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0:03[Music]
0:17hello thank you for watching and welcome
0:20to the next video in my series on basic
0:22statistics now as usual a few things
0:24before we get started number one if
0:27you're watching this video because you
0:28were struggling in a class right now I
0:30want you to stay positive and keep your
0:32head up if you're watching this it means
0:34you've accomplished quite a bit already
0:36you're very smart and talented and you
0:38may have just hit a temporary rough
0:40patch now I know with the right amount
0:43of hard work practice and patience you
0:46can get through it I have faith in you
0:48many other people around you have faith
0:50in you so so should you number two
0:54please feel free to follow me here on
0:56YouTube on Twitter or on LinkedIn that
1:00way when I upload a new video you know
1:02about it and it's always nice to connect
1:04with people who watch my videos and on
1:07the topic of the video If You' like it
1:09please give it a thumbs up share it with
1:12classmates or colleagues or put it on a
1:14playlist cuz that does encourage me to
1:16keep making them for you on the flip
1:19side if you think there is something I
1:20can do better please leave a
1:22constructive comment below the video and
1:24I will try to take those ideas into
1:26account when I make new ones and finally
1:30just keep in mind that these videos are
1:31meant for individuals who are relatively
1:34new to Stats so I'm just going over
1:37basic concepts and I will be doing so in
1:40a very slow deliberate manner not only
1:44do I want you to understand what's going
1:46on but also why and how to apply it so
1:50all that being said let's go ahead and
1:52get
1:55started so this video is the next in our
1:58series on hyp hypothesis formulation and
2:01eventually hypothesis testing using
2:04actual data and the topic of this video
2:07is one that gives many stat students
2:11throbbing headaches it drives them crazy
2:16and that is the concept of the null and
2:18the alternative hypothesis now I'm going
2:21to make this easy for you in just a few
2:24seconds the reality is as human beings
2:29we live every day making thousands of
2:33null hypotheses and then testing them so
2:37for example if you were to go outside
2:40and walk off your front step and maybe
2:43into the sidewalk or on the street or
2:45wherever you might be don't you assume
2:48that the street will be there when your
2:51foot
2:52lands I would guess so if you go outside
2:55and pick up a rock and drop it what do
2:59you expect of is going to happen well
3:02you expect that's going to fall back to
3:03the ground because you assume
3:06gravity so if you pick up a glass or a a
3:10container full of some drink and you're
3:13going to pour that drink into your glass
3:16and you know the drink is in there so if
3:18you pour it and it doesn't come out but
3:20stays in the container you would know
3:23something is very wrong so the reality
3:26is our everyday existence is full of
3:30hundreds if not thousands of null
3:34hypotheses we make assumptions about the
3:36world every Split Second and everything
3:39we do every action we make every time we
3:42talk to someone else or whatever else it
3:44might be and our whole lives are about
3:47living out those no hypotheses those
3:51assumptions and of course if those
3:52assumptions get broken then we really
3:54notice but a n hypothesis is simply an
3:58assumption that we make about something
4:01and then we test whether or not that
4:03assumption holds true so really I just
4:06explain to you in just a couple minutes
4:08what a no hypothesis actually is it's an
4:11assumption we test and we do it every
4:14single day of Our Lives now of course
4:17the alternative is what happens when we
4:20have to fail to accept we reject that
4:24null those are the things we do in
4:26everyday life that are the null and the
4:29alternative hypothesis now of course
4:31we're going to put those into
4:32statistical terms in this video but I
4:35just want you to realize that no
4:37hypothesis formulation and testing is
4:40something you do hundreds and thousands
4:42of times every single
4:46day so let's start with the example in
4:48our previous video so in that video we
4:51talked about water bottles and hybrid
4:53engines so I'll just go over them
4:54briefly here so in the water bottle on
4:57the right that's a 12 fluid oun bottle
4:59of water which is about 355 ml now it
5:03says that on the label that's an
5:06assumption on the label that we are
5:09given so we assume that inside the
5:11bottle there is actually 355 M what it
5:14says on the label so for the customer
5:17what are we asking we're asking well is
