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YouTube transcript (i8xChxbZ3uQ) — Transcript

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0:09Now One More Concept and then we are
0:11done now how does the critical mean
0:14value and error risk change as Alpha
0:19changes so let's look at some
0:21relationships between several moving
0:23Parts here so remember our Alpha of 01
0:27had a zoc critical value of 2
0:3033 so we went ahead and substituted that
0:33into our equation and we came up with a
0:36sample mean of
0:393233 that falls right on our critical
0:43value of
0:462.33 Now with an alpha of
0:4905 our Z critical is
0:541.645 so we go ahead and substitute that
0:58into our equation and we come back with
1:01a sample mean of
1:0631645 so what's happening here so with
1:10an alpha of
1:1101 the sample mean that falls on our
1:15critical Z value is
1:183233 at 05 Alpha
1:2105 now it's
1:2531645 so it's going inward it's going
1:29inward towards the middle now what about
1:32an alpha of
1:33.10 in that case our Z critical value is
1:381.28 so we'll go ahead and substitute
1:40that back in and what do you think is
1:42going to
1:43happen well it should be
1:45lower and it is that is a sample mean of
1:523128 so what is happening to the actual
1:56sample mean that falls on the critical
2:00value as we change
2:02Alpha well it moves inward towards the
2:06middle it moves inward towards the
2:09hypothesized
2:11mean now how's the relative probability
2:14of type one in type 2 error change so
2:19with this Alpha of 01 we have a
2:22relatively low probability of type one
2:26error and I'll explain why that is here
2:28in a second now as we move up our type 1
2:32error increases the probability of type
2:351 error increases of course when we get
2:37to 010 and Alpha of 0.10 we have a
2:41relatively higher level of type 1
2:44probability error what about type two
2:48we'll see it's inverse to type 1 error
2:51so at the alpha of
2:5301 we have a relatively high probability
2:57of type two error that's why I say
2:58relative probability ility now again at
3:0105 it's medium and at an alpha of
3:050.1 it's a relatively low and again this
3:08is relative to each other not some
3:10absolute so again you can see the the
3:14relationship between type one and type
3:16two error as the alpha changes on the
3:20next slide we'll talk about why that
3:23is so let's look at this graphically and
3:26I call this the alpha effect so remember
3:29in Starbucks example we are only
3:31interested in the upper tail because it
3:34was a directional hypothesis we were
3:36interested in whether or not the average
3:39customer satisfaction score was greater
3:42than three remember three was average in
3:45our Liker scale so we're just looking at
3:48the upper tail now in the previous slide
3:51we looked at the effect of the alpha
3:53level on the sample mean that would
3:57align with each critical value value so
4:00one of the ones we looked at was the
4:02alpha
4:04of10 now remember what we're saying here
4:07we are saying that we expect 90% of our
4:10sample means to either be on or to the
4:13left of that red line and the red line
4:17in this case is a z critical value of
4:221.28 now of course that red line
4:25actually corresponded with a customer
4:28satisfaction score we talked about that
4:30in the previous slide but if we got that
4:34score or one that was lower than that
4:37then we would fail to reject our null
4:40hypothesis because it would be in the
4:43non-rejection region however if we got a
4:46sample mean above this critical value
4:49then we would reject the null hypothesis
4:53and then go on to the alternative and
4:55this pattern follows for each Alpha
4:57level so with an alpha of
5:0005 if we get a sample mean that's on or
5:03to the left of that green line we would
5:06fail to reject our null hypothesis and
5:09of course if the sample mean was above
5:11the green line then we would reject our
5:14null hypothesis and that Z critical
5:16value was
5:191.645 now for the alpha of
5:2101 we had a z critical value of
5:252.33 so again if the sample mean is on
5:28that orange line or to the left left we
5:30would fail to reject the null and if the
5:33sample mean is to the right of that
5:35critical value we would reject the null
5:39so you can see how the alpha levels
5:41affect the location of the critical
5:45values now how does this relate to
5:48error now a smaller Alpha creates a
5:52wider net a wider non-rejection region
