Part 2 Dr. Barry Trunk Statistics Lecture for Bellevue — Transcript

Full transcript

1. 0:00come on
2. 0:03hello again class this is Dr trunk with
3. 0:05the second part of a lecture on
4. 0:08statistics that we are doing this week
5. 0:11you may remember that in the previous
6. 0:13video I talked about descriptive
7. 0:15statistics and inferential statistics
8. 0:17with the former being
9. 0:19summative and the latter being causative
10. 0:24we looked at calculations for the most
11. 0:27common forms of central tendency which
12. 0:29are the mean the median and the mode and
13. 0:31we also looked at how to interpret the
14. 0:35standard deviation and variance as well
15. 0:38as the range
16. 0:40what we're going to do today is to look
17. 0:43in a little bit more detail about some
18. 0:44of the
19. 0:45problems on the checkpoints that you're
20. 0:47going to be asked to solve in those
21. 0:49problems you're going to be given a set
22. 0:51of data kind of like this which is the
23. 0:53same data we had yesterday and you
24. 0:55remember we calculated the mean to be 7
25. 0:57and the standard deviation to be 2.31
26. 1:02. so when your homework assignments
27. 1:04you're going to have to do the same
28. 1:05thing you'll have to get a calculator a
29. 1:08recommended something similar to this
30. 1:10the ti-30 from Walmart for about ten
31. 1:13dollars and calculate the mean and the
32. 1:15standard deviation
33. 1:17as well as a few other summary
34. 1:19statistics and then we can start to get
35. 1:22into what we call z-scores now before I
36. 1:24talk about z-scores I need to say a
37. 1:26couple words about this kind of
38. 1:28distribution right here at the Top This
39. 1:31is called the normal distribution it's
40. 1:34not normal because it's the word normal
41. 1:36in everyday life it's just the name of
42. 1:39the function that generates this
43. 1:42particular curve some things to notice
44. 1:44about this is that it is a symmetric
45. 1:48curve so 50 of the scores are on this
46. 1:51side of this line which is right down
47. 1:53the middle and fifty percent of the
48. 1:55scores are on that line
49. 1:58this line separates the two halves and
50. 2:01it is the point that we call the mean
51. 2:04the median and the mode in other words
52. 2:06in a normal distribution the mean median
53. 2:08mode are all the same point
54. 2:12so at this distribution represented this
55. 2:15scores it doesn't but pretend it did if
56. 2:18we knew the mean was seven we would know
57. 2:20that the median is also 7 and the mode
58. 2:22is also seven
59. 2:24what we're going to do with Z scores is
60. 2:27to find the relative location of one of
61. 2:31these scores on this uh figure we'll see
62. 2:35how that works in just a moment
63. 2:37this is an example of a skewed
64. 2:39distribution notice it's not symmetric
65. 2:42like this one here most of the scores
66. 2:44are on the low side and fewer and fewer
67. 2:47as the scores get higher are showing up
68. 2:51in this picture the tail of the
69. 2:53distribution is pointed in the positive
70. 2:55direction so we call that a positively
71. 2:58skewed distribution if I had flipped it
72. 3:01around and the tail was pointing in this
73. 3:03direction it would be a negatively
74. 3:05skewed distribution
75. 3:08I've written the formulas for the
76. 3:11z-score the t-score and the IQ score
77. 3:14this day 9 score there is a table that
78. 3:17allows you to converge z-scores to stay
79. 3:20nine scores so we're not really going to
80. 3:22talk about stay nine scores anymore in
81. 3:25this video
82. 3:26however the most important is the
83. 3:28z-score and if you look at the formula
84. 3:31this little X just stands for one of
85. 3:33these values
86. 3:36so you take a value you subtract the
87. 3:38mean and you divide by the standard
88. 3:40deviation and then you get a z-score
89. 3:44now
90. 3:45one of the scores here we could get a
91. 3:48z-score for any one of these that we
92. 3:50wanted to
93. 3:52but we can also get z-scores for
94. 3:54something that doesn't appear on the set
95. 3:57of scores see we wanted to know the
96. 4:00z-score for five
97. 4:02well that's no problem we would take
98. 4:04five subtract 7 and divide by 2.31 and
99. 4:09you will get a z-score
100. 4:11a z of zero means that the score is
101. 4:15right on the mean and we can see that
102. 4:17because this score is seven and the mean
103. 4:20is 7 and 7 minus seven is zero and
104. 4:23anything with zero in the numerator is
105. 4:26zero so seven is going to be right here
106. 4:29notice that 8 9 and 10 are positive so
107. 4:32the z-score will be positive and these
108. 4:35other numbers like 3 and 6 are less than
109. 4:39the mean so the z-score will have a
110. 4:40negative sign associated with it in
111. 4:43other words scores higher than the mean
112. 4:45will be positive and scores lower than
113. 4:48the mean will be negative but what does
114. 4:50it actually mean
115. 4:52a z-score tells you how many standard
116. 4:54deviations above or below the mean a raw
117. 4:57score is
118. 4:58so if someone had a z-score of one they
119. 5:01are one standard deviation above the
120. 5:03mean for example if we take the mean of
121. 5:07seven and go up one standard deviation
122. 5:10we're at 9.31 we just add these two so
123. 5:15anyone who has a score of 9.31 would
124. 5:18have a z-score of one because they are
125. 5:21exactly one standard deviation above the
126. 5:23mean
127. 5:26the t-score is a converted z-score and
128. 5:30you can see that the calculated t-score
129. 5:32you first find the Z score multiply that
130. 5:36by 10 and add 50.
