YouTube transcript (7l6K0V_x_hw) — Transcript

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1. 0:00[Music]
2. 0:13okay let's look at our water bottle
3. 0:15example and I just walked through this
4. 0:17um before but we'll walk through it
5. 0:18again very quickly so remember a bottle
6. 0:20water manufacturer on the product label
7. 0:22states that each bottle contains 355 M
8. 0:24of water so you work for a government
9. 0:26agency that protects consumers by
10. 0:28testing product volume volumes so you
11. 0:31measure the volume that's actually
12. 0:32stated on the label to make sure it's
13. 0:33actually is true the case so a sample of
14. 0:3650 bottles is tested is there anything
15. 0:38we can assume to be true well yes we
16. 0:42assume that the 355 M on the bottle is
17. 0:46true we assume that to be the case
18. 0:48that's our assumption that's our given
19. 0:50now which hypothesis pair seems to be
20. 0:55appropriate well I would say that the
21. 0:57first one does so our null is an
22. 1:00assumption and our assumption is that it
23. 1:03equals an average of 355 ml and
24. 1:08alternative would be the opposite of
25. 1:13that so this is one we chose we set it
26. 1:16up like this so our null is that the
27. 1:19volume is
28. 1:20355 milliliters therefore the
29. 1:23alternative has to be that it does not
30. 1:27equal 355 M it could be more more than
31. 1:30that or could be less than
32. 1:32that so if the data indicates the
33. 1:35bottles are being filled properly then
34. 1:38we fail to reject the null hypothesis we
35. 1:42fail to reject our
36. 1:45assumption so if it comes back that it's
37. 1:48actually
38. 1:49355 we have to sort of take our
39. 1:52assumption as being the case so we
40. 1:55cannot reject our null hypothesis we're
41. 1:58not saying we have proven the null just
42. 2:02that our assumption has held up so again
43. 2:06think about it as an assumption that we
44. 2:09either reject or fail to reject if the
45. 2:13bottles are being filled properly then
46. 2:15we would fail to reject that null
47. 2:21hypothesis now if the data indicates the
48. 2:23bottles are not being filled properly
49. 2:26then we would reject the null we would
50. 2:30reject our assumption so we kind of like
51. 2:33put a big X through that n
52. 2:36hypothesis so what we're saying is that
53. 2:38our Assumption of 355 milliters is not
54. 2:41held up under analysis we have
55. 2:45statistical support for the validity of
56. 2:48the alternative hypothesis so if we take
57. 2:51our sample of 50 bottles and it comes
58. 2:52back an average of
59. 2:55340
60. 2:58millit well probably we would say you
61. 3:01know that's not that's not 355 it's not
62. 3:03even close enough to 355 to account for
63. 3:06natural variation so unfortunately we
64. 3:10would have to reject our null that says
65. 3:12it does equal 355 and then we would
66. 3:15proceed down to our alternative that
67. 3:17says it's not equal to
68. 3:20355 and that's how the null and
69. 3:23alternative
70. 3:26work so again it is all in the wording
71. 3:29and I alluded to this alluded to this
72. 3:32earlier these are some words I avoid I
73. 3:36avoid the word truth I avoid the word
74. 3:40prove I avoid the word certain like a
75. 3:44certain conclusion when it comes to
76. 3:47Stats I do not like those words because
77. 3:50as I'll say here in a minute stats is
78. 3:52never certain stats never proves
79. 3:55anything stats never says this is true
80. 3:59it's all about
81. 4:01probabilities so instead I prefer these
82. 4:04words that the data supports something
83. 4:07the data leads us to infer something the
84. 4:11data seems to indicate something now
85. 4:15some people might think I'm splitting
86. 4:16hairs here but I really do think the
87. 4:18words on the right are more appropriate
88. 4:20for stats because statistics is never
89. 4:24100% certain but what it does do a good
90. 4:28job of is that it stay states its
91. 4:31limitations
92. 4:32explicitly so we're always talking about
93. 4:35probabilities of this being something or
94. 4:38that being something or what have you so
95. 4:40I avoid the words on the left and
96. 4:41instead try to use the words on the
97. 4:44right I don't always succeed that's what
98. 4:47I try to do to always indicate that
99. 4:50there is no certainty there is no
100. 4:52absolute truth there is no absolute
101. 4:54proof when we're doing statistics
