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0:18hello thank you for watching and welcome
0:20to the next video in my series on basic
0:22statistics now a few things before we
0:25get started number one if you're
0:27watching this video because you are
0:29struggling in a right now I want you to
0:31stay positive and keep your head up if
0:33you're watching this it means you've
0:35accomplished quite a bit already you're
0:37very smart and talented and you may have
0:39just hit a temporary rough patch now I
0:42know with the right amount of hard work
0:44practice and patience you can get
0:46through it I have faith in you many
0:49other people around you have faith in
0:51you so so should you number two please
0:55feel free to follow me here on YouTube
0:57on Twitter or on LinkedIn
1:00that way when I upload a new video you
1:02know about it and it's always nice to
1:04connect with people who watch these
1:06videos wherever in the world you may be
1:10number three on the topic of the video
1:12if you like it please give it a thumbs
1:14up share it with classmates or
1:16colleagues or put it on a playlist that
1:19does encourage me to keep making them
1:20for you on the flip side if you think
1:23there's something I can do better please
1:25leave a constructive comment below the
1:26video and I will try to take those ideas
1:29into account when I make new ones for
1:31you and finally just keep in mind that
1:34these videos are meant for individuals
1:36who are relatively new to Stats so I'm
1:38just going over the basic concepts and I
1:40will be doing so in a very slow
1:42deliberate manner not only do I want you
1:45to understand what's going on but also
1:48why so all that being said let's go
1:51ahead and get
1:54started so this video is the first in a
1:57new topic and that topic is hypothesis
2:01testing so hypothesis testing is a
2:05gigantic part of introductory level
2:08stats so we're going to spend many many
2:11videos on the topic now this video is
2:14just an introduction to try to get your
2:16mind in the right framework to begin
2:19thinking about hypotheses are formed how
2:21we ask questions and then how we set up
2:24statistical tests to find answers or
2:28solutions to those questions
2:30so this video is really about trying to
2:32get your mind wrapped around the idea of
2:35what hypothesis is in the terms of
2:38statistics now if you grew up in the US
2:41at least sort of when I was in school a
2:43hypothesis was always described as an
2:46educated guess now for grade school
2:50that'll work but in statistics we have a
2:52much more formal definition of what a
2:54hypothesis is so this is going to be the
2:57first video in our effort to understand
3:00exactly what we're doing when we talk
3:02about hypothesis tests in stats so all
3:05that being said let's go ahead and Di
3:07right
3:10in so as usual I like to begin my videos
3:13with an example and then we'll talk more
3:15formally about the topic towards the end
3:18so here is our first example a bottled
3:21water manufacturer most popular product
3:24is a 12 fluid ounce bottle of water
3:27which you can see over here on the right
3:30now for this problem and due to its
3:32inherent superiority which I do agree it
3:34is we're going to use the metric system
3:37instead so instead of 12 fluid ounces
3:40we're going to say
3:41355
3:43milliliters now here's the important bit
3:46since this info is actually on the label
3:50so if this bottle had its label on it it
3:52would say 12 flu ounces or 355 milliters
3:56because it's on the label we assume it
3:59to be
4:00true and that's one of the important
4:03things about hypothesis formulation if
4:06we have some bit of information like on
4:07this water bottle or maybe on a can of
4:10soup or on the sticker on a new car that
4:14says whatever it's miles per gallon is
4:17if it's stated on the product or maybe
4:19it's a statistic about the population or
4:22something we assume that that is
4:25true but the question is is it
4:32now as a customer we are concerned that
4:35there is at least 355 Mill in this
4:39bottle if there's a little bit more than
4:42that that's okay because we're getting a
4:44bit more for our money so if there is
4:47360 mlit in this bottle assuming it
4:51would fit we're okay with that because
4:53we're at least getting the 355 that is
4:56on the label now if we're the
5:00manufacturer however we want the volume
5:03to be exactly 355 ml well why is that
5:08well we don't want upset customers if we
5:12underfill it so if we're consistently
5:15making bottles with 350 milliliters and
5:18our customers sort of find out somehow
5:21they are not going to be happy because
5:23they are paying for less than we say
