AP Biology Exam Prep: Error Bars and Standard Error of the Mean — Transcript

Full transcript

1. 0:00Hi everybody, welcome back. It is Mr.
2. 0:02Poser, your AP Biology teacher. Today we
3. 0:04are continuing based on our last one on
4. 0:07graphs. Um we're studying science
5. 0:09practice 4 a little bit for the AP
6. 0:11biology exam. Um and this is kind of an
7. 0:14extension video on like graphs and
8. 0:16representing data here because there's
9. 0:18going to be some stuff that you're going
10. 0:19to see um statistics wise that are going
11. 0:21to be on the AP exam and they're just,
12. 0:24you know, not limited to biology. this
13. 0:26is just you know good to know as far as
14. 0:28uh statistics and data um understanding
15. 0:31data is a huge deal for uh today's
16. 0:34modern world so so I hope this is uh
17. 0:36helpful for a number of reasons um but
18. 0:38today we're going to be looking at these
19. 0:40uh these numbers over here all right so
20. 0:42this is where I left you uh with last
21. 0:44video all right you're doing your AP
22. 0:46exam you come across a question and you
23. 0:48got to make a graph here based on a data
24. 0:50table and then you have these numbers
25. 0:52over here what do they mean and why are
26. 0:54they significant ificant and you'll see
27. 0:57why that's funny in just a second. All
28. 0:58right. Um, but check it out. We have
29. 1:00this uh plus or minus symbol all the way
30. 1:03down here on our data points and then we
31. 1:05have capital S, capital E, and then this
32. 1:07little X that with a bar on top of it.
33. 1:10So, what does that exactly mean? And
34. 1:12what are these numbers um indicating
35. 1:15over here? All right. Well, these
36. 1:17numbers are what we call standard error
37. 1:18of the mean. And it's a measure that
38. 1:20indicates how much the sample differs
39. 1:22from the mean or how confident you are
40. 1:24in your mean value representing your
41. 1:26data points. All right? And that might
42. 1:28not mean a whole lot right now. Um but
43. 1:31when we run through an example and we're
44. 1:32going to calculate this on our own in a
45. 1:35little bit, it'll start to make a lot
46. 1:36more sense. So basically the larger the
47. 1:39uh standard error of the mean value that
48. 1:41you have for a data point, the less
49. 1:43confidence you have in the mean actually
50. 1:46representing the average. All right? So
51. 1:49say for example um I am trying to
52. 1:53collect the average
53. 1:55shoe size of everybody in my AP biology
54. 2:00class. Right? Let's say we're we have
55. 2:03average shoe size but I only have four
56. 2:05kids in my class um and two of them have
57. 2:10size 14 and then the other two have size
58. 2:14six. Okay. And then I average those and
59. 2:17I get an average of about like I think
60. 2:18that would be eight. No, that wouldn't
61. 2:20be eight. That would be like 10, right?
62. 2:22So 10 is a very average shoe size. But
63. 2:24does anybody have that shoe size in my
64. 2:26class? No. Right? So I would have a very
65. 2:29very large standard error of the mean.
66. 2:31How well does the mean actually you know
67. 2:33how different are the values actually
68. 2:35representing the mean? That's what
69. 2:37standard error is. Okay. Um so the
70. 2:40larger the number as I said the larger
71. 2:42the number the greater the standard
72. 2:43error of the mean and the less
73. 2:45confidence we have in the mean actually
74. 2:47representing um that that data point or
75. 2:50that uh that group or that sample.
76. 2:53Right? So check it out. This plus or
77. 2:55minus means here indicates a range. All
78. 2:57right. So the number of flies the
79. 3:00average number of flies with a ebony
80. 3:02body and long wings is 98. But there's a
81. 3:05standard error of the mean about 10
82. 3:07above and below 98. So, most of your
83. 3:09flies that you're going to find are
84. 3:11going to be um in 108 or it's going to
85. 3:16be 108 and 88. All right? Because that's
86. 3:1910 above 98 and 10 below 98. So, it's
87. 3:21kind of representing a range. All right?
