Dr. Trunk Stat Lecture 1 for Bellevue University — Transcript

Full transcript

1. 0:02hello class beginning soon we're going
2. 0:05to be talking about some descriptive and
3. 0:07inferential statistics involving some
4. 0:09simple calculations first thing I want
5. 0:12you to recognize is that this is not
6. 0:14going to be difficult math we're going
7. 0:16to be adding dividing
8. 0:18multiplying subtracting squaring numbers
9. 0:21and taking the square root so just a
10. 0:24simple calculator is really all you need
11. 0:27good one that you might want to get you
12. 0:29can get for about ten dollars as the
13. 0:32ti-30 from Walmart not expensive and
14. 0:36does a lot of really good uh
15. 0:38calculations for this class
16. 0:41so I wanted to do two lectures the first
17. 0:44one we'll cover with the information on
18. 0:46this board and then I will do a second
19. 0:48one to talk about the different kinds of
20. 0:50z-scores and T scores and how to
21. 0:53calculate those things
22. 0:55so to begin with we have to understand
23. 0:57the difference between descriptive and
24. 0:59inferential statistics
25. 1:01descriptive statistics simply summarize
26. 1:04data like if we had a classroom with men
27. 1:06and women in it how many men are there
28. 1:09how many women are there what percent of
29. 1:10the total is female
30. 1:12things of that nature we're not drawing
31. 1:14any conclusions we're just telling what
32. 1:17we have
33. 1:18uh inferential statistics on the other
34. 1:21hand is where we actually use the data
35. 1:23to make decisions so for instance if
36. 1:26there's men and women in the room uh are
37. 1:28there significantly different number of
38. 1:30Democrats than Republicans in other
39. 1:33words this political party depend upon
40. 1:35gender we're using information to go
41. 1:39beyond the description of the data to
42. 1:42what the data seems to be telling us
43. 1:45now descriptive statistics involve these
44. 1:48six main calculations
45. 1:52on the top here I've written mean
46. 1:54meeting and mode that's what we call
47. 1:56measures of central tendency or average
48. 1:59all three of these are measures of
49. 2:01average when I've written below is the
50. 2:04range the variance and the standard
51. 2:05deviation and these tell us the amount
52. 2:08of variability are all the scores kind
53. 2:11of really bunched up if so then the
54. 2:13range and the variance would be small or
55. 2:15the score is really different from each
56. 2:17other the range and all those things
57. 2:19would be much larger so the larger these
58. 2:23numbers the more variability there is in
59. 2:25the data the smaller those numbers the
60. 2:28less variability there is
61. 2:30for inferential statistics which I will
62. 2:33do in a different video
63. 2:35I will be talking about Z scores and T
64. 2:38scores as well as the t-test the
65. 2:41analysis of variance and correlation and
66. 2:44regression
67. 2:45so I've written a simple example here I
68. 2:48hope that you can see it from the board
69. 2:52but I've got seven numbers and you can
70. 2:55see here I've written the capital letter
71. 2:57N in statistics a capital letter n
72. 3:00stands for the number of scores
73. 3:026 10 8 9 6 3 and 7. now these scores can
74. 3:08be fractions these scores can be
75. 3:10negative numbers these scores can
76. 3:12include zero I just used some simple
77. 3:15scores so we can do some hand
78. 3:16calculations with them but there's
79. 3:18nothing you know special about these
80. 3:21numbers you could look at it as you've
81. 3:23got a small class of seven people who
82. 3:25have taken a ten point quiz and this is
83. 3:28how they did
84. 3:29so we want to not make inferences yet
85. 3:32but we want to describe what the data
86. 3:34looks like
87. 3:35so to do that we can calculate the mean
88. 3:39the mean is equal to this little thing
89. 3:42that looks like an e means add up it's a
90. 3:45capital letter Sigma so we're going to
91. 3:47sum each individual's score and then
92. 3:49we're going to divide by the number of
93. 3:51scores and if you add these scores up
94. 3:53comes to 49 and 49 divided by 7 is 7. so
95. 3:58the mean of these distribution is 7.
