WEBVTT 170 00:00:00.934 --> 00:00:04.934 turn things over to one of our first speakers. Felicia Barnett, who is 171 00:00:04.934 --> 00:00:08.934 joining us from U.S. EPA and the office of research 172 00:00:08.934 --> 00:00:09.934 and Feldman to provide opening remarks. 173 00:00:09.934 --> 00:00:11.934 Felicia, whenever you are ready, please begin. 174 00:00:11.934 --> 00:00:14.934 >> Thank you Jean. I just want to welcome everybody. This is the second 175 00:00:14.934 --> 00:00:17.934 in our series of three seminars in the utilization of ProUCL software 176 00:00:17.934 --> 00:00:20.934 tools. It has been introduced in those in the first seminar maybe 177 00:00:20.934 --> 00:00:21.934 remember my name is Felicia Barnett. 178 00:00:21.934 --> 00:00:24.934 I am the director of the EPA office of research and development site 179 00:00:24.934 --> 00:00:30.934 characterization and technical support center. I am going to refer to it 180 00:00:30.934 --> 00:00:34.934 as SCMTSC which is 181 00:00:34.934 --> 00:00:38.934 provide support on hazardous waste issues to 182 00:00:38.934 --> 00:00:43.000 the EPA program and resource offices created using ProUCL as part of 183 00:00:43.000 --> 00:00:45.934 that function. 184 00:00:45.934 --> 00:00:48.934 ProUCL is a statistical software packaged three on the EPA 185 00:00:48.934 --> 00:00:56.934 website for the analysis of temperamental data sets with and without Logitech 186 00:00:56.934 --> 00:00:57.934 observations but provide statistical methods and graphical 187 00:00:57.934 --> 00:01:05.934 tools to address temperamental sampling and statistical issues. 188 00:01:05.934 --> 00:01:08.934 It is not intended to be able to address every situation, and were 189 00:01:08.934 --> 00:01:11.934 to be the only option for environmental statistical analysis. It was developed 190 00:01:11.934 --> 00:01:13.934 to be an easy to use option for many standard statistical issues 191 00:01:13.934 --> 00:01:16.934 encountered when evaluating data. 192 00:01:16.934 --> 00:01:19.934 The second seminar in the series will focus on using ProUCL 193 00:01:19.934 --> 00:01:23.934 for trend analysis. Has genes in the first seminar in the series 194 00:01:23.934 --> 00:01:32.934 is always already available for viewing online. 195 00:01:32.934 --> 00:01:35.934 If you were unable to attend went to view specific parts at your own 196 00:01:35.934 --> 00:01:38.934 pace. We hope you find ProUCL to be a useful tool in these seminars 197 00:01:38.934 --> 00:01:40.934 assist you with understanding both abilities and navigating its program. 198 00:01:40.934 --> 00:01:45.934 We will be responding to all questions here and during the session or after 199 00:01:45.934 --> 00:01:59.934 and documenting those sessions. 200 00:01:59.934 --> 00:02:01.934 Additionally, SCMTSC provides internal and some limited external responses 201 00:02:01.934 --> 00:02:04.934 to your those who use it. Does anyone have questions or issues with using 202 00:02:04.934 --> 00:02:07.934 ProUCL? We did try to enter those as much as possible. On the ProUCL 203 00:02:07.934 --> 00:02:10.934 website, you can find under the contact my name and my contact information. 204 00:02:10.934 --> 00:02:16.934 I recommend contacting me via email with as much detail as possible, 205 00:02:16.934 --> 00:02:19.934 including screenshots. We will try to respond to your questions quickly. 206 00:02:19.934 --> 00:02:24.934 I am going to now turn it over to ProUCL over to Travis Lynn come 207 00:02:24.934 --> 00:02:29.934 Hatfield to start the instruction on the data. 208 00:02:29.934 --> 00:02:32.934 Thank you. Travis. 209 00:02:32.934 --> 00:02:37.934 >> Yes, hello. 210 00:02:37.934 --> 00:02:43.067 So, thank you guys and thanks everyone for joining us for our second part 211 00:02:43.067 --> 00:02:47.000 of the ProUCL series. 212 00:02:47.000 --> 00:02:50.000 As a Jean and Felicia mentioned, we will be focusing on the trend 213 00:02:50.000 --> 00:02:53.000 analysis features in ProUCL today. 214 00:02:53.000 --> 00:02:56.000 However, I am not going to be the one that is giving the majority 215 00:02:56.000 --> 00:02:59.000 of the presentation. Alona Carson will be doing that but I figured 216 00:02:59.000 --> 00:03:04.000 real quick I would give a nice recap of what we 217 00:03:04.000 --> 00:03:07.000 talked about in our first one, just sent some of those aspects 218 00:03:07.000 --> 00:03:08.000 we are going to be using today. 219 00:03:08.000 --> 00:03:14.000 Really what we talked about for most of our last presentation 220 00:03:14.000 --> 00:03:23.000 was really getting to look at exploratory data analysis inside ProUCL, looking 221 00:03:23.000 --> 00:03:25.000 at summary statistics and different graphical methods, including box 222 00:03:25.000 --> 00:03:28.000 plots and histograms and whatnot. 223 00:03:28.000 --> 00:03:34.000 And then we also explored fit tests, as well as Q2 plots to 224 00:03:34.000 --> 00:03:38.000 assess the normality of daytime, which is something that will definitely 225 00:03:38.000 --> 00:03:42.067 be coming up today. We also looked at 226 00:03:42.067 --> 00:03:46.000 layers and options for hypothesis testing in ProUCL. So while we 227 00:03:46.000 --> 00:03:52.000 are going to be definitely using the goodness of fit test today again, 228 00:03:52.000 --> 00:03:56.000 I hope everybody either 229 00:03:56.000 --> 00:03:59.000 got to maybe watch it last time or watch it in between since it 230 00:03:59.000 --> 00:04:03.000 was recorded but if not, hopefully we don't totally lose you. Other 231 00:04:03.000 --> 00:04:06.000 than that, as Jean and Felicia mentioned, 232 00:04:06.000 --> 00:04:09.000 it is definitely available online. 233 00:04:09.000 --> 00:04:13.000 And so will this one be as soon as we are done. 234 00:04:13.000 --> 00:04:18.000 But, with that in mind, I think I will turn it over to Polona 235 00:04:18.000 --> 00:04:20.000 and we can get started talking about trend analysis. 236 00:04:20.000 --> 00:04:25.000 >> Thank you Travis. Today, we will look at tools and features for 237 00:04:25.000 --> 00:04:31.000 trend analysis. First, we will look at some exploratory tools 238 00:04:31.000 --> 00:04:37.000 so time serials is a nice tool for that and then 239 00:04:37.000 --> 00:04:42.067 we will continue with tests for trend analysis. 240 00:04:42.067 --> 00:04:48.000 The first are Mann-Kendall and 241 00:04:48.000 --> 00:04:49.000 Theil-Sen Line Test. 242 00:04:49.000 --> 00:04:53.000 The second half of today's webinar will look at ordinary list square 243 00:04:53.000 --> 00:04:59.000 regression. Some of you may know as linear regression. 244 00:04:59.000 --> 00:05:10.000 So, now I just want to mention 245 00:05:10.000 --> 00:05:12.000 like in previous sessions presented by Travis, I will try to keep the 246 00:05:12.000 --> 00:05:16.000 statistical jargon as slow as possible and do my best to explain so the 247 00:05:16.000 --> 00:05:20.000 practitioners in the audience can follow without hopefully too much 248 00:05:20.000 --> 00:05:26.000 trouble. So, Felicia already mentioned 249 00:05:26.000 --> 00:05:31.000 ProUCL software is intended for basic statistical calculation using 250 00:05:31.000 --> 00:05:34.000 evaluation of contaminated sites. 251 00:05:34.000 --> 00:05:40.000 So, today we will be touching a little bit more advanced 252 00:05:40.000 --> 00:05:49.000 techniques. If you have questions, please ask them during 253 00:05:49.000 --> 00:05:53.000 the session and Jean and Travis will monitor them and try to answer 254 00:05:53.000 --> 00:05:56.000 as many as possible. 255 00:05:56.000 --> 00:06:00.000 But, if we have more, the answers will be available at a later time. 256 00:06:00.000 --> 00:06:05.000 So, at this point, I just want to 257 00:06:05.000 --> 00:06:10.000 refresh our memory from previous time that ProUCL software is accompanied 258 00:06:10.000 --> 00:06:13.000 by two valuable documents. These are user guides 259 00:06:13.000 --> 00:06:19.000 and technical guides. You can find them both in document 260 00:06:19.000 --> 00:06:28.000 folder of the ProUCL installation folder. So consult those when 261 00:06:28.000 --> 00:06:32.000 you are working on your project if you don't know where to go exactly. 262 00:06:32.000 --> 00:06:38.000 Really valuable resources but if you still have an issue where 263 00:06:38.000 --> 00:06:44.000 to go, it is probably a time to consult a statistician for help 264 00:06:44.000 --> 00:06:47.000 with your analysis. 265 00:06:47.000 --> 00:06:52.000 So, at this point, if we can please share 266 00:06:52.000 --> 00:06:54.000 my screen. So that I can start the demonstration 267 00:06:54.000 --> 00:06:57.000 of ProUCL. 268 00:06:57.000 --> 00:07:02.000 >> The other screen, not my screen Jean. 269 00:07:02.000 --> 00:07:08.000 >> I have it here. 270 00:07:08.000 --> 00:07:17.000 It is working. 271 00:07:17.000 --> 00:07:26.000 So we should be good now I hope. 272 00:07:26.000 --> 00:07:32.000 So we are good now. Just a few navigational remarks. 273 00:07:32.000 --> 00:07:38.000 Here in this middle center is where we to auto analysis 274 00:07:38.000 --> 00:07:47.000 so when we see the data on the left-hand side, we have 275 00:07:47.000 --> 00:07:50.000 a navigation panel where ProUCL displays a list of 276 00:07:50.000 --> 00:07:56.000 open data sets and generated outputs. ProUCL does 277 00:07:56.000 --> 00:08:01.000 assign Suffolk splintering output but if you want to make them more 278 00:08:01.000 --> 00:08:10.000 meaningful for your application, then you just go to 279 00:08:10.000 --> 00:08:13.000 file and save. We don't have anything loaded so I can't show you that 280 00:08:13.000 --> 00:08:19.000 but it would be file, save file, and rename it however 281 00:08:19.000 --> 00:08:21.000 you want. 282 00:08:21.000 --> 00:08:25.000 It is disbelieving and green color basically the log of the actions 283 00:08:25.000 --> 00:08:31.000 you are performing. An orange color display and warning messages 284 00:08:31.000 --> 00:08:36.000 and in red color, it displays the ever messages. 285 00:08:36.000 --> 00:08:41.000 So, those two orange and red are something you 286 00:08:41.000 --> 00:08:44.000 may want to pay attention if you don't think you are not accomplishing 287 00:08:44.000 --> 00:08:49.000 what you want to do with the software. 288 00:08:49.000 --> 00:08:55.000 Let's hope we won't have those today for the presentation. So, 289 00:08:55.000 --> 00:09:00.000 we will be using two data sets today. They both 290 00:09:00.000 --> 00:09:04.000 are available within the data folder in ProUCL. Sewn they are some of 291 00:09:04.000 --> 00:09:06.000 the training data sets available. 292 00:09:06.000 --> 00:09:10.000 You can also download them from the 293 00:09:10.000 --> 00:09:13.000 link site for today's webinar. 