102. 5:00okay so example two down on the farm so
103. 5:03according to the United States
104. 5:05Department of Agriculture the US da in
105. 5:092006 the average Farm size in the state
106. 5:12of Texas was 2.3 square
107. 5:16kilometers now since the decades long
108. 5:19trend has been for Farm sizes to
109. 5:22increase due to large aggro businesses
110. 5:25buying up land and setting up bigger
111. 5:27Farms a business analyst wishes to test
112. 5:31if the current 2013 Farm size is larger
113. 5:35than it was in
114. 5:382006 so let's establish a null and
115. 5:41alternative
116. 5:43hypothesis now the first question we're
117. 5:45going to ask ourselves what is our
118. 5:49assumption well in this case we assume
119. 5:52that there has been no change in farm
120. 5:55size since 2006 this is our null
121. 5:59hypothesis now you may be thinking right
122. 6:02now well it says in the problem that the
123. 6:05decades long trend has been for Farm
124. 6:07sizes to
125. 6:08increase well so what the only
126. 6:11information we have the only given
127. 6:14information that we have is that the
128. 6:17average Farm size in 20 2006 was 2.3
129. 6:21Square km so that's our assumption
130. 6:24that's our known that is our given so
131. 6:28again that will be our null
132. 6:32hypothesis so we assume that there's
133. 6:35been no change in farm side since 2006
134. 6:38that's our null are we testing any
135. 6:41preliminary claim or any
136. 6:43conjecture well yes based on our problem
137. 6:47we wish to see if the farm size has
138. 6:50increased since
139. 6:532006 so which hypothesis format should
140. 6:56we choose let's look at the first one
141. 7:00will our null be an equality and our
142. 7:02alternative a
143. 7:04non-equality well no I don't think
144. 7:06that's really appropriate for this one
145. 7:07because we're talking about
146. 7:09increasing uh how about the second one
147. 7:12we wish to see if the farm size has
148. 7:14increased since
149. 7:162006 well I think this one is a good
150. 7:19choice so I would pick this one well why
151. 7:21is that so remember in this case our
152. 7:24preliminary claim our conjecture which
153. 7:26is the same thing as saying our
154. 7:28alternative hypothesis is is that farm
155. 7:31size has increased since
156. 7:342006 therefore our null would be that it
157. 7:38has remained the same or in in some case
158. 7:40maybe even decreased so our null is that
159. 7:44the farm size has remained the same or
160. 7:46decreased and the alternative the
161. 7:48conjecture the preliminary claim is that
162. 7:51it has increased so that's why
163. 7:53alternative is the greater than
164. 7:57sign so how can we set this up so
165. 8:00remember that we wish to see if the farm
166. 8:02size has increased since 2006 so you
167. 8:05look down here at our alternative
168. 8:07hypothesis that is an orange as well so
169. 8:10the increased is an orange and the
170. 8:12alternative is an orange and again our
171. 8:14null is that the form size has remained
172. 8:17the same or possibly even
173. 8:19decreased and the reason is that's the
174. 8:21opposite of increased so we have to
175. 8:24account for all possibilities if our
176. 8:27alternative says increased then our null
177. 8:30has to be stay the same or
178. 8:32decreased so we can write it out like
179. 8:35this so our null hypothesis is that farm
180. 8:38size is less than or equal to 2.3 Square
181. 8:42km because that's what we're given in
182. 8:44the problem that's our assumption our
183. 8:47alternative is that farm size has
184. 8:50increased since
185. 8:532006 so we could go out and collect data
186. 8:56for many farms in the state of Texas
187. 8:59then we could run those statistics we
188. 9:01could do that mean now it's going to be
189. 9:04one of these two things either the farm
190. 9:06size is remain the same or even
191. 9:08decreased or Farm size has increased and
192. 9:12depending on what we get from our
193. 9:14analysis we will know whether or not to
194. 9:16reject or fail to reject our null
195. 9:21hypothesis so if the data indicates that
196. 9:23farm size has increased then we'll have
197. 9:26to reject the null we're going to reject
198. 9:30our top assumption there so our
199. 9:32assumption has not held up under
200. 9:35analysis we have statistical support for
201. 9:37the validity of the alternative
202. 9:44hypothesis okay then our final example
