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0:00[Music]
0:07[Music]
0:18Hello, thank you for watching and
0:20welcome to the next video in my series
0:22on basic statistics. Now, as usual, a
0:25few things before we get started. Number
0:27one, if you're watching this video
0:29because you are struggling in a class
0:30right now, I want you to stay positive
0:32and keep your head up. If you're
0:34watching this, it means you've
0:35accomplished quite a bit already. You're
0:38very smart and talented and you may have
0:39just hit a temporary rough patch. Now, I
0:43know with the right amount of hard work,
0:45practice, and patience, you can get
0:47through it. I have faith in you. Many
0:50other people around you have faith in
0:51you. So, so should you. Number two,
0:55please feel free to follow me here on
0:57YouTube, on Twitter, on Google+ or on
1:00LinkedIn. That way, when I upload a new
1:03video, you know about it. And it's
1:05always nice for me to connect with
1:07people who watch my videos online,
1:09wherever in the world you may happen to
1:11be. Now, on the topic of the video, if
1:14you like it, please give it a thumbs up,
1:17share it with classmates or colleagues,
1:18or put it on a playlist, cuz that does
1:21encourage me to keep making them for
1:22you. On the flip side, if you think
1:25there is something I can do better,
1:27please leave a constructive comment
1:28below the video, and I will try to take
1:30those ideas into account when I make new
1:32ones for you. And finally, just keep in
1:35mind that these videos are meant for
1:37individuals who are relatively new to
1:40stats. So, I'm just going over basic
1:42concepts and I will be doing so in a
1:45very slow, deliberate manner. Not only
1:49do I want you to know what's going on,
1:51but also why and how to apply it. So,
1:54all that being said, let's go ahead and
1:56get started.
2:00Okay, so this is the beginning of part
2:02two on our video about type one and type
2:05two errors. So the first part was really
2:07a conceptual background using some
2:09non-statistical real world examples that
2:12you can then take and then apply to the
2:14more statisticalbased examples in this
2:17part of the video. So, if you're still
2:19unsure about sort of the basic
2:21background of type 1 and type two error,
2:24please go back and watch that video
2:26before proceeding with this one because
2:28I think it really sets the stage for
2:30understanding the statistical side of
2:32type 1 and type two error using some
2:34everyday experiences we talked about in
2:37the previous one. So, all that being
2:39said, let's go ahead and dive right into
2:40these examples. Now, these are adapted
2:43from my previous video on null and
2:45alternative hypothesis. So, we'll just
2:46kind of tweak them a bit and then use
2:48them to talk about type one and type two
2:51error. So, remember our first example
2:53was a bottled water manufacturer that
2:56states on its product label that each
2:59bottle contains 355ml of water. So, you
3:03work for a government agency that
3:05protects consumers by testing product
3:08volumes. So, a sample of 50 bottles is
3:12tested. So, you want to make sure that
3:15the manufacturer is being truthful on
3:18their label and that the amount of water
3:20in the bottle is what actually says on
3:22the label. So, what can we assume to be
3:25true? Well, in cases like this, we
3:27assume the label is correct. So, we
3:30assume there is 355 ml of water in the
3:34bottle. Now, we also decided that this
3:36first pair of hypotheses seem to be
3:39appropriate because the bottle is
3:42stating
3:43355 ml. So, that's an equal sign. So,
3:48therefore, the alternative is that it's
3:51not equal to that. So, our first pair is
3:54what we're going to be
3:57using. So, we can write our null and
4:01alternative hypothesis. So our null
4:03hypothesis is that the mean or mu of all
4:08the bottles produced is 355 milliliters.
4:13So that's our assumption. That's what's
4:15on the label. That's what we're assuming
4:17to be true. Now the alternative is that
4:20the mean or the average for all bottles
4:23is not 355 milliliters. So notice again
4:28that the null and the alternative are
4:32opposites and they account for all
4:35possibilities. So the null is that it's
4:37equal and the alternative is that it's
4:40not equal to
4:42355. Now we can set up our little chart
4:44here like we did in the previous video.