294 00:09:13.000 --> 00:09:17.000 To make it easier for the folder so 295 00:09:17.000 --> 00:09:23.000 I can reach them quickly, let me these two files are 296 00:09:23.000 --> 00:09:25.000 and W189. 297 00:09:25.000 --> 00:09:29.000 We will use a little bit at the beginning of the demonstration and 298 00:09:29.000 --> 00:09:36.000 then for most of the parts, we will use trend and W and 299 00:09:36.000 --> 00:09:42.000 D to. Before we go further, I just wanted 300 00:09:42.000 --> 00:09:45.934 to do a few remarks. 301 00:09:45.934 --> 00:09:48.934 Two data set that we will be using today don't include non-detect. 302 00:09:48.934 --> 00:09:52.934 So we won't be using them today in today's demonstration. But, as 303 00:09:52.934 --> 00:09:57.934 many of you are facing that, I want to help 304 00:09:57.934 --> 00:10:02.934 a little bit how to deal with them and trend analysis. 305 00:10:02.934 --> 00:10:06.934 So, the first thing that I want to highlight is that the time 306 00:10:06.934 --> 00:10:11.934 detect create problems and they should be removed before the analysis. 307 00:10:11.934 --> 00:10:15.934 The reason for this really high non-detect and I mean 308 00:10:15.934 --> 00:10:21.934 non-detect closest to the really high detect value, 309 00:10:21.934 --> 00:10:27.934 the limitation of the laboratory to 310 00:10:27.934 --> 00:10:30.934 perform analysis. They need to do to dilute the samples many times 311 00:10:30.934 --> 00:10:35.934 and especially when they analyze simultaneously, they need to make 312 00:10:35.934 --> 00:10:40.934 a compromise between the dilution and the possible 313 00:10:40.934 --> 00:10:49.934 contamination of the analytical system. They can't always go back 314 00:10:49.934 --> 00:10:50.934 if it's a high non-detect. 315 00:10:50.934 --> 00:10:56.934 Can't always go back and read an alliance at the last 316 00:10:56.934 --> 00:11:01.934 dilution because they may contaminate the system. Or it can also because 317 00:11:01.934 --> 00:11:07.934 the interference with some other contaminants present in the 318 00:11:07.934 --> 00:11:08.934 sample. 319 00:11:08.934 --> 00:11:13.934 So, in this case, if you see the really high non-detect, a good practice 320 00:11:13.934 --> 00:11:17.934 is to reach out 321 00:11:17.934 --> 00:11:22.934 to the laboratory and get a little bit of insight how the samples were 322 00:11:22.934 --> 00:11:32.934 analyzed. So, to rules of them how to treat the non-detect. 323 00:11:32.934 --> 00:11:36.934 If they are greater than highest attempt, you are quite safe to reject 324 00:11:36.934 --> 00:11:43.000 them. If you have non-detect 325 00:11:43.000 --> 00:11:46.934 about 10 times higher than the lowest detected 326 00:11:46.934 --> 00:11:51.934 value, use judgment and you may reach to the laboratory or just 327 00:11:51.934 --> 00:11:57.934 do some investigation to get a feel for how those not 328 00:11:57.934 --> 00:11:59.934 detect where obtained. 329 00:11:59.934 --> 00:12:05.934 Then make a decision based on that if you want to reject. When you 330 00:12:05.934 --> 00:12:11.934 have a data set with non-detect, you can use one of the 331 00:12:11.934 --> 00:12:13.934 substitution method. 332 00:12:13.934 --> 00:12:20.934 The two common substitution method you can substitute the value with 333 00:12:20.934 --> 00:12:26.934 half report or have of the detection limit 334 00:12:26.934 --> 00:12:34.934 but this makes sense to do only when you have 335 00:12:34.934 --> 00:12:35.934 less than 10 or 15% of the non-detect. 336 00:12:35.934 --> 00:12:38.934 When you are dealing with a lot of not detect in your dataset, I 337 00:12:38.934 --> 00:12:45.000 strongly suggest that you work with statistician and consult 338 00:12:45.000 --> 00:12:50.000 how you want to go about that kind of data set. 339 00:12:50.000 --> 00:12:56.000 So, this is about non-detect. Let's go to time series 340 00:12:56.000 --> 00:13:02.000 plot for our first data set. I am going to open 341 00:13:02.000 --> 00:13:08.000 my data set 342 00:13:08.000 --> 00:13:18.000 so and I will 343 00:13:18.000 --> 00:13:19.000 use those the first two columns. 344 00:13:19.000 --> 00:13:24.000 The index of the column is zero and one. Please see we have data 345 00:13:24.000 --> 00:13:28.000 set for fuel as well as and here is the manganese value 346 00:13:28.000 --> 00:13:32.000 concentration in groundwater. These data sets are really 347 00:13:32.000 --> 00:13:37.000 nice to show you the capability of ProUCL to group 348 00:13:37.000 --> 00:13:43.067 parameters. Many times you want to display like 349 00:13:43.067 --> 00:13:47.000 several, you want to compare several wells. I am going 350 00:13:47.000 --> 00:13:52.000 to do this how. The time series plot is found on the statistical 351 00:13:52.000 --> 00:13:56.000 test trend analysis and here on the bottom 352 00:13:56.000 --> 00:14:05.000 we have time series plot and I will select this time just data 353 00:14:05.000 --> 00:14:10.000 so in measured data, we report our concentration of 354 00:14:10.000 --> 00:14:16.000 the contaminant and here we have this grouping, 355 00:14:16.000 --> 00:14:22.000 select group column. I will click at this little row here and 356 00:14:22.000 --> 00:14:25.000 select well I.D. 357 00:14:25.000 --> 00:14:28.000 Let's look under options. 358 00:14:28.000 --> 00:14:34.000 We have event label here, those labels can be changed however 359 00:14:34.000 --> 00:14:37.000 you want. 360 00:14:37.000 --> 00:14:45.000 We can change that but one thing I 361 00:14:45.000 --> 00:14:49.000 want to do at this point is I went to click this little box here, group 362 00:14:49.000 --> 00:14:52.000 and okay. Okay. 363 00:14:52.000 --> 00:14:58.000 Here we have this nice plot comparing three wells on the 364 00:14:58.000 --> 00:15:03.000 same graph. Really nice feature, really easy to do 365 00:15:03.000 --> 00:15:06.000 in UCL. 366 00:15:06.000 --> 00:15:11.000 You may want to use this feature to compare contaminants 367 00:15:11.000 --> 00:15:16.000 and if you want to do that, then you need to be aware of the 368 00:15:16.000 --> 00:15:23.000 scaling may be an issue if you have contaminants in 369 00:15:23.000 --> 00:15:28.000 foreign concentration ranges. You just need to play a little bit of 370 00:15:28.000 --> 00:15:33.000 that option. 371 00:15:33.000 --> 00:15:37.000 So now I want to open our main data set, the other one, that we 372 00:15:37.000 --> 00:15:46.000 will use from now on for most of the presentation. So this is 373 00:15:46.000 --> 00:15:54.000 trend MW real data. I have 374 00:15:54.000 --> 00:15:58.000 a mark because I cheated a little bit for the demonstration. I'm 375 00:15:58.000 --> 00:16:04.000 going to do the time series plot on time and 376 00:16:04.000 --> 00:16:10.000 MW 28 variable. Just a quick 377 00:16:10.000 --> 00:16:13.000 look at this time and date. 378 00:16:13.000 --> 00:16:17.000 We have a few instances here. We have repeated measurement 379 00:16:17.000 --> 00:16:20.000 of the same sampling event. 380 00:16:20.000 --> 00:16:24.000 So, if you have those, make sure you put 381 00:16:24.000 --> 00:16:33.000 in time: the same annotation. 382 00:16:33.000 --> 00:16:39.000 Now statistical test, time analysis, 383 00:16:39.000 --> 00:16:48.000 this time and will use the event so under events, it will 384 00:16:48.000 --> 00:16:54.000 come with time and date and under measured data, 385 00:16:54.000 --> 00:16:57.000 MW 28. 386 00:16:57.000 --> 00:17:05.000 We don't have grouping parameter now. 387 00:17:05.000 --> 00:17:08.000 The options can stay the same, we don't need to put up the graphs 388 00:17:08.000 --> 00:17:11.000 now because we don't have at. Okay. 389 00:17:11.000 --> 00:17:20.000 So this is our time series plot now. 390 00:17:20.000 --> 00:17:25.000 So, before we jump in front of statistical analysis, I just 391 00:17:25.000 --> 00:17:31.000 want to refresh some statistical 392 00:17:31.000 --> 00:17:32.000 totems. 393 00:17:32.000 --> 00:17:35.000 This is where many non-statistician specialist struggle. And trend analysis, 394 00:17:35.000 --> 00:17:43.067 we always deal with two variables and our data are collected in 395 00:17:43.067 --> 00:17:49.000 time intervals. So, our variable in interest, this is the contaminant 396 00:17:49.000 --> 00:17:58.000 in most cases, is called a dependent variable. 397 00:17:58.000 --> 00:18:02.000 To plot it is on the y-axis. 398 00:18:02.000 --> 00:18:08.000 Here is contaminant, dependent variable. The other variable 399 00:18:08.000 --> 00:18:12.000 entities normally set by the design. 400 00:18:12.000 --> 00:18:18.000 So basically, beforehand, we determined time intervals 401 00:18:18.000 --> 00:18:22.000 let's say when we would sample groundwater. These are variables 402 00:18:22.000 --> 00:18:28.000 is displayed on the X axis and it is called independent or exploratory 403 00:18:28.000 --> 00:18:31.000 variable. 404 00:18:31.000 --> 00:18:36.000 Just so what we have those totems refreshed. 405 00:18:36.000 --> 00:18:41.000 So and now let's go into our statistical test for trend analysis. The first 406 00:18:41.000 --> 00:18:47.000 test that we will look at is a non-parametric 407 00:18:47.000 --> 00:18:56.000 test. 408 00:18:56.000 --> 00:19:02.000 So I will use this trend MW data statistical test 409 00:19:02.000 --> 00:19:08.000 trend analysis, this is where 410 00:19:08.000 --> 00:19:17.000 we will find it. The benefit of basically both 411 00:19:17.000 --> 00:19:21.000 nonparametric tests Mann-Kendall and Theil-Sen Line Test if they 412 00:19:21.000 --> 00:19:26.000 don't have any underlying assumptions 413 00:19:26.000 --> 00:19:27.000 about the distribution of the data. 414 00:19:27.000 --> 00:19:30.000 We don't need to think about distribution, we don't need to worry about transforming 415 00:19:30.000 --> 00:19:35.000 the daytime but it is the first step in trend analysis to do those 416 00:19:35.000 --> 00:19:43.934 tests. So, let's look now at the Mann-Kendall test. 417 00:19:43.934 --> 00:19:49.934 Measured value MW 28. 418 00:19:49.934 --> 00:19:55.934 One thing I want to highlight here is that the data you can them 419 00:19:55.934 --> 00:20:00.934 in time and do need to pay attention that you 420 00:20:00.934 --> 00:20:04.934 organize them that way when you and put them in the table. So that 421 00:20:04.934 --> 00:20:07.934 they are ordered by time. 422 00:20:07.934 --> 00:20:13.934 We don't have grouping parameter so you select 423 00:20:13.934 --> 00:20:18.934 your confidence levels the standard confidence level is 95%. 