5:26that we are giving them but we also do
5:29not want to higher cost of production or
5:32overfilling so if we're putting 360 ml
5:35in each bottle times 10 of thousands of
5:38bottles that's a lot more water in the
5:41bottles than we are actually think we're
5:44selling so we're actually putting more
5:46water into current bottles instead of
5:48that water going into future bottles see
5:50what I mean so for the customer we want
5:53to know if there's at least 355 ml if
5:57we're the manufacturer we want it to be
5:59exactly 355 if we underfill we're
6:03cheating the customer if we overfill
6:06we're cheating ourselves because we're
6:08creating higher cost of
6:12production so as the customer we are
6:15assuming there's at least
6:18355 milliliters so we can write that as
6:20a little expression so the quantity of
6:23water has to be greater than or equal to
6:27355 ml for us to be happy again if it's
6:30356 357 that's great because we're happy
6:33we're getting a bit more than we believe
6:35we're paying for now for the
6:38manufacturer we're assuming exactly 355
6:43M so the quantity of water will be equal
6:47to 355 ml so you can kind of see what
6:50we're doing here we're kind of building
6:52the problem outward from the actual text
6:55of the problem and then we're starting
6:57to slowly put it into sort of a mathema
6:59IAL expression as you can see in this
7:01slide and in this case it's about the
7:03Assumption and again the assumption is
7:06an assumption in this case because it's
7:08on the
7:12label now what about some questions so
7:14the customer is saying well is there on
7:18average at least 355 MERS of water in
7:21each bottle so that's actually what a
7:24customer might say so again the quantity
7:27of water greater than or equal to 300
7:29155 millit now what's the manufacturer
7:33asking is there on average exactly 355 M
7:39of water in each bottle and of course
7:41that's our quantity of water equals 355
7:44M so now we're going from the question
7:48to sort of a basic mathematical
7:50expression to an actual question that we
7:53can begin to answer using our
7:55statistical techniques and that's one of
7:58the important things about hypothesis is
7:59formulation going from the problem to to
8:02looking at what the assumptions might be
8:04or we'll talk about claims or assertions
8:06later then developing an actual question
8:09like this of how we might proceed to
8:11answer
8:14it so what sort of experiment what we
8:17set up so we collect 50 bottles from all
8:19over the country or the world to
8:21randomize the sample in terms of
8:23location time manufacturing plant
8:26Etc we then measure the volume of each
8:29bottle in the sample and find the mean
8:32volume for those 50
8:34bottles so using those sample means we
8:38can test the
8:40Assumption of 355 milliters or what we
8:44call the status quo so in this case
8:48we're using our sample measurements to
8:52test the assumption that is stated on
8:55the bottle or what we call the status
8:57quo so we're sort of using the
8:59statistics to back up or test an
9:03assumption that's already out there in
9:05the world so later when we talk about
9:08the null and alternative hypothesis this
9:10comes into play so what we're doing here
9:13is testing an assumption that's already
9:15on the
9:18bottle let's take another example and
9:21that's an example using the hybrid car
9:24engine so an autom manufacturer has
9:26developed a new hybrid engine technology
9:30it claims reduces fuel consumption while
9:34driving in the city the claim is that
9:38the new technology improves full fuel
9:42efficiency making it better than the old
9:44engine that produces 30 m per gallon so
9:49the company will run controlled tests to
9:51look for statistical evidence to support
9:54the claim that the new engine offers
9:56better efficiency than the old model so
10:00notice in there I was always stressing
10:03the word claim and we're going to talk
10:06about the difference between a claim and
10:08an assumption because those are two
10:10different things and it goes into how we
10:13formulate our
10:17hypotheses so let's think about what the
10:19company is actually claiming here so the
10:22company is claiming that the fuel
10:24efficiency in the new engine is greater
10:27than 30 m per gallon
10:29so it could be 35 m per gallon it could
10:32be 40 m per gallon it could be 25 M per
10:37gallon that is the claim that we're
10:39testing now compare that to the water
10:42bottle in the water bottle we knew the
10:45status quo we were given an assumption
10:49that we were testing here the company is
10:51just claiming well this new engine is
10:55greater than 30 MP gallon so the Manu
10:59facturer is making a claim it wishes to