5:58so you can see here that as the Alpha
6:00decreased the non-rejection region
6:03increased because the Orange Line there
6:06represents the largest non-rejection
6:09region so it will catch more means it's
6:13like a wider net that will catch more
6:16sample means and of course this leads to
6:20a smaller type one error rate because
6:24remember type one error is when we
6:28incorrectly
6:29reject the null
6:32hypothesis so this wider net keeps us
6:35from doing that as much but it comes at
6:39a price The Wider net may capture a mean
6:44that belongs to a different distribution
6:48that's off to the side in this case
6:51higher than the one we're looking at and
6:54of course that's called type two error
6:57so let me show you this actually in sort
6:59of graphical terms so let's say we get a
7:02critical value or a mean same thing that
7:05is represented by this blue dot here now
7:09if we're using an alpha of
7:1201 what's going to happen in our
7:15hypothesis well it's inside the
7:18nonrejection region therefore we would
7:21fail to reject the null
7:25hypothesis but what if this mean
7:29actually belongs to a
7:31distribution that's further up the scale
7:35maybe
7:36here now what's happened is that we have
7:40included that
7:43value inside our non-rejection region
7:46because it's so wide but we did so
7:50incorrectly it actually belongs to a
7:53distribution that's further up the scale
7:57so therefore we included it in in the
7:59non-rejection region when we should not
8:01have and that is type two error so you
8:05can see the tradeoff between the alpha
8:08level and the type one and type two
8:11error rates yes a smaller Alpha will
8:15give us a wider net to capture More
8:18Sample means therefore it will lower our
8:21type 1 error rate but because we're
8:23including sample means that are that are
8:26further up the
8:27distribution we're in increasing the
8:30risk that that value is actually part of
8:33a population distribution that's higher
8:36up that is beyond this smooth
8:39distribution we're looking at and see
8:42that is the nuanced relationship between
8:45Alpha type 1 error and type two
8:51error now one more thing and then we are
8:53done and this is called the P Value
8:56method now remember that based on our
8:59Alpha of 01 we know that 1% of our area
9:04the probability is in the upper tail
9:07past our z-critical value of
9:102.33 so we can see that down here in the
9:12lower right so
9:162.33 now in the P Value method we ask
9:20how much area or probability is above
9:24our test statistic which in this case is
9:282.
9:30.5 so we know that 1% of the area is to
9:34the right of our Z critical of
9:372.33 but in the P Value method we ask
9:40how much probability is to the right of
9:43our Z
9:46statistic Now using the Z table or Excel
9:49we can find that this is
9:530.00
9:5562 now since this is less than the alpha
9:58of
10:0001 we would reject the null hypothesis
10:04now it leads to the same decision so in
10:07either case we would reject the null we
10:10would reject it in the first case
10:12because the Z value is above 2.33 it's
10:162.5 but in the P value case we go ahead
10:18and find the area to the right of our
10:22test statistic of 2.5 and that is
10:240.62 Which is less than 01 so the same
10:28conclusion just a different way of
10:30getting to it now this is often referred
10:33to as the observed significance level
10:37and again depending on the study or the
10:39journal or whatever discipline you're in
10:41or whatever field you're in in business
10:44you may be required to actually report
10:46The observed significance level in most
10:49cases we just
10:50say that we rejected the null hypothesis
10:54at an alpha level of 01 it just depends
10:57on what you're writing in or how you're
10:59required to report it but this is again
11:01the P Value method same idea but we're
11:04finding the area to the right of our Z
11:07statistic not the Z critical
11:11value okay just a quick reminder about
11:14the procedure and then we are completely
11:16done always start with a well-developed
11:18clear research problem or question all
11:21the fancy statistics will not make a
11:23difference if it's a bad research
11:26question or problem so always think
11:28through the
11:29before collecting any bit of data always
11:33establish the hypothesis both the null
11:36and the
11:37alternative then determine the
11:39appropriate test that will allow you to
11:41test those hypothesis then of course
11:44select the sampling distribution the Z