88. 3:23And we're going to walk through how to
89. 3:25do that in just a second. But first, in
90. 3:27order to find standard error of the mean
91. 3:29over here, we have to find standard
92. 3:30deviation. And what that is is the value
93. 3:32that shows how much variation there is
94. 3:35from the average for a set of data
95. 3:36points. Okay. Um, so here's uh here's
96. 3:40our standard deviation equation. And you
97. 3:42will be given this on the AP exam. I'm
98. 3:44not sure if you're going to actually
99. 3:46have to calculate it. I'm going to say
100. 3:47probably not. Um, but just this is good
101. 3:50to know where it comes from um for a lot
102. 3:52of uh well, not just for AP biology, for
103. 3:55every other class, right? Or for any
104. 3:56other class that involves data
105. 3:58collection. So any other science class,
106. 3:59right? So here's standard deviation. Um,
107. 4:01and it looks like a big scary formula
108. 4:03here, but it's not that bad. All right?
109. 4:04And then standard error of the mean is
110. 4:06just s standard deviation divided by the
111. 4:08square root of n. Um and that's pretty
112. 4:10much it. All right. So uh we're going to
113. 4:12be walking through an example here um
114. 4:13because that is going to give us the
115. 4:15clearest indication of how this all
116. 4:16works. All right. So check it out. Um I
117. 4:19have uh birds on islands, right? So it
118. 4:21says the number of birds on each island
119. 4:23in an island chain are as follows.
120. 4:24There's 96 on one, 88 on another, 86,
121. 4:2884, 80, and 70. All right. And we're
122. 4:31going to calculate the standard
123. 4:32deviation of this data set. All right.
124. 4:34So, uh how much does the average um or
125. 4:38excuse me, how much do these values vary
126. 4:41from the average? And in order to find
127. 4:43that, we have to find out what the
128. 4:44average is. All right. And Xbar, I
129. 4:47haven't figured out how to make an X
130. 4:48with a little bar on top of it in my uh
131. 4:51program here. So, I wrote Xbar there. Um
132. 4:53that is representing what we call our
133. 4:55mean or our average, right? And we've
134. 4:56been doing this since grade school. like
135. 4:58add them all up divided by the number
136. 5:00the number of terms right so uh what I
137. 5:02did here is that we added up 96 88 86 84
138. 5:0680 and 70 and divided by 6 because
139. 5:08that's how many islands there are and we
140. 5:10get our average as being 84. Yes, we're
141. 5:13doing good. Okay, so xbar is equal to
142. 5:1684. That is step one of uh calculating
143. 5:19standard deviation. Step two is
144. 5:21determine the deviation from the mean of
145. 5:23each value and then add them all up.
146. 5:26Okay. So, how much do our values um vary
147. 5:30or differ from 84? All right. And
148. 5:33there's a mathematical way to do this.
149. 5:34We x is representing each one of our
150. 5:37values. Okay. And the x bar is
151. 5:39representing our mean. So, for example,
152. 5:41well, I did all of them already. Um
153. 5:44check it out. We have um our first
154. 5:45island at 96. All right? So, we have
155. 5:48calculate 96 minus 84 squared. Okay? We
156. 5:51go 88 - 84^ squared. Okay? because
157. 5:55that's our next value. Basically, we're
158. 5:56calculating the difference in our values
159. 5:59from the mean and squaring them. All
160. 6:01right. Um, so if we do that, I encourage
161. 6:03you to try and do this on your
162. 6:04calculator yourself. Okay? 84 is our
163. 6:07average. Um, and these are each of our
164. 6:10values. And if you put them in your
165. 6:12calculator, okay, we get these. All
166. 6:14right? Because, you know, think about
167. 6:15it. 96 - 84 is 12. Square that, it's
168. 6:18144. Um, we add all these numbers up and
169. 6:22we get 376.
170. 6:24Okay. So again, I'm encouraging you to
171. 6:26kind of follow along with me here um as
172. 6:29we uh calculate standard deviation. All
173. 6:32right. Um so basically again what we
174. 6:34did, you see the sigma here, this sigma
175. 6:36symbol means add them all up. It means
176. 6:39sum or summation. That's what it is.
