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Means by group *and* independent samples t-tests! Compare means two ways!
Feb 4, 2025
Using SPSS to look at different averages (means and medians by group) *or* to do independent samples t-tests: a walk though the processes and interpreting the SPSS output.
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[Applause]
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yay so today we are running SPSS and we
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are going to start comparing means by
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group so as usual we go to the analyze
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menu we say compare means and in this
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case we're just looking at means we're
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not going to do any statistics yet we're
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just going to compare them so it gives
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us a dependent list and an independent
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list and the dependent list is the
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things that we want to get means on so
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let's say the number of bedrooms the
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number of bathrooms and the sale price 0
0:38
and days on Market why not do everything
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and we're going to do this for each
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house type okay so we're going to go
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into options just because we can we're
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going to look at this the mean number of
0:51
cases standard deviation and just for
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fun the median let's move this around so
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I'm holding down the mouse button and
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drag in so I can change the order that
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these things come out
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as I say continue I say okay and here it
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is we get our case processing summary
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which as usual we're going to ignore and
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we get our full report so let's make
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this a little bigger so it's important
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to look at the number of cases that
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you're that are in each group so for
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example here we have the by Lev houses
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the sample size is always n and for
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number of things and we see that there's
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just one house on the market which has
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beds baths price and days on Market
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information but there's just one so
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we're going to ignore this because one
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case of anything is kind of meaningless
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so then we're going to look at Ranch
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houses and we've got three Ranch houses
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but that's really still not enough for
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us to really think is going to tell us
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anything serious we would like to see
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preferably 30 but at least say 10 10 or
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20 things uh 10 or 20 houses before we
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can start feeling justified in making
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comparisons so what we've really got
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here to look at is Cape cods the
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Colonials maybe the split levels and we
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can look at here we see that the cape
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cods they have an average of 3.6
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bedrooms 1.8 bathrooms and the selling
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price was an average of about
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$326,000 and they spent an average of
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around 85 days on the market maret if
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you have a colonial you're probably
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better off because if you take a look
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here there's actually fewer bedrooms the
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same number of
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bathrooms and the price is considerably
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higher they get about
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$468,000 for these compared to
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$326,000 for the cape cods on the
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downside they spend 99 days on the
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market versus around 85 days but that
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might be because they've got the higher
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prices the medians are lower more than
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the means and that's true for all of
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these groups and the reason for that is
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there's a certain minimum price that a
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house will sell for the minimum price
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for pretty much any house in tenek is
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going to be around 100 maybe
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$200,000 whereas there's no upper
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boundary on the price for selling a
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house so the problem with using averages
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is that they have a tendency to get
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thrown off by extremes at one end or the
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other of the Curve so when you have
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houses that are worth $2 million where
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most of them are selling for say $
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360,000 the average will be way higher
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than it should be whereas the median is
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a bit more stable because you're just
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lining up all the numbers and picking
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the one in the middle so if the ones at
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the top are $5 and6 million and all the
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other ones are 300,000 the median will
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be
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$300,000 but the average could be
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400,000 so there's times when an average
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make makes more sense and there's times
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when a median makes more sense so if
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you're looking at this and you're saying
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well if I have a four bedroom two B Cape
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Cod how much can I expect to sell it for
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then
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$319,000 doeses seem indicated here all
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else being equal so here we've got the
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mean for each group and here group is
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based on what type of house it is so one
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group is Cape cods one group is
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Colonials one group is ranches is one
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group of split levels so you've got the
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mean for each of these variables so the
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mean for beds the mean for baths the
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mean for Price the mean for days on
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market then you've got the median for
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each of these and again but since you
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can't be on the market for Less Than
4:45
Zero days then you can't get lower than
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one or zero but you can get as high as 7
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or 800 or even a th000 because a house
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can just stay on the market for a couple
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years so the median will be lower see
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then you've got the number of cases if
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you run it slightly differently you can
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make it a little more Compact and you
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can also do clever things here by double
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clicking you get what's called pivot
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trays so you can move your statistics up
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here into
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variables and now you might say it's
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easier to compare means because you can
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see them all right next to each other of
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course you still have to go down to P to
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the sample size to see which ones are
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actually real so again to do that you
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just doubleclick and then you can move
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these things around to your heart's
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content and it will reflect whatever
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you're doing whether it makes sense or
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not so there's all sorts of different
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ways to look at this you're just uh