5:20there on average at least 355 M of water
5:24in each bottle so why do we say at least
5:28well that's because if there's 3 5
5:30that's what we're paying for but if it
5:32happens to be 360 well that's fine
5:35because we're getting a little bit more
5:37than we're paying for so we can put that
5:39in a mathematical expression of quantity
5:41of water is greater than or equal to 355
5:45milliters now what if for the
5:47manufacturer we might ask a different
5:49question is there on average exactly 355
5:54Millers of water in each bottle so we
5:57can write that as an expression quantity
5:59of water equals 355 M why is it
6:02different well if we're the manufacturer
6:05if we underfill the bottles we're
6:08cheating our customers and they may be
6:10very angry with us and the government
6:11may be angri with us and things like
6:14that if we overfill them we're cheating
6:17ourselves because we're making a higher
6:20operating cost for ourselves so instead
6:23of putting that extra water into future
6:26bottles we are overfilling current
6:29bottles so if we're the manufacturer we
6:32don't want to be under 355 or over 355
6:37if we the customer we want it to be at
6:40least 355 either equal to or more than
6:43because in that letter case we'll get a
6:45little bit more than we're paying for so
6:47it's all about how we formulate the
6:49question and our own point of
6:53view so the second example we talked
6:55about was the hybrid car engine so the
6:58company is claiming
7:00that this new engine has greater fuel
7:03economy it's more fuel efficient so the
7:06current engine in production is 30 m per
7:09gallon so they are claiming that this
7:12new engine gets more than that so the
7:15manufactur is making a claim it wishes
7:17to test it is not testing an already
7:22existing assumption it's not testing the
7:25status quo that already exists it's
7:29testing something that it does not know
7:31if it's going to be the case or not so
7:34think of the difference the Assumption
7:37on the water bottle was because it was
7:39actually on the bottle this is sort of a
7:42claim in the engine case about some
7:45unknown we know that the current engine
7:48that's in production is 30 m per gallon
7:51we want to test whether or not the new
7:53one gets more than that and we do not
7:56know it's a complete unknown so that's
7:59the difference between an assumption and
8:02some Claim about an unknown and that's
8:05important when it comes to hypothesis
8:09testing so thinking about hypothesis
8:12when trying to formulate a statistical
8:14hypothesis I want you to ask yourself
8:17the following question am I testing an
8:20assumption or the status quo that
8:24already exists so in that case the water
8:27bottle was that example or am I testing
8:31a claim or an assertion beyond what I
8:35already know or can know and that would
8:39be the Hybrid engine example so they're
8:42making some Claim about an unknown that
8:44they want to test and that's whether or
8:46not the engine gets greater than 30 m
8:49per gallon what if we turn this a little
8:52bit different way if we wanted to test
8:54the gas mileage listed on a current car
8:57sticker in the window we would be
9:00testing an assumption then not some
9:03claim but an unknown so if I go to a car
9:06dealership I look on the the sticker of
9:09the car and it says this car gets 26 M
9:13per gallon on the highway well that is
9:16an assumption that's a given to us that
9:18we can then go test that's our null
9:21hypothesis in this case now in the
9:25engine we were using before we don't
9:27know we were just testing whether or not
9:30it's greater than 30 m per gallon two
9:33different things so think about that in
9:35your mind am I testing the Assumption of
9:36the status quo that already exists or am
9:39I testing an unknown claim or assertion
9:42that's sort of beyond what I can
9:46know so why is this concept so
9:50frustrating well one thing is that it
9:52runs counter to how we think about
9:54things in our everyday life but again as
9:56I said at the beginning of the video we
9:59set up and test no hypotheses hundreds
10:02if not thousands of times a day
10:05unknowingly in our daily lives so
10:08formulating hypothesis can be very
10:10frustrating a real paa or a pain in the
10:15you know what to be honest now the
10:18reason that's the case is that the null
10:20and alternative are two opposing roads
10:22that lead to the same place so it's two
10:25opposite directions that come to the
10:27same place which is this overall
10:29hypothesis
10:31formulation Now by definition the null
10:34and the alternative hypothesis are
10:37opposites they are mutually exclusive so
10:41the null and the alternative cover all
10:44possibilities but never the same