177. 6:41Okay. Um and all I'm doing once again,
178. 6:44here's each of my values is representing
179. 6:46x minus xar uh which is the average and
180. 6:49square that and you add them all up and
181. 6:51this is what we get for our data point.
182. 6:52All right? or for our data set 376. Step
183. 6:56three of this is calculate the degrees
184. 6:58of freedom. And this part is super easy.
185. 7:00All degrees of freedom is is basically
186. 7:02how many uh how many data points do you
187. 7:04have minus one. All right. So uh
188. 7:07basically we have six different islands
189. 7:09which means our data point is or our
190. 7:12degrees of freedom is five just because
191. 7:15it's 6 minus one. Easy, right? So n this
192. 7:18number here is uh representing how many
193. 7:21data points that we have and we have six
194. 7:23of them. All right. So six minus one is
195. 7:25five. All right. And then well um next
196. 7:28step is put together to put it all
197. 7:30together to find s. All right. This uh
198. 7:32top value we already calculated as being
199. 7:34376. This bottom value is five. And then
200. 7:37we take the square root of that. I
201. 7:38encourage you to punch that into your
202. 7:40calculator right now if you haven't
203. 7:42already. And check it out. 375 or 6
204. 7:46divided by 5 75.2. If you take the
205. 7:48square root of that, we get a value of
206. 7:508.67.
207. 7:52That is representing our standard
208. 7:54deviation. How much does our um do our
209. 7:58data points differ or how much do they
210. 8:01vary from our average? Okay.
211. 8:05So uh in order to find standard error of
212. 8:07the mean which is what we're going to be
213. 8:08graphing here in a second you divide
214. 8:10your standard deviation by the square
215. 8:12root of n or number of your values and
216. 8:15this is this is the easy part right so
217. 8:16we uh or n easy part we already
218. 8:19calculated standard deviation 8.67 67
219. 8:21divided by the square<unk> of six and we
220. 8:23get 3.54
221. 8:25um and two standard deviation or excuse
222. 8:27me two standard error of the mean um
223. 8:30like what we see saw in that data table
224. 8:32okay is just 2 times this uh standard
225. 8:36deviation divided by the square root of
226. 8:37n all right so two standard error of the
227. 8:40means for us for this data point would
228. 8:42be uh 7.08 08. Okay. Um, so this number
229. 8:47right here, what this is our golden
230. 8:48ticket here. This number indicates the
231. 8:50size of the error bars on a graph. Okay.
232. 8:53Error bars. That's what this is all
233. 8:55about. All right. We talked about error
234. 8:57bars a little bit um in a previous
235. 8:59video. Okay. Um I don't remember off the
236. 9:01top of my head which one it is. Okay.
237. 9:03But it's in this playlist, I promise
238. 9:04you. Um but error bars represent okay,
239. 9:08how much does that value uh vary? Okay.
240. 9:11Okay. And this is uh my interpretation
241. 9:13of this uh this this is my graph here
242. 9:16that I made. All right. So if I'm um
243. 9:18calculating or if I'm measuring average
244. 9:20population size, I'm counting up by 10.
245. 9:22I got my label here. Um and here's my
246. 9:25bar representing my mean 84. All right.
247. 9:28But this little eye shape over here,
248. 9:30these are error bars. All right. And
249. 9:32that means from this value, I'm going
250. 9:34about seven above the mean and I'm going
251. 9:37about seven below the mean. And this is
252. 9:39how much variability um there is in my
253. 9:43average my data point that I collected
254. 9:45here. All right. So that would be the
255. 9:46size of my error bar. And you will be
256. 9:48expected to put error bars on your bar
257. 9:51graphs and perhaps even on your line
258. 9:53graphs as well. And that's what they
259. 9:55look like. You got to know the stand two
260. 9:57times the standard error of the mean.
261. 9:58It's usually going to uh tell you for
262. 10:00you. All right. And you put your error
263. 10:02bars just like that. Okay? or the top
264. 10:05reach the top uh horizontal section here
265. 10:09um is representing um your average plus.
266. 10:13Okay, the two standard error of the
267. 10:14means and then the bottom is two below
268. 10:17excuse me two standard error of the
269. 10:19means below your mean. Okay. Um so
270. 10:21here's the here's the data table from
271. 10:23before. We're going to graph this now.