96. 4:01the mode of the distribution is 6
97. 4:05because the score of 6 occurs more often
98. 4:07than any other score
99. 4:10uh I didn't write the median down here
100. 4:12we don't usually calculate a median but
101. 4:15to do it
102. 4:16and this is something that you can do
103. 4:18you know on your own see if you can do
104. 4:20it order the scores from lowest to
105. 4:22highest and find the middle score the
106. 4:25median is equal to the score that puts
107. 4:2850 percent of the scores on one side and
108. 4:3050 of the scores on the other side it's
109. 4:33just like the median on the interstate
110. 4:34half the traffic's going north and half
111. 4:37the traffic's going south and the median
112. 4:39separates the two halves
113. 4:43a little bit more complicated are the
114. 4:45measures of
115. 4:47um dispersion or variability
116. 4:50but the first one is relatively simple
117. 4:52the range is just telling you to take
118. 4:56the highest score and subtract the
119. 4:57lowest score so if we look at our data
120. 5:0010 is the highest score and three is the
121. 5:02lowest score and it just so happens to
122. 5:04range is seven now that's just a
123. 5:06coincidence I just made these numbers up
124. 5:08the range you know is not going to equal
125. 5:10the number of scores or anything like
126. 5:12that it just worked out that way
127. 5:16but the most challenging will be these
128. 5:18last two
129. 5:20the variance in the standard deviation
130. 5:24one thing that you do need to know is
131. 5:26that the standard deviation is equal to
132. 5:28the square root of the variance in other
133. 5:31words if you find the variance which is
134. 5:33just going to be a number and then take
135. 5:35the square root of that then you've got
136. 5:37the standard deviation
137. 5:39okay so let me fix this just a little
138. 5:41bit with some of this as
139. 5:44moved
140. 5:47is the letter s
141. 5:48your standard deviation
142. 5:51so the formula that's given in the
143. 5:54classroom
144. 5:55is looks a little bit complicated but it
145. 5:58really isn't
146. 6:00what it's saying is to take
147. 6:03the
148. 6:05sum of seven separate quantities we're
149. 6:09going to take the first score subtract
150. 6:11the mean and square it then add to that
151. 6:14the second score subtract the mean and
152. 6:15square it then add to that the third
153. 6:17score subtract the mean and square it so
154. 6:20you can see that the first score is six
155. 6:23so six minus 7 because the mean is 7.
156. 6:27uh and square it okay and that'll just
157. 6:30be one here's 10 minus three of seven
158. 6:33and that's going to be 3 and 3 squared
159. 6:36is 9.
160. 6:37and then 8 minus seven nine minus seven
161. 6:40all of these numbers squared
162. 6:44add up and divide by this says n minus
163. 6:47one so one less than the number of
164. 6:49scores
165. 6:50so if you square these numbers and then
166. 6:52add them you'll get 32 and if you divide
167. 6:5532 by 6 you'll get 5.3 so the variance
168. 6:59of this distribution is 5.3 but a more
169. 7:04useful statistic for us is the standard
170. 7:07deviation and as I said a moment ago all
171. 7:10you need to do is to find the variance
172. 7:12and take the square root of it and we
173. 7:15get 2.31 as our standard deviation
174. 7:18notice that the smallest the standard
175. 7:20deviation can be a zero because if the
176. 7:23standard deviation is zero all the
177. 7:25numbers are identical
178. 7:28there is no upper limit the standard
179. 7:31deviation could be zero or anything
180. 7:32positive notice also it can't be a
181. 7:35negative number since we're squaring
182. 7:38everything anything squared is always a
183. 7:40positive number so even if we put minus
184. 7:42signs in front of all of these the
185. 7:45variance would be the same as it is here
186. 7:47and so with the standard deviation
187. 7:50so I hope that was helpful to you and I
188. 7:53will come back in the second video and
189. 7:55we will continue with this example
190. 7:57looking at z-scores and T scores and
191. 8:00then some information about the four
192. 8:02major kinds of uh basic inferential
193. 8:05statistics thank you