10:47possibility and you'll see what I mean
10:49by that here in a minute or two now the
10:52null is either rejected or it's not only
10:56if the null is rejected can we proceed
11:00to the alternative and that goes to the
11:02point we'll talk about here in a second
11:04that everything is centered on the null
11:07hypothesis we either reject it or we
11:10don't reject it then we proceed onto the
11:13alternative if we do reject
11:16it now researchers can start with either
11:18the null or the alternative and then
11:21form the other as a complement to the
11:25first now which to start with largely
11:27depends on the point of view of the
11:29researcher or the analyst the context of
11:32the problem and what can or cannot be
11:35assumed to be known UPF front so again
11:38think of the water bottle and think of
11:40the Hybrid engine with the water bottle
11:43we knew the volume from the label so we
11:47could test that that was our assumption
11:49for the Hybrid engine we were just
11:51trying to test whether or not it got
11:54greater fuel economy than our current
11:56model see there's no assumption there
11:59there's there's no assumption there
12:00whatsoever it's a different way of
12:02approaching a problem and in that case
12:04that would have been our alternative so
12:06again we haven't really defined what the
12:08null and alternative are formally which
12:11we'll do here in a few minutes but I
12:13want to set the stage sort of for what's
12:15coming
12:17up now you can think of the null an
12:20alternative as sort of a soup or a word
12:22salad so when we think of the null we're
12:25thinking of things that we can assume
12:27things that are given to us or some
12:29status quo that already exists like the
12:33water bottle label so we accept whatever
12:36the null says as true and then we can
12:39test it and then we can either reject
12:43that null or fail to reject that null
12:47now the alternative is almost always
12:49something we do not know it's some
12:51unknown we're making some unknown claim
12:54or unknown assertion or something we're
12:57testing so think of the hybrid engine so
13:00this is something that might be true
13:03Let's test it if not the truth is
13:06something else so again the null is
13:09about an assumption that we can either
13:11reject or fail to reject the alternative
13:15is like some conjecture it's some
13:18unknown assertion that we're going to
13:20test two very different
13:23things now how about the null and
13:26alternative symbols so the null
13:28hypothesis it's just H Sub 0 the
13:32alternative is H sub a for
13:37alternative now what we mean by null in
13:40the null case null means nothing new
13:43nothing different nothing new to see
13:46here the Assumption or the status quo is
13:49maintained so in our water bottled
13:51example if we take 50 bottles and we
13:54measure the amount of water in each one
13:56and let say it comes out to 300
14:0155.4
14:02milliliters now our null hypothesis was
14:05that it equal
14:07355 so is
14:29n is rejected and that's all it is it's
14:32nothing more than that so if we reject
14:34the null then we move to the alternative
14:37and it's simply the other option and
14:40again we'll talk about how to formulate
14:42these here in a
14:44second now a few helpful properties to
14:47understand how the null and alternative
14:50relate to each
14:51other so we we have the column on the
14:53left which is the null and the column on
14:55the right which is the alternative so
14:58for the null we have an assumption of
15:00the status quo nothing really new and
15:03sort of the opposite of that is the
15:05rejection of that assumption the
15:08rejection of that status quo the null
15:11can be assumed to be true or it's a
15:14given so we assume that the water bottle
15:18is correct we assume that the miles per
15:20gallon on a car sticker is true and then
15:24the alternative is the rejection of that
15:27assumption or the rejection of that
15:30given now you can think of this another
15:33way too let's start with the
15:35alternative the alternative can be a
15:38research question that we want to quote
15:40prove and I put that word in quotes
15:42because I'll I'll tell you about that in
15:43a few minutes I don't like the word
15:45prove in statistical sense but if you
15:48think of the Hybrid engine the
15:50manufacturer was trying to prove that
15:53the new engine uh achieved greater than
15:5630 m per gallon so the alternative is
16:01about proving some
16:03conjecture now the fourth property is
16:05one that's extremely helpful when
16:07setting up these hypothesis in your work
16:10or in your analysis or whatever else it
16:11might be the null hypothesis always