424 00:20:18.934 --> 00:20:24.934 We will disclaim graphics, we 425 00:20:24.934 --> 00:20:29.934 can latest regression line is something that 426 00:20:29.934 --> 00:20:35.934 helps visualize what is going on on the data. Click 427 00:20:35.934 --> 00:20:41.934 okay. Okay. Here is our table with the results. We 428 00:20:41.934 --> 00:20:46.934 have some general 429 00:20:46.934 --> 00:20:50.934 information about the data and the test here in the general statistics 430 00:20:50.934 --> 00:20:56.934 in the next section. And the bottom, we see the result of the Mann-Kendall 431 00:20:56.934 --> 00:21:01.934 analysis. So here is the statistics, the 432 00:21:01.934 --> 00:21:07.934 values were really small and we have this message 433 00:21:07.934 --> 00:21:13.934 helping us to plot the results. So now let's 434 00:21:13.934 --> 00:21:16.934 look at this trend test graphics. 435 00:21:16.934 --> 00:21:19.934 Here is the plot. 436 00:21:19.934 --> 00:21:24.934 It is again like the jacket to plot time 437 00:21:24.934 --> 00:21:31.934 series plot and then I added this regression line, which helps to 438 00:21:31.934 --> 00:21:34.934 visualize what is going on with the data and on the right-hand side, 439 00:21:34.934 --> 00:21:40.934 we have the Mann-Kendall test table and 440 00:21:40.934 --> 00:21:44.934 the interpretation. Statistical significant evidence 441 00:21:44.934 --> 00:21:49.934 of decreasing trend in this data. 442 00:21:49.934 --> 00:21:54.934 So the Mann-Kendall test only gives us an idea about the 443 00:21:54.934 --> 00:21:59.934 modernist city of the trend. Basically what does that mean is if the trend 444 00:21:59.934 --> 00:22:03.934 consistently decreases or increases. 445 00:22:03.934 --> 00:22:08.934 It doesn't give us any information about slope of the trend. So, the 446 00:22:08.934 --> 00:22:13.934 rate of the which the contaminant concentration is 447 00:22:13.934 --> 00:22:15.934 increasing or decreasing. 448 00:22:15.934 --> 00:22:21.934 So, one benefit of this test is that we can perform it with 449 00:22:21.934 --> 00:22:24.934 as little as four data points. You need to know 450 00:22:24.934 --> 00:22:29.934 that if you have a really small data set, the power of this test 451 00:22:29.934 --> 00:22:34.934 is very low. 452 00:22:34.934 --> 00:22:39.934 So the test may not detect the trend, even if the trend is present. 453 00:22:39.934 --> 00:22:44.000 But let Satan groundwater analysis we keep disabling 454 00:22:44.000 --> 00:22:48.000 kinetic points. Over time, we are gathering more and more evidence 455 00:22:48.000 --> 00:22:53.000 and basically increasing the power of these tests whilst we are adding 456 00:22:53.000 --> 00:23:05.000 the data. So, eventually the test will detect it. 457 00:23:05.000 --> 00:23:11.000 So this is about the Mann-Kendall 458 00:23:11.000 --> 00:23:16.000 test. Now we can go to the next step 459 00:23:16.000 --> 00:23:20.000 in to do so we see here the decreasing trend, now we can go to the next 460 00:23:20.000 --> 00:23:28.000 step, perform Theil-Sen Line Test. This gives us a little bit more 461 00:23:28.000 --> 00:23:32.000 information. It does give us some idea about the 462 00:23:32.000 --> 00:23:38.000 rate of the decay of the contaminant and the slope 463 00:23:38.000 --> 00:23:42.067 of it. So, I am selecting again my data set, 464 00:23:42.067 --> 00:23:46.000 going to statistical test, trend analysis, 465 00:23:46.000 --> 00:23:52.000 Theil-Sen Line Test, we need to again 466 00:23:52.000 --> 00:23:58.000 select variables, time under options 467 00:23:58.000 --> 00:24:06.000 let's display Theil-Sen Line 468 00:24:06.000 --> 00:24:11.000 Test. This is a nice feature. Previously I printed out 469 00:24:11.000 --> 00:24:17.000 that the data set contains a few events when several 470 00:24:17.000 --> 00:24:22.000 samples were obtained at the same interval. 471 00:24:22.000 --> 00:24:25.000 Here we have 705 twice, 90 six twice. 472 00:24:25.000 --> 00:24:31.000 1535 twice. It was also two samples 473 00:24:31.000 --> 00:24:35.000 were taken. 474 00:24:35.000 --> 00:24:40.000 When you click this box, the results will be average. And this is really 475 00:24:40.000 --> 00:24:46.000 important the Theil-Sen test only can handle one 476 00:24:46.000 --> 00:24:52.000 data point sampling event. 477 00:24:52.000 --> 00:25:01.000 So let's see now. Analysis 478 00:25:01.000 --> 00:25:07.000 so immediate advantage of this test is that 479 00:25:07.000 --> 00:25:12.000 we can estimate slope as opposed to just 480 00:25:12.000 --> 00:25:18.000 the identification of increasing or decreasing trend with Mann-Kendall 481 00:25:18.000 --> 00:25:23.000 test. Since slope is negative, 482 00:25:23.000 --> 00:25:32.000 let me just pull down the results, so here we have 483 00:25:32.000 --> 00:25:37.000 the values. Slope is negative, the filter is really 484 00:25:37.000 --> 00:25:43.067 small. That confirms the Mann-Kendall test. 485 00:25:43.067 --> 00:25:49.000 One thing about this method it is robust against extreme values. 486 00:25:49.000 --> 00:25:54.000 What it does is Theil-Sen test finds the medium, 487 00:25:54.000 --> 00:26:00.000 medium slope and divides the points we have available 488 00:26:00.000 --> 00:26:04.000 into two sections so half of them 489 00:26:04.000 --> 00:26:10.000 will be above the line, half of them will be below the line. 490 00:26:10.000 --> 00:26:15.000 Because of that, it is robust against a couple of those values. 491 00:26:15.000 --> 00:26:21.000 Basically, it is the formative to ordinary square 492 00:26:21.000 --> 00:26:25.000 regression. The intent of this test is it 493 00:26:25.000 --> 00:26:33.000 can only handle one observation at sampling point. 494 00:26:33.000 --> 00:26:38.000 So here is now the spot. This is the regression line on a median 495 00:26:38.000 --> 00:26:42.067 slope. This divides the points into sections. 496 00:26:42.067 --> 00:26:49.000 Half of them below, half of them about. 497 00:26:49.000 --> 00:26:53.000 Another disadvantage of this test is that it does require a fair amount 498 00:26:53.000 --> 00:26:59.000 of data to provide a reliable conclusion. 499 00:26:59.000 --> 00:27:05.000 When it starts with the 500 00:27:05.000 --> 00:27:10.000 Mann-Kendall test, we can use it to confirm the sign of the slopes 501 00:27:10.000 --> 00:27:12.000 or do we have a decreasing or increasing trend 502 00:27:12.000 --> 00:27:16.000 and gives us additional information about the rate of the change in 503 00:27:16.000 --> 00:27:27.000 contaminant because it does give us that estimate of the slope. 504 00:27:27.000 --> 00:27:32.000 So here is now time for a short break before we go to the ordinary 505 00:27:32.000 --> 00:27:35.000 list square regression. 506 00:27:35.000 --> 00:27:38.000 So, if we can have a couple of 507 00:27:38.000 --> 00:27:40.000 quiz questions. 508 00:27:40.000 --> 00:27:46.000 >> We will also be taking a couple of quick question and answer 509 00:27:46.000 --> 00:28:01.000 session as well. 510 00:28:01.000 --> 00:28:03.000 >> I will remind the audience there is still an opportunity to send 511 00:28:03.000 --> 00:28:06.000 in questions using the Q&A window in the lower corner. We are going 512 00:28:06.000 --> 00:28:09.000 to turn on a quiz in the proportion of the screen and test her knowledge 513 00:28:09.000 --> 00:28:12.000 but there will be questions that will appear and you can click on 514 00:28:12.000 --> 00:28:15.000 the answer that you think is correct then we will keep track of who 515 00:28:15.000 --> 00:28:18.000 is is going well. Our first question is appearing now. Remember, just 516 00:28:18.000 --> 00:28:23.000 click on the box you think is the correct answer. 517 00:28:23.000 --> 00:28:27.000 The quiz score will keep track and let you know if you got that 518 00:28:27.000 --> 00:28:29.000 right or wrong. The sooner you pick the right into, the sooner the higher 519 00:28:29.000 --> 00:28:33.000 your score will be. It looks like we've got some people who know their 520 00:28:33.000 --> 00:28:49.067 stuff. Moving on to our next question. 521 00:28:49.067 --> 00:28:55.000 This one seems to be tripping few people up. A handful of you got 522 00:28:55.000 --> 00:29:04.000 that one correct. Just reminding everybody, 523 00:29:04.000 --> 00:29:07.000 with that, we will go ahead and go back to our split screen view 524 00:29:07.000 --> 00:29:09.000 and take a quick break for questions. 525 00:29:09.000 --> 00:29:12.000 I am going to start earlier. This first question comes in asking if 526 00:29:12.000 --> 00:29:17.000 ProUCL can use J. Crew did values for trend analysis. 527 00:29:17.000 --> 00:29:30.000 >> Yes, by j coded, I assume you mean not detect. 528 00:29:30.000 --> 00:29:37.000 I totally understand but in ProUCL right now, there is not 529 00:29:37.000 --> 00:29:40.000 a great way to have a directly handled you're not detect problems. Which 530 00:29:40.000 --> 00:29:46.934 is why we kind of decided he would give some general rules of thumb 531 00:29:46.934 --> 00:29:49.934 if you want to take a look at it basically really, if you are trying 532 00:29:49.934 --> 00:29:54.934 to do trend analysis and you have interesting sets of not detect in 533 00:29:54.934 --> 00:30:00.934 your data, you should probably consult 534 00:30:00.934 --> 00:30:03.934 a statistician. On how your data is set up, how many detect in the 535 00:30:03.934 --> 00:30:05.934 mood to have, what percent of your data are not detect, all those different 536 00:30:05.934 --> 00:30:09.934 confounding factors, you are going to get different answers each time 537 00:30:09.934 --> 00:30:14.934 and I think Jean, this also falls into the 538 00:30:14.934 --> 00:30:19.934 second question wouldn't be substitution method 539 00:30:19.934 --> 00:30:23.934 of doing half the deduction limit or whatnot artificially 540 00:30:23.934 --> 00:30:28.934 alter the distribution of the data and 541 00:30:28.934 --> 00:30:33.934 decreased the variance. The answer is yes, that totally could do that. 542 00:30:33.934 --> 00:30:39.934 With not detect, you are making 543 00:30:39.934 --> 00:30:41.934 the best of a bad situation. 544 00:30:41.934 --> 00:30:50.934 How to do that again is going to come down to a case-by-case basis. 545 00:30:50.934 --> 00:30:52.934 Not to beat a dead horse here if you're going to want to consult 546 00:30:52.934 --> 00:30:57.934 a statistician if there isn't something that is immediately solvable to 547 00:30:57.934 --> 00:30:59.934 you. And, in the case of lots of not detect, multiple detect limit, 548 00:30:59.934 --> 00:31:04.934 that is not easily solvable situation I would say. 549 00:31:04.934 --> 00:31:07.934 So, sorry to kind of breeze over all of those not detect questions 550 00:31:07.934 --> 00:31:13.934 with basically the answer is consult a statistician. 