Nonparametric Test

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by Leon Cygman266 views·Updated Sep 28, 2020
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  1. Hi. So today we begin our discussion of non Parametric
  2. tests, all throughout stats one and the first part of
  3. stats to we assume that our population was normal, what
  4. non Parametric tests are, or hypothesis tests that are able
  5. to work with non normal data.
  6. So Parametric tests the ones that you've been doing.
  7. That's what they've been called Parametric require a certain distribution
  8. of the data, and in other words, they have to
  9. be normal.
  10. Uh, non Parametric tests do not have to be normal.
  11. They can come from populations that are different distributions than
  12. normal. So this is more real life stuff.
  13. A little bit of misleading terminology here.
  14. The term, uh, non parametric is misleading because it sounds
  15. like it's not based on the parameter when in fact
  16. it is based on some parameters, usually the medium.
  17. Um, so it really should say non normal Parametric.
  18. But that's the terminology we use in this science or
  19. will keep it non parametric.
  20. So I wanna give you an overview of some of
  21. the things we'll be doing in this class.
  22. As I said, we'll be doing four tests.
  23. There are more than four tests and each of the
  24. four tests that were doing correspond to, um, correspond to
  25. test that we've already done in, uh, in in Parametric
  26. stuff. So, for example, we did the independent t tests,
  27. and that's that will do the man with me for
  28. that one.
  29. We did the paired test paired T test, and that
  30. one will call the Wilcox and signed rank test.
  31. We did a one way in Nova and that's called
  32. the Wallace text.
  33. And we did, um, repeated in Nova.
  34. And that's the Friedman test.
  35. So we'll do four tests for Parametric tests that correspond
  36. to the four tests that we've already done in this
  37. course. So here are some of the advantages of non
  38. Parametric tests.
  39. Um, first of all there.
  40. Ah, lot less rigid and therefore they could be applied
  41. to mawr situations.
  42. Um, for example, Parametric tests could be categorical data, A
  43. ZX well, as numeric data.
  44. However, the disadvantage of of these kinds of tests is
  45. that they're not as effective as Parametric tests.
  46. So generally, what we like to see is larger population
  47. sizes, uh, in order to reject another hypothesis Now, in
  48. the four tests that we're going to do, we're gonna
  49. do something called Ranking.
  50. It's ah, manual way of ordering data from largest to
  51. smallest from worst to best and so on and so
  52. forth. And and generally speaking, ranking is is done fairly
  53. easily in terms off.
  54. Um, you know, the first number of the lowest number
  55. is ranked one, and the second number is ranked two
  56. and so on and so forth.
  57. Um, so let me show you some some ranking examples.
  58. Um, but before I do that, I want to explain
  59. to you how toe handle ties when there is a
  60. tie involved.
  61. In other words, two numbers in the sample have the
  62. same value.
  63. Then what you do is you average their ranks and
  64. assign the average to each of those numbers.
  65. Let me show you an example of what I mean
  66. by that.
  67. So here's an example of Ah, a sample that already
  68. has been sorted from 4 to 12.
  69. So the first number gets Ah, one makes sense.
  70. Now there are three fives coming up.
  71. So generally we would use the the next three numbers.
  72. You know, 234 and five.
  73. However, because they're all the same, they can't have different
  74. ranks. So What we do is we sum up two
  75. and three and four, divided by three and end up
  76. with three.
  77. So the number five is ranked three now, the next
  78. number in our sequence that we were left counting is
  79. five. So 10 becomes 5.
  80. 11 becomes six, Um 12 should be seven and eight.
  81. But in reality, you can't have two different ranks for
  82. the same number.
  83. So what again we'll do.
  84. We'll take 78 divided by to get 7.5.
  85. So the 2 12 or rank 7.5.
  86. So, as you can see, each number has a separate
  87. ranking and numbers that are the same get the same
  88. ranking with this unusual bit of, uh, finding out the
  89. averages, um, to do it with with two samples, it's
  90. a little bit more involved.
  91. What I do these, you see, the first column is
  92. not sorted.
  93. Neither is a second column.
  94. What I do is is sort them and, uh, I
  95. kind of line them up with their equal values across
  96. each other.
  97. In this way, I can clearly see what numbers are
  98. repeated. So the 12 and three get 12 and three.
  99. The four would be, you know, four and five, divided
  100. by two would be 4.5 Onda.
  101. Next number would be six.
  102. The sixes then would be six and seven, which was
  103. 15. Divided by two would be 7.5, and then next
  104. number would be nine and 10.
  105. So that's the way I would rank these kinds of
  106. numbers now.
  107. Luckily for us, uh, there is a function in spreadsheets
  108. called rank Average, which has three parameters.
  109. Has a base number a range and assorted parameter at
  110. the end.
  111. Do the rank average in class, and it's really important
  112. that you understand how it works and how to use
  113. it, because all these four different non Parametric tests have
  114. ranking, and that's kind of the most awkward part of
  115. working with them.
  116. But if you can use the rank average function effectively,
  117. the problems become less rigorous and easier to understand and
  118. easier to do.
  119. So that's the introduction toe non Parametric tests.
  120. There are four of them, each correspondent to a test
  121. we've already done in this class on the Parametric side,
  122. and I'll show you how to use the rank average
  123. and class in order to, uh, do The ranking for
  124. these various tests is okay, That's all for now.
  125. I'll see you in class by