272. 10:25Okay. We're uh I brought this back from
273. 10:27the beginning of the video. We got 98
274. 10:29plus or - 10 abony body longwing flies.
275. 10:3228 plus or - 7, so on and so forth. I'd
276. 10:35like you to try and graph this on your
277. 10:37own. I'm going to show you mine in just
278. 10:39a second. Um, pause if you want to try
279. 10:41it yourself, but if not, I'm going to go
280. 10:42ahead and move on. This is Oh, hang on.
281. 10:47There we go. This is my graph. All
282. 10:49right, here it is. I got the number of
283. 10:52flies over here. I counted up by 20s as
284. 10:54my scale. Remember, scaling in units is
285. 10:56still important. You know, we're still
286. 10:57talking about graphs. There's my uh data
287. 11:00table. Here's my labels down here. And
288. 11:02most importantly, check it out. Here are
289. 11:04my error bars. All right, so ebony body
290. 11:07long wings are uh standard error of the
291. 11:10mean or two times standard error of the
292. 11:12mean was 10. All right, so I went 10
293. 11:13below the mean and 10 above the mean to
294. 11:16represent that error bar. Um I think
295. 11:18this one was 25, so I went 25 above and
296. 11:2125 below. All right, and uh yeah, this
297. 11:24is this is how you do it. All right. And
298. 11:25if this were a line graph, you'd do the
299. 11:27same thing except for a data point,
300. 11:29you'd put some uh um error bars on each
301. 11:32one of those points. Okay. Um and why,
302. 11:35as I put over here, why bother to put
303. 11:37error bars? Why does error bars matter?
304. 11:40Okay. Overlapping error bars indicates
305. 11:42that there is no statistically
306. 11:43significant difference between groups of
307. 11:45variables. Okay? And this is going back
308. 11:47to testing independent versus dependent
309. 11:50variable accepting or rejecting the null
310. 11:52hypothesis or the uh alternative
311. 11:54hypothesis. Right? So if this were my
312. 11:56data here, if these were my data here
313. 11:57and check out these gigantic error bars,
314. 12:00um these are overlapping. Okay, that
315. 12:03means that the standard error of the
316. 12:04mean is large enough that I cannot
317. 12:07actually say statistically that there is
318. 12:09a difference in the values between these
319. 12:11three um these three data points.
320. 12:13there's no difference between um calcium
321. 12:16sensitivity in phosphate oxalate or uric
322. 12:19acid. Okay, so this would be a scenario
323. 12:21where I accept the null hypothesis
324. 12:24because these error bars are so big and
325. 12:26check it out. They're overlapping one
326. 12:27another. All right, so check it out.
327. 12:28Here's this gigantic range for uric
328. 12:31acid. Okay, the other ranges of these
329. 12:34other uh error bars fall into that.
330. 12:37Okay, you don't have statistically
331. 12:38significant data there. the independent
332. 12:40variable does not affect the dependent
333. 12:42variable. Um, so that means the matrix
334. 12:44does not affect calcium sensitivity
335. 12:48there. Okay. Um, so check it out on our
336. 12:51graph here. Is the data statistically
337. 12:53significant? Do our error bars overlap?
338. 12:57Well,
339. 12:58yes, it is statistically significant.
340. 13:01There's no overlap in the error bars.
341. 13:03Maybe uh maybe a little bit between
342. 13:05ebony body long wings and graybody
343. 13:07vestigial data. excuse me, vestigial
344. 13:09wings. Um, but the rest of these do not
345. 13:12uh overlap at all. Okay. And we can
346. 13:14indicate that yes, the dependent
347. 13:16variable is affected by the independent
348. 13:18variable. The uh there is a significant
349. 13:20difference in the number of flies of
350. 13:23each phenotype um over here. So there's
351. 13:25something going on genetically. Um if
352. 13:27you want to know what that this is all
353. 13:29about, I believe this is topic 5.6
354. 13:32um in my other videos. All right. Um but
355. 13:36that will be it for today. Please let me
356. 13:38know if you have any questions and we'll
357. 13:40see you next