551 00:31:13.934 --> 00:31:23.934 >> Okay. 552 00:31:23.934 --> 00:31:26.934 Going to bounce back to some questions about dates and times in the data 553 00:31:26.934 --> 00:31:27.934 set you have been working with. 554 00:31:27.934 --> 00:31:30.934 One of the attendees noted that the data set didn't appear to have 555 00:31:30.934 --> 00:31:32.934 a column for the date of the sampling event and we were wondering if ProUCL 556 00:31:32.934 --> 00:31:35.934 automatically convert the date to a corresponding event number or 557 00:31:35.934 --> 00:31:37.934 is it calculating the number of days in between these event? 558 00:31:37.934 --> 00:31:43.000 >> I believe Polona mentioned earlier but just in case it got messed, 559 00:31:43.000 --> 00:31:47.934 ProUCL needs to have numbers in the date 560 00:31:47.934 --> 00:31:56.934 column. Because of if you want to put in the March third 2020. 561 00:31:56.934 --> 00:31:59.934 like that is not going to work, to were going to need to convert 562 00:31:59.934 --> 00:32:04.934 it to a numeric representation of date or time or sampling event. 563 00:32:04.934 --> 00:32:14.934 You can either do that by just saying a set number of weeks after an 564 00:32:14.934 --> 00:32:16.934 initial sampling event or days or months or if you are coming back 565 00:32:16.934 --> 00:32:22.934 and forth from maybe different software, you can convert things to a 566 00:32:22.934 --> 00:32:25.934 set up where is it is cutting a number of seconds from 567 00:32:25.934 --> 00:32:30.934 a given starting point. That is going to give you a 568 00:32:30.934 --> 00:32:34.934 couple of weird x-axis but it might play a little better if you are 569 00:32:34.934 --> 00:32:40.934 bobbing back and forth between our or Python or what have you. 570 00:32:40.934 --> 00:32:47.000 But in ProUCL, door time variable does 571 00:32:47.000 --> 00:32:51.000 need to be numeric not a character or data string. 572 00:32:51.000 --> 00:32:58.000 >> If I can just hear that it is really easy and Excel 573 00:32:58.000 --> 00:33:02.000 to convert the date into a number of dates, number of days between 574 00:33:02.000 --> 00:33:06.000 the events. 575 00:33:06.000 --> 00:33:09.000 >> Okay. I did just want to comment. 576 00:33:09.000 --> 00:33:12.000 I see a lot of the dialogue and comments that are coming in from 577 00:33:12.000 --> 00:33:20.000 what I believe are statisticians about how to handle 578 00:33:20.000 --> 00:33:22.000 J coded values and whether they are estimates or documents that 579 00:33:22.000 --> 00:33:26.000 something is there, we just can't be certain of what the value is 580 00:33:26.000 --> 00:33:30.000 as we can to zero it out so I want to thank everyone that has been 581 00:33:30.000 --> 00:33:41.000 coming in with comments and input on how to 582 00:33:41.000 --> 00:33:44.000 handle J coded values. I will certainly work to take the speculative. This 583 00:33:44.000 --> 00:33:46.000 could be a topic for a future webinar in itself. Thanks for everyone present 584 00:33:46.000 --> 00:33:49.000 in the methods but think of the interest of time, we have about 585 00:33:49.000 --> 00:33:53.000 50 minutes left, but we transitioned back to the presentation. People 586 00:33:53.000 --> 00:34:07.000 pause again for Q&A and will encourage 587 00:34:07.000 --> 00:34:10.000 those parts bins to get this questions incomes coming on input if you haven't 588 00:34:10.000 --> 00:34:13.000 to join us late, if we don't get your question live, we will be looking 589 00:34:13.000 --> 00:34:15.000 to get a written response to what the questions that were submitted 590 00:34:15.000 --> 00:34:18.000 that we may not have addressed live during the webinar. With that, I 591 00:34:18.000 --> 00:34:20.000 will turn it back to Travis and Fran eight. 592 00:34:20.000 --> 00:34:23.000 >> So, yes, I will speak up from here again. So, the third option 593 00:34:23.000 --> 00:34:25.000 for trend analysis in ProUCL is ordinary list square aggression. 594 00:34:25.000 --> 00:34:29.000 This is the most advanced method of three but gives the most information. 595 00:34:29.000 --> 00:34:37.000 So, without getting in-depth on the mass of ordinary list square 596 00:34:37.000 --> 00:34:41.000 regression, what is really trying to do is to fit 597 00:34:41.000 --> 00:34:46.000 a line between the data point that maximizes the square distance 598 00:34:46.000 --> 00:34:51.000 between the points and the line. 599 00:34:51.000 --> 00:34:55.000 So, since this is a little bit more and then 600 00:34:55.000 --> 00:35:01.000 advanced analysis, I am first providing you the steps to do about it. 601 00:35:01.000 --> 00:35:06.000 So, first you select dependent and independent variables. 602 00:35:06.000 --> 00:35:11.000 Then, fit the regression. Then you need to evaluate the 603 00:35:11.000 --> 00:35:14.000 regression model that you get. 604 00:35:14.000 --> 00:35:19.000 First to go to the steps, then you need to 605 00:35:19.000 --> 00:35:24.000 check the assumptions that they were met. There are three assumptions, 606 00:35:24.000 --> 00:35:28.000 we will explain them a little bit later but you need to check 607 00:35:28.000 --> 00:35:34.000 them, and then based on the evaluation of the model and assumptions, you 608 00:35:34.000 --> 00:35:42.067 interpret your results. Okay, let's go ahead and 609 00:35:42.067 --> 00:35:46.000 analyze our data set with ordinary list square regression features. 610 00:35:46.000 --> 00:35:52.000 I am selecting this trend MW real data set going 611 00:35:52.000 --> 00:35:56.000 to do a statistical test and ordinary list square regression 612 00:35:56.000 --> 00:36:03.000 is just about trend analysis option. Now 613 00:36:03.000 --> 00:36:09.000 here we have this dependent variable, remember, dependent variable is 614 00:36:09.000 --> 00:36:17.000 our variable of concern. The contaminant MW 615 00:36:17.000 --> 00:36:26.000 28. Then we have independent variable, which is our time and date. 616 00:36:26.000 --> 00:36:32.000 Under options, to 617 00:36:32.000 --> 00:36:36.000 select the confidence level. You want to 618 00:36:36.000 --> 00:36:42.067 apply the regression people with regression results. We will display 619 00:36:42.067 --> 00:36:49.000 a diagnostic as well. Just take a look at it. 620 00:36:49.000 --> 00:36:53.000 You want to display a regression plot. On 621 00:36:53.000 --> 00:36:57.000 regression plot, we also want confidence prediction interval for this demonstration. 622 00:36:57.000 --> 00:37:02.000 So, okay. Okay. 623 00:37:02.000 --> 00:37:08.000 Here we display the results. Let first pop up the regression. 624 00:37:08.000 --> 00:37:14.000 This is now the regression line. 625 00:37:14.000 --> 00:37:23.000 The gray dotted line in the middle is and were fitted regression line. 626 00:37:23.000 --> 00:37:28.000 The two green lines on at this point are confidence intervals of 627 00:37:28.000 --> 00:37:35.000 the mean and the two plants are protection 628 00:37:35.000 --> 00:37:39.000 intervals. Let me explain the meaning of the confidence and protection 629 00:37:39.000 --> 00:37:44.000 interval in a plain language as I can do that. So, 95 confidence 630 00:37:44.000 --> 00:37:50.000 interval if we take a bunch of samples 631 00:37:50.000 --> 00:37:54.000 of time, let's say here we have a 632 00:37:54.000 --> 00:38:02.000 point of 160. if we would take several samples of that time and then 633 00:38:02.000 --> 00:38:07.000 average them, we expect the meaning of those samples to be within the 634 00:38:07.000 --> 00:38:12.000 green lines 95% of the time. 635 00:38:12.000 --> 00:38:16.000 So, but then on the other hand, if we only take one random sample 636 00:38:16.000 --> 00:38:22.000 the same time, we expect 637 00:38:22.000 --> 00:38:27.000 the value of that sample to be 95% of the time 638 00:38:27.000 --> 00:38:32.000 between the redlines. We are 95% confident that its value will be 639 00:38:32.000 --> 00:38:38.000 within the redline. 640 00:38:38.000 --> 00:38:43.067 So, here on this plot, we have also the results of the regression 641 00:38:43.067 --> 00:38:47.000 analysis. At this point, I will move back to the table because we 642 00:38:47.000 --> 00:38:59.000 have a little bit more information there. So, let's look. 643 00:38:59.000 --> 00:39:02.000 Here in the middle, we have regression 644 00:39:02.000 --> 00:39:05.000 estimates and interference table. 645 00:39:05.000 --> 00:39:11.000 So, in regression, we are estimating two parameters. Intercept 646 00:39:11.000 --> 00:39:14.000 and slope of the regression line. 647 00:39:14.000 --> 00:39:20.000 These are the values for the estimates 648 00:39:20.000 --> 00:39:24.000 and on the slide, to hear see the table 649 00:39:24.000 --> 00:39:29.000 that is a regression model, regression equation. Our contaminant is equal 650 00:39:29.000 --> 00:39:35.000 to intercept, 2164 minus 651 00:39:35.000 --> 00:39:45.934 a decreasing trend is negative slope minus one point 637. 652 00:39:45.934 --> 00:39:50.934 Ordinary list square regression gives us more information then the 653 00:39:50.934 --> 00:39:57.934 Theil-Sen. It gives us the estimate of the 654 00:39:57.934 --> 00:39:59.934 ever of those parameters. Parameter estimates. Here is the estimate 655 00:39:59.934 --> 00:40:04.934 of the error and then it performs the t-test for significant of those 656 00:40:04.934 --> 00:40:06.934 parameters. 657 00:40:06.934 --> 00:40:12.934 Basically, the value is how strong is the relationship between 658 00:40:12.934 --> 00:40:18.934 observed valuables. With the really care about 659 00:40:18.934 --> 00:40:27.934 is the P-Value 660 00:40:27.934 --> 00:40:30.934 of the slope. This is a measure of 661 00:40:30.934 --> 00:40:34.934 how good is the model. How strong is the relationship between two 662 00:40:34.934 --> 00:40:38.934 parameters. P-Value is really small in this case. We have a strong relationship 663 00:40:38.934 --> 00:40:44.934 between the two variables. If P-Value is large, what does 664 00:40:44.934 --> 00:40:47.934 this mean? 665 00:40:47.934 --> 00:40:49.934 It means slope is zero so basically the slope 666 00:40:49.934 --> 00:40:55.934 is constant, there is no relationship between the variables. 667 00:40:55.934 --> 00:41:02.934 So slope is negative. 668 00:41:02.934 --> 00:41:06.934 That is nice, but is agreement between the previous two tests, which we 669 00:41:06.934 --> 00:41:11.934 hope that will be the outcome. And we can move on from this point down 670 00:41:11.934 --> 00:41:13.934 to the next table. 671 00:41:13.934 --> 00:41:19.934 So, in the second table, we have another table put we have 672 00:41:19.934 --> 00:41:25.934 sources of variation looking down in regression, 673 00:41:25.934 --> 00:41:31.934 which means how much of the variability 674 00:41:31.934 --> 00:41:35.934 is explained with the model that we just don't. So, with the equation 675 00:41:35.934 --> 00:41:39.934 we just informed it the ever totem is explained variation. 