11:02test it's not testing an assumption or a
11:06status quo that already exists can you
11:10see the difference so when we're testing
11:13this claim we don't know what the answer
11:17really is as compared to the previous
11:20water bottle example when we were given
11:23the Assumption we were given the status
11:25quo we were given the state of the world
11:28and then were testing that this is much
11:32different and when we get into null in
11:35alternative hypothesis this is where
11:38this idea comes into
11:42play so how do we think about hypothesis
11:45in general when trying to formulate a
11:48statistical hypothesis I want you to ask
11:50yourself the following
11:53question am I testing an assumption or
11:57the status quo that already exists so in
12:02this case it was the water bottle the
12:05Assumption was already stamped on the
12:07label of the water bottle or am I
12:11testing a claim or an
12:14assertion beyond what I already know or
12:19can know in this case the Hybrid
12:22engine so our claim or our assertion
12:26with the Hybrid engine was that its fuel
12:29consumption was less than the current
12:33model or what we consider the old the
12:35old model but it's not really out there
12:38in the world yet we're making a claim or
12:41an assertion that may be
12:44true now for the water bottle the ounces
12:48or milliliters on the bottle we are
12:50assuming is true and that's the
12:52difference the Assumption of the status
12:55quo is assumed to be true the gas
12:58mileage on the
13:00engine we cannot assume to be true
13:02because we're testing if it's different
13:05than the current
13:07model now if we wanted to test the gas
13:09mileage listed on a current car sticker
13:13so you go to the car dealership and it
13:14says this car gets 32 m per gallon on
13:17the
13:18interstate that's an assumption that we
13:21could then test it's not some assertion
13:24or claim that may be true if it's on the
13:26sticker we assume that it's the case so
13:29then we could go out and test it like we
13:31do the water bottle so in your mind just
13:35keep these things um separate so you can
13:37sort of get the distinction between the
13:39two am I testing an assumption or the
13:41status quo that already exists or am I
13:45testing a claim or an assertion about
13:48the world beyond what I already know or
13:51can know and that's important when we're
13:54talking about null hypothesis and the
13:57alternative hypothesis which which we'll
13:59just get into towards the end of this
14:03video so here are some basic null and
14:06alternative frustrations now I know we
14:08haven't really formally defined what
14:10these two things are but I would imagine
14:12if you're watching this you've at least
14:14probably heard of these in your stats
14:15class or in a previous class or
14:17something like that but again in the
14:18next video next series of videos we'll
14:20really pick these apart about what they
14:22are but I want to give you some you know
14:24some basic reasons why these are in fact
14:26so frustrating so formulating hypothesis
14:30can be very frustrating A real pain in
14:33the to be honest and the reason is is
14:37that the null and alternative hypothesis
14:40are two opposing roads that lead to the
14:43same place you know sort to see what we
14:46mean by that as we go but that's why
14:48they can seem so confusing because they
14:51are two opposing things that end up
14:54leading to the same
14:56place now by definition the null and
14:59alternative hypothesis are opposites
15:03they are mutually
15:05exclusive so they both cannot be true so
15:09we'll talk about rejecting the null and
15:10all that kind of stuff later but just
15:12keep in mind that they are opposites
15:14they are mutually exclusive the null is
15:17either rejected or it's not now only if
15:21the null is rejected can we then proceed
15:24to the alternative hypothesis and again
15:26we'll talk about this in the next video
15:28I'm the sort of setting up the
15:30frustration of what can happen you know
15:32when you try to try to set them up now
15:34researchers can start with either the
15:36null or the alternative and then form
15:41the other as a complement to the first
15:45so again it just depends on the question
15:48we're trying to ask and the question
15:50we're trying to you know obviously solve
15:52or answer in the end but you can start
15:55at either place you can start with a
15:57null hypothesis and then form the
15:59alternative based on that or you can
16:02start with the alternative hypothesis
16:04and then form the null based on that so
16:08you can start at either
16:10place now which to start with largely
16:13depends on the point of view of the