131. 5:38okay so let's say again that the um
132. 5:43score we're using for example is seven
133. 5:4610 times the z-score of seven you may
134. 5:49remember is zero because seven is equal
135. 5:52to the mean and seven minus seven is
136. 5:54zero ten times seven I'm sorry 10 times
137. 5:570 is 0 plus 50 is 50. the T score has a
138. 6:02mean of 50 and a standard deviation of
139. 6:0610. the z-score has a mean of 0 and a
140. 6:10standard deviation of 1.
141. 6:12to convert to IQ scores as you're being
142. 6:14asked in your homework your checkpoints
143. 6:16just again take the z-score
144. 6:20multiply by 15 and add
145. 6:24100
146. 6:26okay so here are a couple of examples
147. 6:29that I've worked out for you what is the
148. 6:31z-score for a score of eight
149. 6:33well what we would do is we would take
150. 6:36the score the raw score X subtract the
151. 6:39mean which is 7 and divide by the
152. 6:41standard deviation which is 2.31 and we
153. 6:44get 0.43 now what does that 0.43 mean it
154. 6:48means that this person first of all we
155. 6:50notice it's positive because 8 is bigger
156. 6:53than 7 and 7 is the mean that's why the
157. 6:56Z is positive
158. 6:57this person is .43 standard deviations
159. 7:00above the mean in other words if you
160. 7:03took 0.43 times the standard deviations
161. 7:06and added it to 7 you would get eight
162. 7:09they are 0.43 almost a half a standard
163. 7:12deviation bigger than the mean
164. 7:15what is a z-score of five okay it
165. 7:17doesn't matter that 5 isn't in there
166. 7:20we can still find the z-score and it
167. 7:22doesn't matter that it could be 5.5 or
168. 7:258.1 there's nothing special about
169. 7:28decimals
170. 7:30we take our formula which is a 5 minus 7
171. 7:34the score minus the mean and divide by
172. 7:372.31 now we get negative because 5 is
173. 7:40less than the mean of seven so this
174. 7:42person is negative 0.87 standard
175. 7:45deviations not quite a whole standard
176. 7:48deviation lower than the mean
177. 7:51to convert to T scores we simply use our
178. 7:54formula 10 times Z so for the score of 8
179. 7:58Z was 0.43 we have 50 and we get 54.3
180. 8:04these two things are identical to one
181. 8:06another if this person was 0.43 standard
182. 8:10deviations above the mean for Z they're
183. 8:12going to be 0.43 standard deviations
184. 8:15above the mean for
185. 8:18the t score
186. 8:19and the same thing the T of the z-score
187. 8:22for five was negative 0.87 so we
188. 8:27multiply that by 10 we add 50 and now we
189. 8:30get 41.3 remember the mean of the T
190. 8:34score is 50 this person was below the
191. 8:36mean for Z so they're going to be below
192. 8:38the mean for t as well
193. 8:41and finally for IQ scores we just do the
194. 8:45same thing we just plug our z-score in
195. 8:47here and you can do the math yourself
196. 8:49you can see that the mean is a hundred
197. 8:51and this person is above the mean how
198. 8:54far above the mean 0.43 standard
199. 8:57deviations where standard deviation is
200. 9:0015.
201. 9:01and for the same thing here notice that
202. 9:04this is below 100 because the z-score is
203. 9:07below 100.