676 00:41:39.934 --> 00:41:44.934 And then this total is basically the sum of two. It is the total 677 00:41:44.934 --> 00:41:49.934 variation. Here on the right-hand side we have a test for regression 678 00:41:49.934 --> 00:41:55.934 and here I want to mention this is 679 00:41:55.934 --> 00:42:01.934 basically the only part really and regression analysis 680 00:42:01.934 --> 00:42:07.934 that is sensitive to non-normality of the residuals. I 681 00:42:07.934 --> 00:42:13.934 will explain what residuals are in a moment I 682 00:42:13.934 --> 00:42:16.934 want to highlight there is really no requirement for normality of 683 00:42:16.934 --> 00:42:22.934 our data. But all assumptions are about the residuals. 684 00:42:22.934 --> 00:42:26.934 So, P-Value is a small, which again confirms that 685 00:42:26.934 --> 00:42:31.934 our model shows a strong relationship between the 686 00:42:31.934 --> 00:42:37.934 two variables. Here on the bottom, we have our 687 00:42:37.934 --> 00:42:46.000 square and probably most of you are very familiar bull 688 00:42:46.000 --> 00:42:51.000 with that. Statisticians are making the decisions based on the our square. 689 00:42:51.000 --> 00:42:54.000 Adjusted our square is a little bit more conservative. 690 00:42:54.000 --> 00:42:59.000 That is why I am suggesting you to basically use 691 00:42:59.000 --> 00:43:05.000 adjusting our square as a measure, another measure 692 00:43:05.000 --> 00:43:08.000 to evaluate the model. 693 00:43:08.000 --> 00:43:17.000 What it means, this number is basically 83.3% 694 00:43:17.000 --> 00:43:22.000 in this case of variation is explained by this regression model. Basically, 695 00:43:22.000 --> 00:43:28.000 the meaning is present variability explained by the regression 696 00:43:28.000 --> 00:43:31.000 model. 697 00:43:31.000 --> 00:43:35.000 It is not the best measure. We still need to look into the assumptions 698 00:43:35.000 --> 00:43:41.000 but it gives us some ideas about how good is the model. 699 00:43:41.000 --> 00:43:46.000 So, main advantages of the ordinary list 700 00:43:46.000 --> 00:43:51.000 square regression arm is a pretty standard approach 701 00:43:51.000 --> 00:43:57.000 so most of the users are familiar with it. 702 00:43:57.000 --> 00:44:01.000 It provides more information than either 703 00:44:01.000 --> 00:44:06.000 of the nonparametric tests. Besides the estimate for slope and intercept, 704 00:44:06.000 --> 00:44:10.000 we also get our information about the uncertainty 705 00:44:10.000 --> 00:44:20.000 of both parameters. Regression analysis also provides us confidence 706 00:44:20.000 --> 00:44:23.000 Benz. There's confidence bends can be used to determine compliance 707 00:44:23.000 --> 00:44:28.000 with the extent of cleanup levels, even with the trend is apparent. 708 00:44:28.000 --> 00:44:32.000 Even when concentration of the pollutant is changing, we 709 00:44:32.000 --> 00:44:38.000 can still use those confidence bands to compare 710 00:44:38.000 --> 00:44:44.000 with standards and make conclusions. 711 00:44:44.000 --> 00:44:49.000 So, the downside of the regression analysis is that it is really sensitive 712 00:44:49.000 --> 00:44:57.000 to extreme outliers. 713 00:44:57.000 --> 00:45:00.000 And underlying assumptions. There are three assumptions for residuals 714 00:45:00.000 --> 00:45:04.000 that we need to check to make the final conclusion about the result 715 00:45:04.000 --> 00:45:10.000 of the regression model. So, in the next step, I will 716 00:45:10.000 --> 00:45:16.000 show you how to go about the the residual analysis. 717 00:45:16.000 --> 00:45:21.000 First, let's explain what residuals are. If we 718 00:45:21.000 --> 00:45:26.000 take our regression equation that we talked about a little bit ago 719 00:45:26.000 --> 00:45:32.000 and Clark in time and date, 720 00:45:32.000 --> 00:45:37.000 the results that we get our cold fitted values were model outcomes. 721 00:45:37.000 --> 00:45:43.067 Because our model doesn't perfectly fit the data, we 722 00:45:43.067 --> 00:45:46.000 said before this model for our training data 723 00:45:46.000 --> 00:45:49.000 explained that 83% of variation. 724 00:45:49.000 --> 00:45:54.000 So the fitted values are different from 725 00:45:54.000 --> 00:45:57.000 the observations. 726 00:45:57.000 --> 00:46:01.000 So, the residuals are actually the difference between the two. 727 00:46:01.000 --> 00:46:07.000 Observed values minus fitted values gives us residuals. 728 00:46:07.000 --> 00:46:15.000 Regression analysis give us this bottom table, regression 729 00:46:15.000 --> 00:46:21.000 table, where we have the 730 00:46:21.000 --> 00:46:24.000 fitted values and residuals. 731 00:46:24.000 --> 00:46:27.000 It calculates that for us. 732 00:46:27.000 --> 00:46:32.000 There are three assumptions that we need to 733 00:46:32.000 --> 00:46:34.000 check. 734 00:46:34.000 --> 00:46:39.000 First, they are all related to residuals. The first one is constant 735 00:46:39.000 --> 00:46:43.067 variance, or total elasticity 736 00:46:43.067 --> 00:46:46.000 of residuals. We need to confirm the residuals are independent into 737 00:46:46.000 --> 00:46:51.000 that the residuals are normally distributed. 738 00:46:51.000 --> 00:46:56.000 So, remember there is no requirement for data itself to be normally distributed 739 00:46:56.000 --> 00:47:04.000 but this requirement needs to hold for the residuals. 740 00:47:04.000 --> 00:47:10.000 Many times, checking these assumptions is overlooked. 741 00:47:10.000 --> 00:47:15.000 We do need to check then. So, I will 742 00:47:15.000 --> 00:47:24.000 so you know how to do that. We need to do little bit of extra work. 743 00:47:24.000 --> 00:47:30.000 We need to copy this part of the 744 00:47:30.000 --> 00:47:36.000 regression table. The easiest way to copy and paste it in Excel and 745 00:47:36.000 --> 00:47:40.000 open it again in Excel. When you do that, sometimes 746 00:47:40.000 --> 00:47:46.000 when you paste the data in the XL, you have 747 00:47:46.000 --> 00:47:51.000 leading blank spaces that they don't like 748 00:47:51.000 --> 00:47:57.000 to do the analysis because that makes the values not numerical. 749 00:47:57.000 --> 00:48:03.000 So we provided you on the slide help with how to remove 750 00:48:03.000 --> 00:48:07.000 those leading spices. They are listed there but I am not going 751 00:48:07.000 --> 00:48:12.000 to for the six of them, I am not going to demonstrate it. 752 00:48:12.000 --> 00:48:18.000 I did that before so we can just move on with ProUCL 753 00:48:18.000 --> 00:48:24.000 features. So I am opening now the file, which 754 00:48:24.000 --> 00:48:36.000 is residuals. 755 00:48:36.000 --> 00:48:42.067 >> You will need to switch it to XL. 756 00:48:42.067 --> 00:48:48.000 >> Thank you Travis. It is the 757 00:48:48.000 --> 00:48:51.000 XLS file. 758 00:48:51.000 --> 00:48:59.000 Residual analysis, this one, right? 759 00:48:59.000 --> 00:49:03.000 Here we have the same table that we put into 760 00:49:03.000 --> 00:49:09.000 the ProUCL. What we do now, we will basically use of the time 761 00:49:09.000 --> 00:49:12.000 series plot to make some plots of those residuals. 762 00:49:12.000 --> 00:49:18.000 The first plot that I will create is 763 00:49:18.000 --> 00:49:24.000 the residuals for fitted value. I am selecting 764 00:49:24.000 --> 00:49:34.000 this data set, statistical test, trend analysis, time series plot. 765 00:49:34.000 --> 00:49:40.000 We will need the event data now plodding 766 00:49:40.000 --> 00:49:45.934 on the event so under X axis, I am plodding fitted values. 767 00:49:45.934 --> 00:49:49.934 There by axis, I am plotting our residuals. 768 00:49:49.934 --> 00:49:55.934 And okay. 769 00:49:55.934 --> 00:50:00.934 So now I will do this plot a little bit nicer so that 770 00:50:00.934 --> 00:50:04.934 we are not too distracted. I am going into properties, 771 00:50:04.934 --> 00:50:10.934 series, I want this to be scatterplot 772 00:50:10.934 --> 00:50:15.934 and I am going to make bullets a little bit bigger so it will be 773 00:50:15.934 --> 00:50:21.934 easier to see. Okay, this is now our plot. 774 00:50:21.934 --> 00:50:26.934 I can just show you real quickly how to change 775 00:50:26.934 --> 00:50:29.934 the title. 776 00:50:29.934 --> 00:50:34.934 You right-click and this little menu pops up and 777 00:50:34.934 --> 00:50:40.934 you can have it 778 00:50:40.934 --> 00:50:43.934 residuals, fitted values. 779 00:50:43.934 --> 00:50:46.934 Okay. 780 00:50:46.934 --> 00:50:52.934 So we want this picture to be, the scatter of the plot, to 781 00:50:52.934 --> 00:50:53.934 be as random as possible. 782 00:50:53.934 --> 00:50:58.934 This is not completely random but it is not the worst I have seen. 783 00:50:58.934 --> 00:51:02.934 In this case, I am going to do what I would say 784 00:51:02.934 --> 00:51:08.934 variance is roughly constant. This plot tells us about the 785 00:51:08.934 --> 00:51:14.934 first assumption, the variance residuals constant. 786 00:51:14.934 --> 00:51:20.934 We will say okay, assumption is 787 00:51:20.934 --> 00:51:23.934 satisfied. 788 00:51:23.934 --> 00:51:31.934 The second plot is to check the second assumption 789 00:51:31.934 --> 00:51:34.934 for the independent. I will again create a timeseries plot of residuals 790 00:51:34.934 --> 00:51:40.934 and this time I will plot them against the consecutive event number. 791 00:51:40.934 --> 00:51:49.934 Basically, let me Paul the data. 792 00:51:49.934 --> 00:51:54.934 Timeseries plot again. 793 00:51:54.934 --> 00:51:57.934 This time, event is our observation. 794 00:51:57.934 --> 00:52:02.934 This column that tells us the number of the observation. 795 00:52:02.934 --> 00:52:05.934 Observation and residuals. 796 00:52:05.934 --> 00:52:17.934 Again, we will create, sorry for that. 797 00:52:17.934 --> 00:52:23.934 Observations, residuals. Okay. 798 00:52:23.934 --> 00:52:35.934 Where is the plot? 799 00:52:35.934 --> 00:52:52.000 Try again. 