4:46So what we're comparing here is the
4:49conclusion of our analysis and the
4:52actual state of reality or the actual
4:54condition over here on the right. So
4:57let's talk about our two conclusions. So
5:00our first conclusion is that we cannot
5:02or do not reject the null hypothesis. So
5:06we take a sample of 50 bottles and they
5:09seem to be pretty close. The average is
5:11maybe 355.2 or 354.6
5:15six or something like that very close to
5:17355 ml. Therefore, we do not reject that
5:22null
5:23hypothesis. But maybe we get a weird
5:26sample just by chance and the mean is
5:29like
5:30340 milliliters, so way underfilled. In
5:34that case, we would most likely reject
5:36the null hypothesis that states the
5:38average bottle volume is 355. So we
5:42would reject our null hypothesis and
5:45then proceed to the alternative that
5:47says the mean volume for bottles is not
5:51355. Now this has to correspond with
5:54some actual state of reality. So the
5:58reality is the bottles overall do have a
6:01mean of 355 or they do not have a mean
6:05of 355. So we have our conclusion from
6:09our analysis and the actual state of
6:11affairs, the actual state of the volume
6:14in all the bottles. Now two of these
6:17generate correct conclusions. So if we
6:21take a sample and it's around 355, we
6:24will not reject our null. And if the
6:28actual state of affairs is that the
6:30bottles are around 355, then that is
6:33correct. We did not reject our null in
6:36our analysis and the bottles are being
6:38filled correctly. Therefore, we're
6:40correct. Now, maybe the bottles are not
6:44being filled correctly. So, we get a
6:46sample. It's not close to 355.
6:49Therefore, we reject the null
6:51hypothesis and the actual state of
6:54affairs is that they are indeed not
6:57being filled correctly. So if we reject
6:59our null and the state of affairs, the
7:02actual condition is that it's not being
7:05filled correctly, then again we've made
7:07a correct conclusion, a correct decision
7:09there. Now, of course, we have type one
7:12and type two error. Let's look at type
7:14one error first. So let's say we get a
7:16sample of or 50 bottles and we come up
7:21with a mean for that sample of
7:25343 millilit a lot lower than
7:28355. Therefore we would probably reject
7:31our null
7:33hypothesis. Now what if our sample is
7:37flawed? Maybe we we got a weird sample
7:40just by chance. And that's the point of
7:42statistics. There's always going to be
7:43this case where we get sort of a weird
7:45sample that's not representative or
7:48something along those lines, but the
7:50bottles in actuality overall are being
7:54filled correctly. So, we rejected our
7:56null hypothesis, but the bottles are
8:00being filled correctly. It's just our
8:02sample has some problem with it. In that
8:04case, we committed a type one error. We
8:08rejected the null hypothesis when we
8:11should not have and that is classic type
8:14one error. Let's talk about type two
8:16error. Let's say that we get a sample
8:20and it's around
8:23355. But in actuality the bottles are
8:26not being filled correctly. So we do not
8:30reject the null hypothesis but the state
8:32of reality is that the bottles are not
8:35being filled correctly. And that is a
8:37type two error. So we do not reject the
8:41null hypothesis when we should have. So
8:44it's a failure to not reject the null
8:48hypothesis. And that is classic type two
8:52error. So again, we're going to walk
8:53through two more examples. So just kind
8:55of think about this for a second and
8:56then apply it as we
8:59go. So example two, down on the farm. So
9:03according to the United States
9:04Department of Agriculture, the
9:06USDA, in 2006, the average farm size in
9:10the state of Texas was 2.3 km. Now,
9:14since the decadel long trend has been
9:16for farm sizes to increase due to large
9:19agra businesses buying up land and
9:21making business bigger farms, a business
9:24analyst wishes to test if the current
9:272013 farm size is larger than it was in
9:322006. So, establish or null and
9:34alternative hypothesis first. So, before
9:36we do that, what is our assumption? What
9:38do we have in the problem to work with?