16:15contains an equality so it always has an
16:18equal sign or the less than or equal to
16:22sign or the greater than or equal to
16:24sign either way it always contains the
16:28equality part part the alternative does
16:31not contain inequality so not equal to
16:35or just less than or just greater than
16:38some value so when you're setting up
16:41your null and your alternative and you
16:44if you can remember this very simple
16:45rule it makes it a whole lot easier
16:48trust me so using this last very helpful
16:52property we can logically derive the
16:54possible null and alternative pairs so
16:58we could have this where the null is
17:00equal to some value and therefore the
17:03alternative is not equal to that value
17:07we could have this case where the null
17:09is less than or equal to some value
17:12therefore the alternative has to be
17:14greater than that value and finally the
17:17null can be greater than or equal to
17:20some value therefore the alternative has
17:23to be less than that value so notice
17:26that the equality sign is always in the
17:29all and then the opposite of that is in
17:31the alternative so when you're pulling
17:33information out of problems and you set
17:36them up this can be an extremely helpful
17:39rule of thumb to
17:43remember okay this is arguably the most
17:46important slide in the first half of
17:47this video because it's about how we set
17:49up and interpret our null and
17:52alternative statements now first and
17:54foremost always remember that all
17:57statistical conclusions are made in
17:59reference to the null
18:02hypothesis as researchers we either
18:04reject the null hypothesis or fail to
18:08reject the null hypothesis we do not
18:11accept the null so think of the no
18:15hypothesis as something we either we set
18:18it up and the data either knocks it down
18:23or fails to knock it down so we either
18:27reject the null or fail to reject the
18:30null there is no accepting the null now
18:33this is due to the fact that the null
18:34hypothesis is assumed to be true from
18:37the start again it's an assumption so
18:39we're either rejecting or failing to
18:43reject that assumption we already
18:47made now if we do reject the no
18:49hypothesis then we conclude the data
18:52supports the alternative
18:56hypothesis however if we fail to reject
18:59the null hypothesis it does not mean we
19:02have proven the null hypothesis is
19:07true so again the the ideas of Truth and
19:11proving and things like that I'll talk
19:13about uh here in a bit I don't like
19:16those words very much so think of like
19:18support fail to support and things like
19:22that so if we reject the null hypothesis
19:25we conclude the data supports the
19:27alternative if we fail to reject the N
19:30hypothesis it does not necessarily mean
19:32we have proven the null hypothesis is
19:34true so think about this in terms of the
19:37water bottle so we set up an hypothesis
19:40that says the water in the bottle is 355
19:45MERS so we go out and collect 50 bottles
19:48and we take the mean of that 50 bottle
19:51sample and let's say the sample mean of
19:53that is
19:57355.00 m
20:00now our null says it was
20:03355
20:05M do we think that
20:09355.00 is high enough to reject that
20:14Assumption of
20:15355 well I would say no so in that case
20:20we would say we fail to reject the null
20:23hypothesis of
20:25355 M that's another way of saying our
20:29assumption held up what we were given
20:33held true sort of our status quo is
20:37upheld we could not reject it we failed
20:41to reject it now if it comes back that
20:44the bottle is
20:48340
20:50milliliters that's pretty low so will we
20:54say that
20:55340 is the same as 355
20:59five well I would guess probably not so
21:02what would happen in that case well in
21:04that case we would probably reject the
21:07long hypothesis we would go on to the
21:11alternative that says the average is not
21:16355 milliliters so again we're going to
21:18walk through that example here in a
21:20second actually in the next slide I want
21:22to give you an example of how we you set
21:25up the null to either be rejected
21:29or fail to be rejected and only if we
21:33reject it do we then proceed on to the
21:37alternative and of course this is
21:39because the null was assumed to be true
21:42from the
21:43outset now failure to reject the null
21:46does not equate to proof about its truth
21:51we're only setting up an assumption
21:54we're only setting up an assumption to
21:57either reject or fail to reject and
22:00that's all that's all the null
22:02hypothesis is an assumption to either be
22:04rejected or we fail to reject

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