800 00:53:11.000 --> 00:53:16.000 Let me just explain to you. We will play the same plot. Is on the 801 00:53:16.000 --> 00:53:22.000 slide. Similar plot, we want scatterplot to be random and we 802 00:53:22.000 --> 00:53:26.000 don't want to see any unusual patterns. If you 803 00:53:26.000 --> 00:53:32.000 see on the slide that we presented, you seem the 804 00:53:32.000 --> 00:53:38.000 second half of this life if maybe Travis you can 805 00:53:38.000 --> 00:53:43.067 get the green arrow or it is some kind of curvature. We 806 00:53:43.067 --> 00:53:46.000 don't want those curvatures in the plot. That is 807 00:53:46.000 --> 00:53:51.000 an indication that we have what is called black feet. In 808 00:53:51.000 --> 00:53:56.000 this case, the second assumption is not 809 00:53:56.000 --> 00:54:02.000 completely satisfied. So we can move on to the third 810 00:54:02.000 --> 00:54:06.000 assumption. The third assumption is about the normality 811 00:54:06.000 --> 00:54:11.000 of the residuals. So prove for sprints at the normality of the 812 00:54:11.000 --> 00:54:19.000 residuals, we will do the goodness of fit test. So, 813 00:54:19.000 --> 00:54:23.000 I will again pull the staple, go to statistical test, goodness 814 00:54:23.000 --> 00:54:28.000 of fit, we want the one for normality. And we want 815 00:54:28.000 --> 00:54:33.000 to perform this test on residuals. Okay. Let's 816 00:54:33.000 --> 00:54:39.000 cross our fingers that this will work. 817 00:54:39.000 --> 00:54:45.000 So, here we see this point. They are very close to 818 00:54:45.000 --> 00:54:50.000 the line. This is not perfect but it is a reasonable line. 819 00:54:50.000 --> 00:54:53.000 If we look at the results of the normality 820 00:54:53.000 --> 00:54:59.000 test here on the right-hand side, we see here 821 00:54:59.000 --> 00:55:06.000 in the middle part where I am circling now it says 822 00:55:06.000 --> 00:55:12.000 data appears normal. So this test confirms that our residuals are 823 00:55:12.000 --> 00:55:17.000 normally distributed, so the third assumption is also 824 00:55:17.000 --> 00:55:20.000 confirmed. 825 00:55:20.000 --> 00:55:25.000 So, to summarize, if any of the assumptions are 826 00:55:25.000 --> 00:55:31.000 substantially violated and a list square 827 00:55:31.000 --> 00:55:36.000 regression has a little bit of variance. If the assumption 828 00:55:36.000 --> 00:55:42.067 is violated, that might indicate that the trend is either 829 00:55:42.067 --> 00:55:48.000 nonlinear or the magnitude independent, the main concentration 830 00:55:48.000 --> 00:55:54.000 level. We have what we call a lack of fit. 831 00:55:54.000 --> 00:55:58.000 What does it mean is that the model we have built is not perfect. We 832 00:55:58.000 --> 00:56:03.000 can improve it but there is an opportunity to improve 833 00:56:03.000 --> 00:56:09.000 it but when this really matters, when we want to improve the model 834 00:56:09.000 --> 00:56:12.000 but this really matters when we are interested for predictions. 835 00:56:12.000 --> 00:56:16.000 If you just want to evaluate whether you have a friend to present, a 836 00:56:16.000 --> 00:56:22.000 downward or upward trend on your data then 837 00:56:22.000 --> 00:56:27.000 not a perfect model will show you that. If you want to predict or 838 00:56:27.000 --> 00:56:32.000 if you want to make conclusions about the rate of decay, 839 00:56:32.000 --> 00:56:38.000 in that case, you want to improve the model. 840 00:56:38.000 --> 00:56:42.067 ProUCL is a very limited in what kind of improvements 841 00:56:42.067 --> 00:56:51.000 it can make. Basically the only improvement in the model 842 00:56:51.000 --> 00:56:55.000 we can handle and ProUCL is transforming the data. Even 843 00:56:55.000 --> 00:57:01.000 that is not really encouraged. We need to make some 844 00:57:01.000 --> 00:57:07.000 extra steps with the data. The other options are like adding 845 00:57:07.000 --> 00:57:12.000 the variables or adding polynomial toward hymns but these are 846 00:57:12.000 --> 00:57:17.000 more advanced techniques when I strongly recommend you 847 00:57:17.000 --> 00:57:25.000 go to statistician and work with a statistician if you want to protect 848 00:57:25.000 --> 00:57:30.000 so before we jump into transforming the data, 849 00:57:30.000 --> 00:57:35.000 I will demonstrate how you can do it. I want to give you some additional 850 00:57:35.000 --> 00:57:40.000 guidelines when you can kind of 851 00:57:40.000 --> 00:57:45.000 get an information from the site if transformation of the data as 852 00:57:45.000 --> 00:57:47.000 the right way to go. 853 00:57:47.000 --> 00:57:53.000 So, if you have a visible exponential decay express the next financial 854 00:57:53.000 --> 00:57:59.000 trend on the timeseries plot and let me be a consequence of 855 00:57:59.000 --> 00:58:04.000 the first order reaction. In this case, the 856 00:58:04.000 --> 00:58:06.000 rate of decay of the contaminant is proportional to 857 00:58:06.000 --> 00:58:08.000 the amount of contaminant present. 858 00:58:08.000 --> 00:58:14.000 More contaminant present that you are observing faster is the decay. 859 00:58:14.000 --> 00:58:19.000 Practical example of this is the 860 00:58:19.000 --> 00:58:25.000 solution of contaminated groundwater, which no absorption of it from 861 00:58:25.000 --> 00:58:28.000 the soil. 862 00:58:28.000 --> 00:58:36.000 In this case, when we know these kinds of reactions 863 00:58:36.000 --> 00:58:39.000 can be present on the site and receive the exponential pattern 864 00:58:39.000 --> 00:58:45.000 on the data, the data makes sense. 865 00:58:45.000 --> 00:58:52.000 Another case may be that we have zero order reaction, which is expressed 866 00:58:52.000 --> 00:58:55.000 as a linear decay rate. 867 00:58:55.000 --> 00:59:03.000 It is basically the decay rate is limited by a limiting factor. 868 00:59:03.000 --> 00:59:06.000 It is constant instead of exponential. 869 00:59:06.000 --> 00:59:12.000 So some examples of zero order reaction so that maybe 870 00:59:12.000 --> 00:59:20.000 in the media are bio 871 00:59:20.000 --> 00:59:22.000 dictation limiting the toxicity of contaminant or nutrient limited 872 00:59:22.000 --> 00:59:29.000 biodegradation or we have maybe absorbed contaminant that is distorting 873 00:59:29.000 --> 00:59:34.000 groundwater pollutes contaminant concentration. So, in this case, 874 00:59:34.000 --> 00:59:40.000 transformation of data won't help. 875 00:59:40.000 --> 00:59:43.934 But if we see that the model is not perfect, we need 876 00:59:43.934 --> 00:59:48.934 to take some other approach. So, options are non-linear fit so 877 00:59:48.934 --> 00:59:53.934 polynomial regression or adding more exploratory variables 878 00:59:53.934 --> 00:59:59.934 but these are advanced techniques that need assistance of a 879 00:59:59.934 --> 01:00:06.934 study to Titian into some better software with more capabilities. 880 01:00:06.934 --> 01:00:12.934 So, okay. Now let's show how you can 881 01:00:12.934 --> 01:00:15.934 do transformations. 882 01:00:15.934 --> 01:00:21.934 For transformation, you will need to go to XL and and 883 01:00:21.934 --> 01:00:28.934 an additional column to your data whether you are 884 01:00:28.934 --> 01:00:36.934 in XL or some other spreadsheet software. 885 01:00:36.934 --> 01:00:43.000 So, here in my spreadsheet, I have already done that. Just 886 01:00:43.000 --> 01:00:47.934 so you want to take a note, I used the natural logarithm. You can do 887 01:00:47.934 --> 01:00:51.934 the logarithm as well but I used the natural logarithm so that you 888 01:00:51.934 --> 01:00:56.934 can replicate what I am working on here. So and 889 01:00:56.934 --> 01:01:02.934 now we can repeat the regression analysis 890 01:01:02.934 --> 01:01:07.934 with this log transformed variable. There 891 01:01:07.934 --> 01:01:15.934 are some downsides of the regression with log transformed data 892 01:01:15.934 --> 01:01:20.934 so it is really probably this is the time to go to a statistician. 893 01:01:20.934 --> 01:01:23.934 But for some of you, let me be a little bit more 894 01:01:23.934 --> 01:01:29.934 advanced. Demonstrate how you can do that in ProUCL. So, I 895 01:01:29.934 --> 01:01:36.934 will, instead of the variable 896 01:01:36.934 --> 01:01:39.934 in the original skill, I will use now the log transformed as a dependent 897 01:01:39.934 --> 01:01:48.934 variable and then the time and date of independent variable. Okay? 898 01:01:48.934 --> 01:01:50.934 Before, we will first looked at the regression plot. 899 01:01:50.934 --> 01:01:55.934 So regression plot here with the confidence and protection intervals, 900 01:01:55.934 --> 01:02:01.934 we see a little bit in those 901 01:02:01.934 --> 01:02:07.934 points around the regression plot but it 902 01:02:07.934 --> 01:02:09.934 is not too bad. 903 01:02:09.934 --> 01:02:13.934 Now let's look at the results of the regression. Again, I will 904 01:02:13.934 --> 01:02:16.934 switch to the spreadsheet because it has more information. So, in 905 01:02:16.934 --> 01:02:22.934 the regression estimate table, we have intercept 906 01:02:22.934 --> 01:02:25.934 and slope. 907 01:02:25.934 --> 01:02:30.934 Remember now that these are log transformed data 908 01:02:30.934 --> 01:02:35.934 so the values may not be straightforward to interpret. 909 01:02:35.934 --> 01:02:41.934 In terms of the rate of decay, let's say. P-Value's appeared 910 01:02:41.934 --> 01:02:47.000 here are the errors. Let's look at the P-Value 911 01:02:47.000 --> 01:02:53.000 for slope. 912 01:02:53.000 --> 01:02:55.000 P-Value is a small, which indicate that there 913 01:02:55.000 --> 01:02:57.000 is a relationship between the statistical significant relationship between 914 01:02:57.000 --> 01:02:58.000 the dependent and independent variable. 915 01:02:58.000 --> 01:03:01.000 During the contaminant and time. 916 01:03:01.000 --> 01:03:09.000 And another table, we have ever 917 01:03:09.000 --> 01:03:12.000 terms and here is the statistical test for aggression. Statistical 918 01:03:12.000 --> 01:03:17.000 test indicates that regression is statistically significant and if 919 01:03:17.000 --> 01:03:33.000 we look at adjusted R Square as 920 01:03:33.000 --> 01:03:36.000 one of the indicators for regression, adjusted R square we set is more 921 01:03:36.000 --> 01:03:39.000 conservative, it is a little bit higher now. 0.874. which, many 922 01:03:39.000 --> 01:03:44.000 people would quickly say, okay, we have a better model. But remember, 923 01:03:44.000 --> 01:03:48.000 we really can't make final conclusions before we look 924 01:03:48.000 --> 01:03:51.000 at the residuals. 925 01:03:51.000 --> 01:03:57.000 Here on the bottom, we have again the residual table. 926 01:03:57.000 --> 01:04:01.000 So, you will take the same steps as before, take 927 01:04:01.000 --> 01:04:07.000 this table in XL and bring it in 928 01:04:07.000 --> 01:04:10.000 ProUCL. 929 01:04:10.000 --> 01:04:15.000 I prepared a data table in excel already 930 01:04:15.000 --> 01:04:18.000 so I will open it now. 931 01:04:18.000 --> 01:04:21.000 It should be XLS again. 932 01:04:21.000 --> 01:04:26.000 I think I have and it in. Longoria 933 01:04:26.000 --> 01:04:32.000 longer correction. These are my residuals for 934 01:04:32.000 --> 01:04:38.000 log regression. I am opening now this table. You see here 935 01:04:38.000 --> 01:04:42.067 log transformed data. These are fitted values and residuals. 