9:41Well, we can only assume based on what
9:43we have that there has been no change in
9:46farm size since 2006. This is our null
9:50hypothesis. That's all we're given in
9:53the problem. Now, you might say, well,
9:54it says in there that the trend has been
9:57for farm size to increase. Well, so
10:00what? All we can do in our assumption is
10:04test whether or not the farm size has
10:08remained 2.3 km or maybe even decreased.
10:12And then our research hypothesis, our
10:15alternative hypothesis will be that has
10:19increased. So we assume there's been no
10:22change in farm size. We can set up our
10:23hypothesis like this. So our null
10:26hypothesis is that the mean farm size is
10:29equal to or maybe even less than 2.3
10:33square km. That's from our problem. Then
10:36our alternative hypothesis is that the
10:38farm size has indeed increased. So the
10:41average farm size mu is greater than 2.3
10:46square kilmters. So we can go up and set
10:48up our table here. So again, I'm not
10:50going to go into it as much depth as I
10:51did in the last one, but we have two
10:53conclusions. We can we either do not
10:55reject our null hypothesis or we do
10:59reject our null hypothesis based on our
11:02analysis. Now it has to be one of two
11:04actual conditions. Either the farm size
11:07has not changed or even decreased or it
11:11has
11:12increased. If we do not reject the null
11:15and the farm size is in fact less than
11:18or equal to 2.3 km then we are correct.
11:23Now if we reject the null hypothesis so
11:26maybe we get a farm size that's 3.7 km
11:30and indeed the farm size is greater than
11:332.3 km square km then again we are
11:37correct. Those are our two correct
11:39outcomes. Now let's look at the type one
11:42error situation. So in this case we
11:44reject our null hypothesis. So maybe we
11:48get a sample of farms that are a bit
11:50larger than average and therefore our
11:54analysis comes up with a larger farm
11:57size. Now what if the actual state of
12:00affairs the actual condition is that
12:02farm size has not increased or maybe
12:04even decreased. Well there our
12:06conclusion does not match the reality.
12:09So this is classic type one error. We
12:12incorrectly rejected the null. we
12:16wrongly rejected the null hypothesis
12:19when we should not have that is type one
12:22error. Let's look at type two of course
12:25in that case we do not reject the null
12:28hypothesis. So maybe we get um a farm
12:32size that you know is relatively small
12:35or right around 2.3 square kilometers
12:39when in fact farm size has increased. We
12:43just happened to get a
12:46non-representative sample and when we
12:48did our analysis we got you know 2.4
12:52square kilm or something that was not
12:54enough to reject our null hypothesis but
12:57in reality farm size has increased. It's
13:00just our sample was not representative
13:03or something was wrong with our sample
13:05and that is of course type two error. So
13:09we do not reject the null hypothesis
13:12when we should have and the end that is
13:15type two. So type one error is rejecting
13:20the null hypothesis when we should not
13:22have and type two error is not rejecting
13:26the null hypothesis when we should
13:31have. Okay. Our final example and that
13:33is our Manchester United example. So
13:37during the 2010 2011 English Premier
13:40League season, Manchester United home
13:42matches had an average attendance of
13:4774,961. So a club marketing analyst
13:50would like to see if attendance
13:53decreased during the most recent season.
13:56So establish our null and alternative
13:58hypothesis for this analysis. We can
14:00only assume the attendance remain the
14:02same or maybe even increased because
14:05remember our research question, our
14:07alternative hypothesis, our research
14:09question is did the attendance decrease?
14:13But our assumption is that it remained
14:15the same or maybe even
14:20increased. So we can set up our
14:22hypothesis like this. So our null
14:24hypothesis is that the average
14:26attendance was greater than or equal to
14:3174961. So it was the same or it even
14:35increased. Now our alternative
14:37hypothesis, the research hypothesis is
14:40that the average attendance decreased.