204. 9:09if you have any questions on that as
205. 9:11you're doing the problems or after
206. 9:12you've done the checkpoint just give me
207. 9:14a call or write me an email and we can
208. 9:16go over it together
209. 9:18the last thing I want to quickly tell
210. 9:19you about are these statistics here
211. 9:23actually statistical tests
212. 9:27we are not going to actually be running
213. 9:29these statistical tests that would be
214. 9:31for people going on to write a master's
215. 9:33thesis or a doctoral dissertation or
216. 9:35publish a research paper but basically
217. 9:37if we read a journal article and they
218. 9:41mention Anova what does it mean you know
219. 9:44what did they do so it's kind of like
220. 9:46right now I don't understand how my car
221. 9:49engine works but I understand how to
222. 9:52work my car right we don't need to know
223. 9:55the mathematics or the details of how to
224. 9:58do this test just like I don't need to
225. 10:00understand how my engine works in order
226. 10:02to drive my car I just need to know how
227. 10:05to drive my car we just need to know
228. 10:07basically what these do so what do they
229. 10:09do
230. 10:10the t-test looks at significant
231. 10:13differences between two groups so let's
232. 10:16say that we had scores for women on a
233. 10:18quiz and we had scores from Men on a
234. 10:20quiz the women would have an average we
235. 10:23would just add up the women's scores and
236. 10:25divide by how many women took the quiz
237. 10:27and the men's scores would have an
238. 10:29average we would just add up the men's
239. 10:31scores and divide how many scores the
240. 10:33men did
241. 10:34well those two numbers will be different
242. 10:36but are they significantly different by
243. 10:39significantly different I mean probably
244. 10:41enough to make a difference probably not
245. 10:44by chance
246. 10:45if I've got five dollars in my pocket
247. 10:47and you've got five dollars and one cent
248. 10:49it's true you have more money but do you
249. 10:52have significantly more money what if I
250. 10:55have five dollars and you have six
251. 10:56dollars or I have five dollars you have
252. 10:58seven dollars five dollars you have
253. 10:59eight dollars at what point does it
254. 11:02become so different that it's unlikely
255. 11:05that they really are just varying due to
256. 11:07chance
257. 11:08you can remember the T and notice it's a
258. 11:11lowercase T this uppercase t is a t
259. 11:14score this lowercase T is a t-test and
260. 11:17it's easy to get them confused the
261. 11:20t-test looks at two groups oh I have a
262. 11:23visitor you guys this is Molina I don't
263. 11:26know if you can see her or not but she
264. 11:28just kind of jumped and jumped up here
265. 11:30I'll let her say hi to you guys she's
266. 11:33really into statistics as you can see so
267. 11:35this is Molina and you might be
268. 11:38interested to know that the word Molina
269. 11:39means raspberry in Russian yay
270. 11:45okay go away I mean that was Molina
271. 11:50so back to the important things
272. 11:54we have by the way five cats which is
273. 11:56statistically significant
274. 12:00a-n-o-v-a stands for Anova Anova stands
275. 12:04for analysis of variance
276. 12:07analysis of variance it's always in
277. 12:10capital letters
278. 12:13the analysis of variance is like the
279. 12:16t-test
280. 12:17it's like the t-test but involves more
281. 12:21than two groups
282. 12:24sorry my wife is filming this and she's
283. 12:27laughing because I said significantly
284. 12:29with cats so
285. 12:31a little humor that happens when we're
286. 12:34live can't help it so analysis of
287. 12:37variance we'll look at maybe three
288. 12:38groups or four groups or five groups
289. 12:40[Music]
290. 12:47cut
291. 12:49all right my wife is going away to
292. 12:53hysterically laugh sorry about that you
293. 12:55guys but this is a real household and
294. 12:57things happen so the analysis of
295. 12:59variants might look at freshman
296. 13:02sophomores Juniors and seniors that's
297. 13:04four groups notice it's still one
298. 13:05variable but it is four groups
299. 13:09so if we looked at the grade point
300. 13:12averages for the Freshman Class the
301. 13:13sophomore class the junior class and the
302. 13:16senior class
303. 13:18do those four GPA significantly differ
304. 13:21from one another we can't do the t-test
305. 13:23because T only looks at two groups since
306. 13:26this one has four groups we would do an
307. 13:29analysis of variance correlation looks
308. 13:32at a linear relationship between
309. 13:33variables correlation as you will be
310. 13:37reading and maybe even know doesn't mean
311. 13:39that something causes something else it
312. 13:41just means they go together correlations
313. 13:43can range between negative one and
314. 13:46positive one and as the correlation
315. 13:49moves away from zero the stronger it is
316. 13:53regression is related to correlation and
317. 13:56that regression makes a prediction for
318. 13:58instance
319. 14:00if we had a list of people's grade point
320. 14:03averages in high school could we predict
321. 14:06from that their grade point average in
322. 14:08college
323. 14:09grade point average
324. 14:12is correlated with high school grade
325. 14:14point average so if there is a
326. 14:16significant correlation we could
327. 14:18probably make reasonable predictions
328. 14:20about their High School are from their
329. 14:23high school GPA to their college GPA
330. 14:28um these top four are called parametric
331. 14:30statistics or parametric statistical
332. 14:33tests and the reason is that they
333. 14:35involve real numbers like GPA gas
334. 14:39mileage income
335. 14:41this last one that I've written down
336. 14:43here is called chi-square and chi-square
337. 14:47is a non-parametric test what I mean by
338. 14:50that is that chi-square
339. 14:53looks at frequencies for example here at
340. 14:57Bellevue taking my class we have men and
341. 14:59women and let's just say that we have
342. 15:01Republicans and Democrats is there a
343. 15:04relationship between gender which is a
344. 15:06nominal variable and political party
345. 15:09which is a nominal variable since we
346. 15:11have two nominal variables where we're
347. 15:14just labeling them the one and two but
348. 15:16the one and two don't really mean
349. 15:17anything we could label them at negative
350. 15:20665 any two numbers that are different
351. 15:23would work
352. 15:25is there a relationship between the
353. 15:27gender you are and the political
354. 15:29affiliation you have that's the kind of
355. 15:32question that chi-square would ask
356. 15:34so thank you for listening to this video
357. 15:37again I hope that the cats weren't too
358. 15:40distracting for you so I'm going to uh
359. 15:43wish you well say goodbye for now and
360. 15:46again if you have any questions just
361. 15:47please let me know thank you