936 01:04:42.067 --> 01:04:48.000 We will again repeat the same plot as we did before for diagnostic 937 01:04:48.000 --> 01:04:51.000 the regression model. 938 01:04:51.000 --> 01:04:56.000 So, first I am going to plot residuals 939 01:04:56.000 --> 01:04:59.000 versus fitted values. 940 01:04:59.000 --> 01:05:05.000 I am going to the data 941 01:05:05.000 --> 01:05:11.000 table. Statistical test, trend analysis, we both use time 942 01:05:11.000 --> 01:05:17.000 series plot and tweak it a little bit, just the same as before. 943 01:05:17.000 --> 01:05:23.000 Residuals as measured data, why is event. On 944 01:05:23.000 --> 01:05:29.000 X axis, okay, here is our plot now. 945 01:05:29.000 --> 01:05:35.000 I am tweaking it, going to properties, series 946 01:05:35.000 --> 01:05:39.000 scatterplot, making bullets a 947 01:05:39.000 --> 01:05:48.000 little bit bigger so it is easier to see. Okay. 948 01:05:48.000 --> 01:05:52.000 So with 949 01:05:52.000 --> 01:05:57.000 that before checking the first assumption, we want this scatter 950 01:05:57.000 --> 01:06:01.000 to be as random as possible. It's assumption is that the residuals 951 01:06:01.000 --> 01:06:06.000 are not having a constant variance. 952 01:06:06.000 --> 01:06:16.000 This picture is not too bad. I would say first assumption is approved. 953 01:06:16.000 --> 01:06:19.000 That the variance is reasonably constant. Now, let's create the 954 01:06:19.000 --> 01:06:31.000 second plot to check the second assumption that residuals 955 01:06:31.000 --> 01:06:37.000 so, I am taking residuals into measured value 956 01:06:37.000 --> 01:06:43.067 and observation as event on X part. Okay. 957 01:06:43.067 --> 01:06:49.000 Oh, this time it worked. Nice. I am tweaking it again. 958 01:06:49.000 --> 01:06:59.000 Series scatterplot. 959 01:06:59.000 --> 01:07:04.000 It is always better to look at scatterplot so we are not distracted 960 01:07:04.000 --> 01:07:07.000 with the line. 961 01:07:07.000 --> 01:07:12.000 So, this time we see this curvature may be even 962 01:07:12.000 --> 01:07:16.000 more pronounced. It is going the other direction upwards 963 01:07:16.000 --> 01:07:20.000 but it is maybe even more pronounced, so 964 01:07:20.000 --> 01:07:26.000 this definitely indicates there is a lack of fit. 965 01:07:26.000 --> 01:07:32.000 So, the residuals are not completely independent. 966 01:07:32.000 --> 01:07:36.000 Now, the third assumption, we need to do another 967 01:07:36.000 --> 01:07:42.067 goodness of fit test for log transformed data. 968 01:07:42.067 --> 01:07:45.000 So, let me do that. 969 01:07:45.000 --> 01:07:50.000 I am going to log regressions, statistical test, goodness 970 01:07:50.000 --> 01:08:03.000 of fit. We want to check for normality. Taking residuals, okay. 971 01:08:03.000 --> 01:08:07.000 So, this plot doesn't look at that nice now. Let me just make 972 01:08:07.000 --> 01:08:13.000 those bullets a little bit bigger so that we see better. 973 01:08:13.000 --> 01:08:19.000 We see this around 974 01:08:19.000 --> 01:08:25.000 the plot and if we look at the outcome 975 01:08:25.000 --> 01:08:30.000 of the goodness of fit test, here in the middle 976 01:08:30.000 --> 01:08:35.000 it says that they are not normal. 977 01:08:35.000 --> 01:08:40.000 So the third assumption definitely is not confirmed. 978 01:08:40.000 --> 01:08:46.000 So, no, what did we learn from all this? 979 01:08:46.000 --> 01:08:52.000 So, you really can't rely on R square. 980 01:08:52.000 --> 01:09:05.000 R square was a little bit better but it really didn't 981 01:09:05.000 --> 01:09:07.000 contribute to the problem with residuals. You need to look at residuals, 982 01:09:07.000 --> 01:09:10.000 need to take the assumptions. To give us a lot of information about 983 01:09:10.000 --> 01:09:14.000 the regression model. So, plotting residuals will actually read the 984 01:09:14.000 --> 01:09:18.000 lack of a fit of the model. What we haven't seen in our example but 985 01:09:18.000 --> 01:09:24.000 will also show on residual pots extreme value outliers. 986 01:09:24.000 --> 01:09:30.000 That is another reason why to take time and analyze. 987 01:09:30.000 --> 01:09:35.000 The point to remember is that when you can't confirm the assumptions 988 01:09:35.000 --> 01:09:41.000 for the residuals, and you 989 01:09:41.000 --> 01:09:47.934 do have a need to improve the model to can do some 990 01:09:47.934 --> 01:09:51.934 predictions, then that is definitely the time to work with statisticians 991 01:09:51.934 --> 01:09:56.934 and find a way to best analyze your data. This brings us almost to the 992 01:09:56.934 --> 01:10:00.934 end of the first session. Next slide we will see 993 01:10:00.934 --> 01:10:09.934 on the screen is the comparison of three trend 994 01:10:09.934 --> 01:10:12.934 tests we explored today. So, at the beginning we looked at the two 995 01:10:12.934 --> 01:10:14.934 nonparametric tests that are both nice starting point when we are 996 01:10:14.934 --> 01:10:17.934 looking for trends in the data. 997 01:10:17.934 --> 01:10:23.934 So Mann-Kendall will tell us if we have a consistent or monotone 998 01:10:23.934 --> 01:10:29.934 trend, statically increasing or study decreasing. 999 01:10:29.934 --> 01:10:33.934 The nice thing about this test is that it will give us a reasonable 1000 01:10:33.934 --> 01:10:37.934 outcomes with as little as four points. Remember the power of the 1001 01:10:37.934 --> 01:10:43.934 test when we have a small Beta test low. 1002 01:10:43.934 --> 01:10:46.934 Even if the trend is present, it may not 1003 01:10:46.934 --> 01:10:51.934 show because of the low power of the test. So, the next task nonparametric 1004 01:10:51.934 --> 01:10:57.934 test is Theil-Sen. It identifies the transit 1005 01:10:57.934 --> 01:11:05.934 confirms the trend observed with Mann-Kendall. It also gives a slope 1006 01:11:05.934 --> 01:11:10.934 estimate. 1007 01:11:10.934 --> 01:11:15.934 But, for the contrast of the Mann-Kendall test requires a fair amount of 1008 01:11:15.934 --> 01:11:20.934 data and it only works when we have one observation per time interval. 1009 01:11:20.934 --> 01:11:25.934 However, it averages repeated measurements of the same sampling 1010 01:11:25.934 --> 01:11:30.934 event. So, if you have repeated measurements, remember 1011 01:11:30.934 --> 01:11:33.934 to check that box. 1012 01:11:33.934 --> 01:11:41.934 And the third metric we looked at in ProUCL is 1013 01:11:41.934 --> 01:11:45.934 OLS Regression. This is the most advanced of the three methods. 1014 01:11:45.934 --> 01:11:50.934 Because of that, it also gives us the most information. It evaluates 1015 01:11:50.934 --> 01:11:56.934 slope and intercept. It gives us estimate for both parameters 1016 01:11:56.934 --> 01:12:00.934 and there are three assumptions for 1017 01:12:00.934 --> 01:12:05.934 residuals that need to be confirmed. 1018 01:12:05.934 --> 01:12:11.934 So, it does require a little bit more work but it really gives 1019 01:12:11.934 --> 01:12:16.934 us the residual analysis can reveal a lot about 1020 01:12:16.934 --> 01:12:24.934 the data. Another downside of the ordinary square regression 1021 01:12:24.934 --> 01:12:27.934 is it also requires a fair amount of 1022 01:12:27.934 --> 01:12:38.934 data to obtain reliable perimeter estimates. 1023 01:12:38.934 --> 01:12:41.934 So, this is a more or less everything we wanted to cover today. It is 1024 01:12:41.934 --> 01:12:47.000 time for a second quiz. If we can show that on the screen now. 1025 01:12:47.000 --> 01:12:53.000 And then Travis will make a short recap and if he has something 1026 01:12:53.000 --> 01:12:57.000 to add. 1027 01:12:57.000 --> 01:13:05.000 >> Okay. We are going to stick that second quiz questions. Travis or 1028 01:13:05.000 --> 01:13:07.000 Polona, we have had people ask if you could read questions out 1029 01:13:07.000 --> 01:13:10.000 loud because some are following along on the phones. Going to start 1030 01:13:10.000 --> 01:13:14.000 that quiz now. Feel free to read them out to them. 1031 01:13:14.000 --> 01:13:19.000 >> I don't see them if you can with them Travis. 1032 01:13:19.000 --> 01:13:23.000 >> The R square and adjusted R square 1033 01:13:23.000 --> 01:13:26.000 values tell us what? 1034 01:13:26.000 --> 01:13:31.000 Proportion of the variation that is explained by the cut off but 1035 01:13:31.000 --> 01:13:35.000 his post as a model at the end there and see, the estimate of our 1036 01:13:35.000 --> 01:13:46.000 OLS slope. 1037 01:13:46.000 --> 01:13:52.000 All right. Non-normality of our OLS residuals indicate a lack of 1038 01:13:52.000 --> 01:13:56.000 fit, be our model is 1039 01:13:56.000 --> 01:14:00.000 not optimal, see, the confident in our predicament is not relabeled, 1040 01:14:00.000 --> 01:14:04.000 or the, all of the above. 1041 01:14:04.000 --> 01:14:06.000 >> Okay. 1042 01:14:06.000 --> 01:14:19.000 It looks like the right answer for that one was the. Job everybody. 1043 01:14:19.000 --> 01:14:22.000 >> Just. Real quick. I think we will just make a couple final remarks 1044 01:14:22.000 --> 01:14:26.000 and answer a few more questions at the end. Just to recap everything 1045 01:14:26.000 --> 01:14:32.000 that Polona sat there. 1046 01:14:32.000 --> 01:14:35.000 When you are looking to do trend analysis, really make 1047 01:14:35.000 --> 01:14:37.000 sure you spend time exploring your data before you start doing your 1048 01:14:37.000 --> 01:14:43.067 tests. And, want to have to figure out, especially with OLS, don't 1049 01:14:43.067 --> 01:14:49.000 totally rely on your R square and adjusted R square 1050 01:14:49.000 --> 01:14:54.000 values because they might not be revealing the problems that your 1051 01:14:54.000 --> 01:15:02.000 underlying assumptions need to have validated. 1052 01:15:02.000 --> 01:15:06.000 Also, if you are thinking, transforming your data, take time to think about 1053 01:15:06.000 --> 01:15:11.000 the processes that might be underlining that need, 1054 01:15:11.000 --> 01:15:15.000 such as the first order or zero order reactions that we discussed 1055 01:15:15.000 --> 01:15:21.000 for a moment there. 1056 01:15:21.000 --> 01:15:24.000 And, really as always, when in doubt consult 1057 01:15:24.000 --> 01:15:27.000 a statistician. I know that was brought up a bunch with the nondetectable 1058 01:15:27.000 --> 01:15:32.000 stuff and I can't say it enough there that 1059 01:15:32.000 --> 01:15:37.000 that one is a tricky subject and you are not totally sure on what, 1060 01:15:37.000 --> 01:15:40.000 you need to talk to people who might know better. That doesn't 1061 01:15:40.000 --> 01:15:42.067 even mean just one. Maybe a fuel. 1062 01:15:42.067 --> 01:15:46.000 People will have different opinions on how to handle non-detect in different 1063 01:15:46.000 --> 01:15:52.000 situations. 