16:16researcher the context of the problem
16:19we're asking and what can or cannot be
16:22assumed to be known
16:25upfront so what I'm telling you here is
16:27that there is no TR trick there is no
16:30easy answer there is no sort of golden
16:33key that unlocks null and alternative
16:38hypothesis you just have to think you
16:41just have to analyze you just have to
16:42pick it apart and figure out where
16:45you're starting from and of course we're
16:47going to do lots of those in upcoming
16:49videos so just stay cool stay calm if
16:53this is confusing to you because again
16:55we're going to do more as we go I'm just
16:58trying to set the stage here for what's
17:00coming
17:02up so what about the null and
17:05alternative word salad and here I'm
17:07going to sort of put everything on one
17:09slide so you can see them as opposed to
17:12each other and what they're different so
17:15let's think of the null so in the null
17:17hypothesis we're talking about what we
17:19can assume we talk about what the status
17:22quo is or what we're given so think of
17:26the water bottle we can assume there is
17:29355 m in it because it's on the label we
17:34assume that that's the status quo that
17:37that's the way every bottle is and of
17:39course we're given that on the actual
17:42label physically itself so think of this
17:45as this is accepted as
17:48true Let's test it now what about the
17:53alternative so in the alternative
17:56hypothesis we might have something that
17:58is unknown to us we're making some
18:01assertion about the world that we really
18:05don't know we're making a claim about
18:08something that we really do not know so
18:11it's about something that we're unsure
18:13of we cannot assume to be true or
18:16something along those lines so think of
18:18this as this might be true Let's test it
18:23if not the truth is something else so
18:27over here on the null side we're saying
18:29whatever our null hypothesis is stating
18:32we're saying that this is accepted as
18:33true Let's test it on the alternative
18:37hypothesis side we're saying this might
18:40be true we're not quite sure let's test
18:43it and if not the truth is something
18:48else so you might want to look at these
18:50two slides or let it sink in and then
18:52later when we actually talk about
18:54forming hypothesis based on the wording
18:56in a question you'll see exactly how
18:59this works so again I just want to set
19:00up the stage sort of prepare you for
19:04what we're going to be doing the nuts
19:05and bolts of hypothesis formulation and
19:08testing in upcoming
19:12videos okay so that wraps up our
19:15introduction to hypothesis formulation
19:18so remember just in your mind for right
19:20now just to keep separate we're talking
19:22about null hypothesis and alternative
19:25hypothesis the null is all about the
19:27things that we assume to be true or that
19:30we are given or that are stated for us
19:34and then on the alternative side we're
19:36talking about things we're making a
19:38claim about something that might be true
19:40we're making an assertion about
19:42something that might be true so again on
19:44the water bottle we have the actual
19:46volume stamped on the bottle so we
19:48assume that to be true in the Hybrid
19:50engine all we're doing is testing
19:53whether or not its fuel consumption is
19:55less than the current model or the
19:58previous model
19:59we don't know what it is we don't even
20:01know if it's less or not so we're sort
20:03of making some assertion or a claim
20:05we're going to test that claim which may
20:07or may not be true okay so just a few
20:10reminders if you're watching this video
20:12because you struggling in a class right
20:14now I want you to stay positive and keep
20:15your head up you're smart and talented
20:18and you may just hit a temporary rough
20:19patch please feel free to follow me here
20:22on YouTube on Twitter or in LinkedIn
20:25that way when I upload a new video you
20:26do know about it and it's always nice
20:28for me to connect with people who do
20:30watch these videos wherever you may be
20:32in the world and finally I just want you
20:34to keep in mind that the fact that
20:36you're on here trying to learn trying to
20:38improve yourself trying to better
20:39yourself that's what really matters in
20:42learning I firmly believe that if you
20:44have the right learning process in place
20:47the results will take care of themselves
20:50so thank you very much for watching I
20:52wish you the best of luck in your
20:54studies and in your work and I look
20:56forward to seeing you again next time
20:58[Music]

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