14:43So it's less than
14:4774961. So we can set up our table again.
14:50So we have two conclusions. do not
14:52reject the null hypothesis or reject the
14:55null hypothesis and then two actual
14:58conditions either the attendance stayed
15:00the same or increased or did in fact
15:02decrease. So if we do not reject the
15:05null hypothesis, so we take a so we look
15:08at the season's attendance and it was
15:10right at you know around
15:1374961 or maybe a little bit higher then
15:17we our analysis would indicate that
15:19we're not going to reject that null
15:21hypothesis. It says greater than or
15:23equal to and the actual condition is
15:25that it actually did remain the same or
15:27increase. So that's correct conclusion.
15:30Now we could reject the null hypothesis.
15:32So we do our analysis of the most recent
15:34season and in fact attendance is down to
15:37maybe like 68,000 or something like
15:39that. In that case we would reject the
15:42null hypothesis and then go on to the
15:44alternative that says it is less than
15:4774961. So if we reject the null
15:50hypothesis based on our analysis the
15:52actual condition was that it is less
15:54than
15:5574961 then that case again we are
15:58correct.
16:00Now let's say we reject our null
16:02hypothesis but the attendance actually
16:05remained the same or increased. So maybe
16:09we this is believe it or not we missed a
16:12number. So let's say there were 13 home
16:16matches but we only typed 12 into the
16:20calculator but then we divided by 13.
16:23That could mess up our average right? So
16:26we incorrectly reject the null
16:29hypothesis when indeed the actual
16:32condition is that the attendance
16:34remained the same or increased. That
16:35does happen. So that would be a type one
16:38error. Then of course we could have
16:40where we fail to not reject the null
16:43hypothesis. So we take a sample or we
16:46look at our our data and maybe we
16:49actually type in a number twice into our
16:51calculator and of course we divide by 13
16:55or we divide by one less than is
16:57actually there. So therefore our
16:58attendance
17:00is higher than it actually is. So in
17:03that case we do not reject the null when
17:05we should have and again that is type
17:08two error. So again, I know this can be
17:11confusing because we're talking in
17:13sometimes double negatives and things
17:15like that, but if you really just got to
17:16pause the video and look at it, you'll
17:18actually see how this sort of works.
17:20This follows the same pattern. Type one
17:23error is simply the incorrect rejection
17:27of the null hypothesis. The type two
17:30error is simply not rejecting the null
17:34hypothesis when you should have. And
17:38that's the difference. So again, look at
17:39these examples again, go back to part
17:41one, and that can really refresh your
17:44mind too as to whether or not you're
17:46dealing with type one error or type two
17:50error. Okay, so some very simple causes
17:53of type one and type two error. So that
17:55remember when selecting samples, we are
17:57always subject to the laws of chance. We
18:00may by random chance alone select a
18:03sample that is not representative of the
18:06population.
18:08So we may select a sample of underfilled
18:12or overfilled water bottles just by
18:15chance
18:16alone. We may select a sample of very
18:20small or very large farms again just by
18:24chance in our sample
18:26selection. Or the sample is in the far
18:29out tails of the sampling distribution.
18:32again just by chance alone cuz remember
18:36the sample means have their own sampling
18:40distribution. We talked about that
18:42several uh videos ago and we may by
18:45chance just get a sample that's way out
18:48in the tails of the sampling
18:50distribution again just by chance. Now
18:53our sampling techniques may be flawed.
18:56So there's a whole branch of statistics
18:58that talks about sampling techniques and
19:01things like that. So we may have to look
19:03at our sampling technique. The
19:05assumptions in our null hypothesis may
19:08be flawed. So in the farm case, maybe
19:11the USDA data is incorrect or it has
19:14flaws in it. So we're using this USDA
19:17data for our null hypothesis, but it
19:21doesn't actually correspond to the state
19:23of the farm size in Texas. So whatever
19:27we're basing our null hypothesis off of
19:29may be incorrect.