1064 01:15:52.000 --> 01:15:55.000 As always, similar to the outliers with last time, 1065 01:15:55.000 --> 01:15:57.000 make sure you are really documenting all the steps in your analysis and 1066 01:15:57.000 --> 01:16:01.000 the decisions that you decide to make. Yeah, real quick, if we want 1067 01:16:01.000 --> 01:16:06.000 to jump into a shoe questions that we had, Jean, did you want to be 1068 01:16:06.000 --> 01:16:10.000 the one I had highlighted there? 1069 01:16:10.000 --> 01:16:13.000 >> One of the participants is asked what should you do if your data 1070 01:16:13.000 --> 01:16:17.000 appear to exhibit a seasonal trend? 1071 01:16:17.000 --> 01:16:23.000 >> So, I picked that one because it can apply to all of them. 1072 01:16:23.000 --> 01:16:28.000 If you are doing ordinary least squares regression 1073 01:16:28.000 --> 01:16:38.000 and when you view your data you don't see a linear trend whether 1074 01:16:38.000 --> 01:16:40.000 that be a seasonal trend or when we look at it initially there looked 1075 01:16:40.000 --> 01:16:44.000 like there was be a quadratic print to it, something nonlinear that 1076 01:16:44.000 --> 01:16:47.000 you want to figure out if there are any transformations 1077 01:16:47.000 --> 01:16:52.000 that work best for your situation, so far as we had happened to look 1078 01:16:52.000 --> 01:16:55.000 at the lognormal transformation because it is something 1079 01:16:55.000 --> 01:17:01.000 that is effective for fixing a quadratic curve. For seasonal things, you 1080 01:17:01.000 --> 01:17:05.000 might want to look at aggregating your data in some way to get rid 1081 01:17:05.000 --> 01:17:15.000 of that seasonality but again, really any of those are going to 1082 01:17:15.000 --> 01:17:20.000 beat this dead horse that you should talk to a statistician. The answer 1083 01:17:20.000 --> 01:17:24.000 isn't clear to you as to how you want to 1084 01:17:24.000 --> 01:17:27.000 handle it, you need to make sure to talk to someone but it is clear 1085 01:17:27.000 --> 01:17:33.000 to them. And then so there were some other questions in their 1086 01:17:33.000 --> 01:17:36.000 but individuals had asked and I got a little ahead of myself and 1087 01:17:36.000 --> 01:17:40.000 at entered directly to them. I realize some of them might be helpful for 1088 01:17:40.000 --> 01:17:43.067 you all. 1089 01:17:43.067 --> 01:17:50.000 Some one had asked the question that, in a previous 1090 01:17:50.000 --> 01:17:55.000 webinar of how do you save all of the work that you have done inside 1091 01:17:55.000 --> 01:17:56.000 of ProUCL. 1092 01:17:56.000 --> 01:17:57.000 >> I can show. 1093 01:17:57.000 --> 01:18:05.000 >> You are just going to highlight. 1094 01:18:05.000 --> 01:18:09.000 >> I highlighted here on the navigation 1095 01:18:09.000 --> 01:18:15.000 panel the name of the item that you want to save. Go to file, save 1096 01:18:15.000 --> 01:18:18.000 as and to save it. 1097 01:18:18.000 --> 01:18:26.000 >> Yes. Cool. 1098 01:18:26.000 --> 01:18:30.000 Someone else had asked as far as ProUCL's need to have a numeric 1099 01:18:30.000 --> 01:18:35.000 value for the time estimates, could you also have a text column in their. 1100 01:18:35.000 --> 01:18:46.000 The answer is to cut but 1101 01:18:46.000 --> 01:18:49.000 if you need it for some sort of presentations at the, feel free 1102 01:18:49.000 --> 01:18:52.000 to throw it in there. You are not going to be able to use it for any 1103 01:18:52.000 --> 01:18:54.000 of the data analysis. When you are selecting your independent and dependent 1104 01:18:54.000 --> 01:18:57.000 variable, you just going to want to make sure you don't select that 1105 01:18:57.000 --> 01:19:02.000 character: and in fact select the numeric one. 1106 01:19:02.000 --> 01:19:10.000 >> And another remark here is that it is especially important 1107 01:19:10.000 --> 01:19:15.000 because if you don't capture that your events are unevenly 1108 01:19:15.000 --> 01:19:20.000 placed, let's say five days followed by 1109 01:19:20.000 --> 01:19:25.000 10 days in between the event and something like that, you may miss 1110 01:19:25.000 --> 01:19:29.000 the shape of your trend. 1111 01:19:29.000 --> 01:19:36.000 >> I think that was, also I am aware there were a lot 1112 01:19:36.000 --> 01:19:41.000 of questions asking for a ProUCL session just on dealing with non-detect 1113 01:19:41.000 --> 01:19:42.000 and trend analysis. Agreed. 1114 01:19:42.000 --> 01:19:47.934 I think that would be a great one to do. The main focus on the 1115 01:19:47.934 --> 01:19:49.934 three part webinar with just getting people 1116 01:19:49.934 --> 01:19:54.934 comfortable with all of the available tools that we have in ProUCL at 1117 01:19:54.934 --> 01:19:58.934 the moment. Since that is such a large 1118 01:19:58.934 --> 01:20:04.934 topic, it deserves release on webinar and not be shoved in five 1119 01:20:04.934 --> 01:20:08.934 minutes of trying to explain it. That is why we pushed 1120 01:20:08.934 --> 01:20:14.934 it off a bit on this one. It is a tricky topic that we couldn't 1121 01:20:14.934 --> 01:20:19.934 recover and cover everything else that we 1122 01:20:19.934 --> 01:20:23.934 did today as well. Just wanted to let everyone know that their concerns 1123 01:20:23.934 --> 01:20:27.934 are noted. Yes. Jean, anything else? 1124 01:20:27.934 --> 01:20:33.934 >> I think we have a couple of other reminders in terms of the sessions. 1125 01:20:33.934 --> 01:20:37.934 Coming up to our scheduled time and a few 1126 01:20:37.934 --> 01:20:43.934 more remotest walk-through. Preface or Polona, can you take the audience 1127 01:20:43.934 --> 01:20:51.934 through a few final reminders? 1128 01:20:51.934 --> 01:20:54.934 >> Next session, which I believe is on March 9th, correct Jean? Is 1129 01:20:54.934 --> 01:21:06.934 going to be discussing background site comparisons as well as 1130 01:21:06.934 --> 01:21:12.934 UCL's. We finally get 1131 01:21:12.934 --> 01:21:15.934 to the UCL part of ProUCL. 1132 01:21:15.934 --> 01:21:18.934 As always, our contact information is going to be available at the 1133 01:21:18.934 --> 01:21:20.934 end if you want to get hold of us. 1134 01:21:20.934 --> 01:21:36.934 Yes, I think that is most of the housekeeping staff. 1135 01:21:36.934 --> 01:21:41.934 >> Okay. All right. With that, let me walk through a few final reminder 1136 01:21:41.934 --> 01:21:43.934 before we officially close out today's session. What to think the nearly 1137 01:21:43.934 --> 01:21:46.934 500 people who joined us for today's live broadcast. We will walk-through 1138 01:21:46.934 --> 01:21:48.934 just a couple of things. We often get questions about how you can 1139 01:21:48.934 --> 01:21:51.934 stay informed when webinars like this get announced or are available. 1140 01:21:51.934 --> 01:21:56.934 I encourage you to visit us at clue in.work or sign in for a free monthly 1141 01:21:56.934 --> 01:22:03.934 newsletter. We will announce topics like this and 1142 01:22:03.934 --> 01:22:05.934 other topics such as cleaning up hazardous waste the site and most 1143 01:22:05.934 --> 01:22:07.934 of his letters. Copies of the presentation materials are available to download 1144 01:22:07.934 --> 01:22:10.934 from the seminar links and resources page, as well as contact information 1145 01:22:10.934 --> 01:22:12.934 before the organizers. You will see those links already available 1146 01:22:12.934 --> 01:22:18.934 under related URL. School to public interest, click it 1147 01:22:18.934 --> 01:22:20.934 for those of you replaying the recorded version of, those links 1148 01:22:20.934 --> 01:22:25.934 are still active. I have also pasted the URLs into the queue and a window. 1149 01:22:25.934 --> 01:22:30.934 The links are still active even if you were replaying the recorded 1150 01:22:30.934 --> 01:22:37.934 version. I would ask you to fill out our online feedback 1151 01:22:37.934 --> 01:22:39.934 form to let us know what you thought of today's delivery. One of the 1152 01:22:39.934 --> 01:22:56.000 most common questions I get is if we offer certificate 1153 01:22:56.000 --> 01:23:00.000 and we will generate a participation certificate for you within us to 1154 01:23:00.000 --> 01:23:02.000 fill out and submit your feedback. 1155 01:23:02.000 --> 01:23:05.000 Be sure to check the box at the very bottom of the form certifying 1156 01:23:05.000 --> 01:23:07.000 you either here for the whole life event or replace the whole recorded 1157 01:23:07.000 --> 01:23:10.000 the and picture your email address is entered quickly on that one. 1158 01:23:10.000 --> 01:23:13.000 As long as those two things are done, as soon as you submit your 1159 01:23:13.000 --> 01:23:15.000 feedback, you will be able to print out or save a copy of the parts 1160 01:23:15.000 --> 01:23:18.000 patient certificate, something like this one, for your own records. 1161 01:23:18.000 --> 01:23:21.000 If you join together as a group, each person in that room can fill 1162 01:23:21.000 --> 01:23:23.000 out the form on their own whether you would state as an individual 1163 01:23:23.000 --> 01:23:26.000 or not. If you happened to get a bunch of coworkers together to join 1164 01:23:26.000 --> 01:23:29.000 you, please be sure to share the link with that feedback form so 1165 01:23:29.000 --> 01:23:39.000 they can fill out the form and get their own certificates 1166 01:23:39.000 --> 01:23:42.067 for their own records. As noted, today's session was recorded, just 1167 01:23:42.067 --> 01:23:44.000 like the others in the series. In just a few days, to get an automatic 1168 01:23:44.000 --> 01:23:47.000 email from me with instructions of how you can replay today's training. 1169 01:23:47.000 --> 01:23:49.000 If you weren't able to follow along and real-time committee will be 1170 01:23:49.000 --> 01:23:52.000 able to follow those instructions to download the sample data sets 1171 01:23:52.000 --> 01:23:55.000 in ProUCL and once the webinar and it pops and restart it as needed 1172 01:23:55.000 --> 01:23:57.000 to follow along with the exercises. 1173 01:23:57.000 --> 01:23:59.000 Hopefully, will be on for our third and final webinar this weekend please 1174 01:23:59.000 --> 01:24:02.000 be sure to take time to turn your feedback for or broadcast. We do 1175 01:24:02.000 --> 01:24:09.000 read each and every one of those missions and some proof delivery. 1176 01:24:09.000 --> 01:24:11.000 With that, I will formally conclude today's broadcast. Thank you so 1177 01:24:11.000 --> 01:24:12.000 much for joining us. 1178 01:24:12.000 --> 01:24:15.000 >> Thank you everybody. Thank you Gene. 1179 01:24:15.000 --> 01:24:20.000 >> Thanks everyone.