203. 9:46Manchester United so during the 2010
204. 9:502011 English Premier League season
205. 9:54Manchester United home matches had an
206. 9:56average attendance of 74,000
207. 10:01961 now a club marketing analyst would
208. 10:04like to see if attendance decreased
209. 10:08during the most recent season so let's
210. 10:11establish a null and alternative
211. 10:13hypothesis for this analysis so what is
212. 10:18our assumption given to us in this
213. 10:20problem we can only assume that the
214. 10:23attendance remained the same or possibly
215. 10:27even increased cuz remember we're
216. 10:29looking at the bottom here he's
217. 10:31concerned or she is concerned if the
218. 10:33attendance decreased but for now we can
219. 10:35only assume the attendance remained the
220. 10:39same are we testing some preliminary
221. 10:42claim well yes the marketing analyst
222. 10:45wishes to see if attendance has
223. 10:47decreased since 2010 2011 so which
224. 10:52hypothesis format should we
225. 10:54choose well I would pick this one and
226. 10:57why is that well keep in mind that our
227. 11:00assumption has inequality so they're in
228. 11:02the top and our alternative hypothesis
229. 11:05the conjecture we want to test is if
230. 11:08it's decreased so if you look down here
231. 11:10in the alternative we have the less than
232. 11:15sign so we can set up like this remember
233. 11:18we're saying if it's decreased that's
234. 11:20our research sort of hypothesis so that
235. 11:22would be our alternative and our
236. 11:24assumption is that it has remained the
237. 11:26same or even possibly increased now in
238. 11:28this case I'm not sure it could increase
239. 11:30any further because I'm sure those are
240. 11:31all sellouts but I guess it is possible
241. 11:35but we're concerned about decrease so
242. 11:37that's our alternative so we would set
243. 11:39up a hypothesis like this so our null is
244. 11:43that the attendance has increased or
245. 11:45remain the same and alternative is the
246. 11:48opposite of that that it's decreased and
247. 11:51again that is the claim or the
248. 11:54preliminary conjecture that this analyst
249. 11:57wants to test
250. 12:00so again if the data indicates that
251. 12:02attendance has decreased then we would
252. 12:04reject our null we would reject our
253. 12:08assumption that attendance has stayed
254. 12:10the same or even increased we would
255. 12:12therefore have to go on to the
256. 12:14alternative so we would say our
257. 12:16assumption has not held up under
258. 12:18analysis we have statistical support for
259. 12:21the validity of the alternative
260. 12:23hypothesis which is that attendance has
261. 12:26in fact decreased since
262. 12:302010
263. 12:342011 okay just a couple reminders and
264. 12:36then we are done so remember when trying
265. 12:39to formulate a statistical hypothesis I
266. 12:40want you to ask yourself the following
267. 12:42question am I testing assumption or the
268. 12:44status quo that I already know or it
269. 12:47exists or am I testing a claim an
270. 12:50assertion or some conjecture beyond what
271. 12:53I already know or can
272. 12:55know and they always follow this pattern
273. 12:59the equality sign is always in the null
274. 13:02hypothesis and then the opposite of that
275. 13:04is always in the alternative hypothesis
276. 13:08so always think about assumptions always
277. 13:10think which will always be in the null
278. 13:12think about unknown conjectures or
279. 13:15unknown claims or assertions or research
280. 13:18hypotheses those are going to be in the
281. 13:20alternative hypothesis remember these
282. 13:23are always in opposition to each other
283. 13:25they can not both be true
284. 13:30so a few reminders all statistical
285. 13:32conclusions are made in reference to the
286. 13:34null hypothesis as researchers are
287. 13:36inless we either reject the null
288. 13:38hypothesis or fail to reject the null
289. 13:42hypothesis we do not accept the null so
290. 13:45this due to the fact that non hypothesis
291. 13:47is assumed to be true so we either
292. 13:49reject or fail to reject our assumption
293. 13:53if we reject the null hypothesis then we
294. 13:56conclude the data supports the alter
295. 13:59alternative hypothesis so if we do the
296. 14:01data for Manchester United and we come
297. 14:04up with a average attendance of