19:31But overall the most common cause is
19:35chance and chance alone because again
19:38our sampling means have a sampling
19:41distribution. We talked about that in
19:43the previous videos. And there is a
19:46chance that we get one a sample mean
19:49that's just far out in the tails of the
19:53sampling distribution. That has to deal
19:55with confidence intervals and all kinds
19:57of things like that. Now, of course,
19:59when we actually do hypothesis tests in
20:02upcoming videos using actual data and
20:04numbers and curves and and things like
20:06that, we will deal with that. But the
20:09most common cause of type one and type
20:12two errors is chance and chance
20:16alone. Now, remember that this sort of
20:19conclusion table always holds up when
20:21we're dealing with these two
20:23diametrically opposed hypothesis. So our
20:26conclusion is either we do not reject
20:27the null or we reject the null. The
20:30actual condition is that the null is
20:32true or I say true in quotes or the
20:36alternative is true. If we do not reject
20:38the null and the null is true, that's
20:43correct. If we reject the null and the
20:46alternative is true, that's correct. Now
20:50if we reject the null but the null is
20:53true then that's type one error. We
20:56incorrectly rejected the null. Now if we
20:59do not reject the null and we assume it
21:01holds up but the alternative hypothesis
21:05is true then we've committed type two
21:08error. So in the previous part of this I
21:11talked about type one error as sometimes
21:14being like the false alarm. So we reject
21:18the null hypothesis but in fact the null
21:21is true. So for type two we do not
21:24reject the null when we should have
21:27because the alternative is true. So
21:30again go back and look at the previous
21:31video and these examples and it really
21:33should click sort of in your
21:37mind. Okay. So that wraps up part two of
21:41our video on hypothesis formulation type
21:44one and type two errors. Now, I know
21:46this can be a very confusing concept
21:48because the way the wording works, we're
21:50using a lot of double negatives uh here
21:52and there, but I really think if you go
21:54back and look at part one and again part
21:56two, you really grasp the fundamental
21:58concepts of type one and type two error.
22:02It's simply when our conclusion based on
22:05our analysis does not match the actual
22:09state of reality, the state of affairs.
22:13So if our our null hypothesis is not
22:17rejected therefore the null should be
22:20true. If we reject the null then the
22:24alternative should be true. And if we
22:26don't do that that's where we involve
22:29type one and type two errors. Okay. So
22:32again that wraps up this entire video on
22:35type one and type two errors. Just a few
22:37reminders before we wrap up. If you're
22:39watching the video because you are
22:40struggling in a class, I want you to
22:42stay positive and keep your head up.
22:44You're very smart and talented and you
22:46may have just hit a temporary rough
22:47patch. I know you're smart. Everyone
22:50around you knows you're smart and
22:51talented, so so should you. Please feel
22:54free to follow me on YouTube, on
22:55Twitter, on Google+, or on LinkedIn.
22:58That way, when I upload a new video, you
23:00know about it. And it's always nice for
23:02me to connect with people who watch my
23:04videos online, wherever in the world you
23:06may happen to be. If you like the video,
23:09please give it a thumbs up, share it
23:11with classmates or colleagues, or put it
23:13on a playlist because that does
23:14encourage me to keep making them for
23:16you. On the flip side, if you think
23:18there is something I can do better,
23:20please leave a constructive comment
23:21below the video and I will try to take
23:23those ideas into account when I make new
23:26ones. And finally, just keep in mind
23:28that the fact that you're on here trying
23:30to learn, putting the effort in to
23:32improve yourself as a student or as an
23:34employee, that's what really matters. I
23:37firmly believe that if you have the
23:39right learning process in place, the
23:41results will take care of themselves.
23:44So, thank you very much for watching. I
23:46wish you the best of luck in your
23:47studies and in your work. And look
23:49forward to seeing you again next time
23:51when we talk about actual hypothesis
23:54testing.

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