Supportive A B C D E
  124. 124. Veterans Supportive A B C D E 1 = supportive 2 = not supportive
  125. 125. Veterans Supportive A 2 B 2 C 1 D 1 E 1 1 = supportive 2 = not supportive
  126. 126. Veterans Supportive A 2 B 2 C 1 D 1 E 1 1 = supportive 2 = not supportive If the question is stated in terms of percentages (e.g., 60% of veterans were supportive), then that percentage is nominal proportional data
  127. 127. If your data is nominal proportional as shown in these examples, select
  128. 128. If your data is nominal proportional as shown in these examples, select Scaled Ordinal Nominal Proportional
  129. 129. That concludes this explanation of scaled, ordinal and nominal proportional data.

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