298. 14:0968,000 then we would probably reject the
299. 14:12null that says it's
300. 14:1574,700 or more we would reject that move
301. 14:19on to our alternative which says it's
302. 14:21less than that if we had an average
303. 14:24attendance of say
304. 14:2668,000 however if we fail to reject the
305. 14:29null hypothesis it does not mean we have
306. 14:32proven the null is true again important
307. 14:36distinction failure to reject the null
308. 14:39does not mean we have proven the null is
309. 14:41true we failed to reject our assumption
310. 14:45and why is that because remember from
311. 14:46the outset we assumed it was true from
312. 14:49the beginning failure to reject the null
313. 14:51does not equate to proof about its truth
314. 14:55we're only talking about the null as an
315. 14:57assumption to either be held up or
316. 15:00knocked
317. 15:04down okay so that wraps up our video on
318. 15:07the null and alternative hypothesis so
319. 15:11again in the future I plan on doing some
320. 15:12more videos about the null and
321. 15:13alternative and we're going to talk
322. 15:15about type one and type two errors more
323. 15:18specifically in our next video so the
324. 15:20null and alternative will come up in
325. 15:22future videos this was again just a
326. 15:24basic introduction to how they are
327. 15:26formulated how we interpret them how we
328. 15:28talk about them and write about them and
329. 15:30how we formulate them in mathematical
330. 15:33equalities or greater than less than and
331. 15:36things of that nature and again I wanted
332. 15:38to use some real word examples so you
333. 15:39can see how you pull information out of
334. 15:42a problem to set them up now I'm not
335. 15:45sure if your stats Professor or teacher
336. 15:48will be as picky as I am about the
337. 15:50language as far as when you talk about
338. 15:53proving something or something is true
339. 15:56again I prefer words like support or
340. 16:00indicate um which a little bit softer
341. 16:03words than deterministic words like
342. 16:05truth and certainty and proof so again
343. 16:08just keep in mind that we live our lives
344. 16:11in one great big null hypothesis every
345. 16:14second of every day we make no
346. 16:17hypotheses about the world around us and
347. 16:19about ourselves and we assume that those
348. 16:23are indeed true so I gave several
349. 16:26examples at the front I won't go into
350. 16:27them but remember we always assume the
351. 16:29world Works a certain way so we proceed
352. 16:33through life with those assumptions
353. 16:34those are our null hypothesis and of
354. 16:37course when one of them is broken then
355. 16:39we have to proceed to the alternative
356. 16:42that something else might be the case so
357. 16:44if I drop a rock in my backyard and it
358. 16:46floats in the air and goes up to space
359. 16:49then I will know that my null Assumption
360. 16:50of gravity has a problem with it now I
361. 16:54don't think that's going to happen but
362. 16:55that's sort of an assumption we make
363. 16:57right okay so that wraps up this video
364. 17:00so just for a few reminders if you're
365. 17:02watching this video because you're
366. 17:03struggling in a class stay positive and
367. 17:05keep your head up you're smart and
368. 17:07talented I know that many of the people
369. 17:09around you know that so you should think
370. 17:10that as well if you like the video
371. 17:13please give it a thumbs up share it with
372. 17:15classmates or colleagues or put it on a
373. 17:17playlist that does encourage me to keep
374. 17:19making them please feel free to follow
375. 17:21me here on YouTube on Twitter or on
376. 17:24LinkedIn that way when I upload a video
377. 17:27you know about it and I always like
378. 17:29connecting with people who watch my
379. 17:30videos online and finally just keep in
380. 17:33mind that the fact that you're on here
381. 17:35trying to learn trying to improve
382. 17:37yourself as a student or as a business
383. 17:39person that's what really matters I
384. 17:41firmly believe that if you have the
385. 17:43right learning process in place the
386. 17:46results will take care of themselves so
387. 17:49thank you very much for watching I wish
388. 17:51you the best of luck and your studies
389. 17:53and in your work and I look forward to
390. 17:55seeing you again next time
391. 18:00[Music]