11:46distribution if you know Sigma the T
11:49distribution if you are estimating it
11:51with the sample standard deviation then
11:54choose your type one error rate and
11:56again this was your personal choice the
11:59depending on maybe the field you're in
12:00there's a standard one that is chosen um
12:03or you want to strike a balance between
12:05type 1 and type two error so you might
12:06choose 05 that's the most common that I
12:10see um but you might see also 01 it can
12:13just
12:14depend now then State the decision rule
12:18based on the sampling distribution you
12:20are using and the type 1 error rate and
12:23things like that then and only then
12:26gather your sample data of course using
12:29quality sampling
12:31techniques then based on the sample data
12:34and the other information you've chosen
12:36calculate your test
12:39statistics now once you calculate the
12:41test statistic compare that to your
12:43decision Rule and then you will come to
12:46a conclusion as of whether to not to
12:49fail to reject the null or to reject the
12:51null and of course once you come to that
12:54conclusion you can then make real world
12:56practical decisions based on that
12:58conclusion
12:59and I will point out here real quickly
13:01that a statistically significant
13:05difference does not mean a practical
13:09difference those are two different
13:10things so you could have a statistical
13:13difference that in Practical terms is
13:16not really significant so how you report
13:19that in your place of work or whatever
13:22else it might be that will just depend
13:24on the requirements of the job
13:30okay so that wraps up our first video on
13:32hypothesis testing again in this case
13:35we're using a sing Single sample with
13:37known Sigma so we were given the
13:41population standard deviation therefore
13:43we used the Z distribution to find our
13:46critical values and then evaluate our
13:49hypotheses based on those of course in
13:52the next video we will look at single
13:54samples when we do not know Sigma and
13:57therefore have to estimate the
13:59population standard deviation using the
14:01sample standard deviation and of course
14:04in that case we will use the T
14:07distribution but I really wanted you to
14:09see in this video the relationship
14:10between several things so we talked
14:13about the relationship between Alpha the
14:17critical values that that produced based
14:19on this Z distribution and the tradeoff
14:22between Alpha type one error and type 2
14:26error now most people I know and work
14:28with chosen the alpha of
14:3005 because it's sort of the middle
14:32ground tradeoff between type 1 and type
14:352 error and it's a little bit easier to
14:37work with from memory to be honest um
14:40but again it just depends on the study
14:42you're doing the field you're working in
14:44um the sample size you might be working
14:46with because remember a larger sample
14:48size will pick up more minute
14:51differences now we haven't really talked
14:53about that but the larger the sample
14:55size the more likely or the more easily
14:58we can pick up smaller and smaller
15:01differences as to typically significant
15:04but again we'll talk about that as we go
15:06so just a few reminders if you're
15:08watching the video because you're
15:09struggling in a class stay positive and
15:11keep your head up I know you're smart
15:13many other people around you know you're
15:14talented so just hang with it you will
15:17get through it if you like the video
15:19please give it a thumbs up share it with
15:21classmates or colleagues or put it on a
15:23playlist that does encourage me to keep
15:24making them for you please feel free to
15:26follow me here on YouTube on Twitter on
15:29Google+ or LinkedIn it's always nice to
15:32hear from you the world is much too big
15:34and life is Much Too Short not to
15:36connect with others when we have the
15:37chance and finally just keep in mind
15:39that the fact that you're on here trying
15:40to learn trying to improve yourself
15:42trying to better yourself as a student
15:44or business person that's what really
15:47matters I firmly believe if you have the
15:49right learning process in place the
15:51results will take care of themselves so
15:54thank you very much for watching I wish
15:56you the best of luck in your studies and
15:58in your work and I look forward to
15:59seeing you again next time

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