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changing the way that the table is set
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up and then you get out of it the usual
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way and this is crossplatform it works
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works the same way if you're using a Mac
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as if you're using Windows so that was
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fun but now we're going to get rid of it
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so the two types that we can really
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compare the most easily are the cape
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cods and the Colonials because we have
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29 of one and 159 of the others and I
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have a theory that Colonials sell for a
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significantly higher price than the cap
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cods in other words that the difference
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in price that I saw before is not just
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due to random chance it's actually
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something that exists in real life into
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Variable View here's style and the ones
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that we're looking for are cape cods and
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Colonials 2 and three compare means
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independent samples T Test I say
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style two and
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three and now I get this lovely um
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output so what do I do let's look at
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group statistics first so group
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statistics is looking at each of these
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variables and it says okay for Price
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there were 29 reports of price for Cape
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cods and 159 for Colonials here's the
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mean selling price for Cape cods
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326,885
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196 about then we have the standard
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deviation and look at that whopping rate
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standard deviation it is
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$213,800 so you know that there's a lot
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of variability going on so there's
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probably some very expensive Colonials
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mixed in with the others now let's move
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to the independent samples T Test and
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this is a little weird okay we're
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looking at whether there's a difference
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between the two groups but there's two
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different formulas that we can use and
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one of them is much more complicated
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than the other so you've got your two
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different formulas and the computer is
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not saying I'm going to to choose the
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correct formula it's saying I'm going to
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give you the information and do it both
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ways so that you can decide whether to
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assume equal variances or not now
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typically what we do is we assume that
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you have equal variances if the
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significance of this F test here is
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above
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.005 so what that means is that if the
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significance is at 0.05 or less it means
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that there's a 5% or less chance that we
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are seeing differences in the variance
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due to chance so essentially if we have
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a low significance here 05 or below then
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we do not assume equal variances so we
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go to the second line if significance is
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above 005 then we assume equal variances
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and we use the top line now I will admit
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I generally don't look at this right
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away first I look over here here this is
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the significance for the T test for
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equality of means so this table is
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basically two tables in one so here's
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one table here around lavine's F test
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for equality of variances I know it's an
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F test because it has the letter F over
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there and then there's this test over
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here which is the T test for equality of
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means and that's everything to the right
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of this line starting with t going on to
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DF which means degrees of and all the
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others mean differ by the way let's just
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clarify one thing here mean difference
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sounds more complicated than it is it's
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just one mean minus the other so it's
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468 396 subtracted from 326
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470 so if I type this in so if I take
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the mean 326 470 69 minus 468
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39623
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equal 141 925
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54 and there it is there different by
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.03 because they give you an extra
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decimal point here than they do here
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mean difference is just one mean minus
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the other so for here we would expect it
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to be 02 because 3.62 minus 3.42 equal 2
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and here it is
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rounded 2 again they kind of mess things
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up by having an extra decimal place here
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let's go back to what we are trying to
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do we are trying to say is there
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significant difference between price and
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number of bedrooms between cape cods and
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Colonials and here we see that price
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there is a definitely a difference or to
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be more scientific there is less than
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one chance in 1,000 that we would see
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such a large difference between these
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two given these standard deviations and
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given the number in the sample there's
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there's less than a one in a, chance
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that we would see this huge difference
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just due to Randomness and chance and
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weird factors so that's a pretty big uh
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significance level and we can say all
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right this is a big difference in price
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we can see that with our eyes it's
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141,000
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$142,000 about so we're going to say
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okay there is a significant difference
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between these two the official way that
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we're supposed to say that is that we
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have to reject the null hypothesis that
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there's no difference so for number of
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bedrooms though it's a little muddier
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here you notice that there's very little
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difference 3.62 versus 3.42 bedrooms and
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their standard deviations are not that
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high first we look at what line to look
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at we cannot assume equal variances
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because this is significant which means
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that there is a difference between the
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variances so we go to the second line
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and we come down here and we see aha
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093 is the significance you got to
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reject that most of the time if I'm
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doing one or two tests I will set my
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Criterion at 0.05 that means that five
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times out of 100 which is what 0.05
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means or 5% of the time which is also
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what 5.05 means I will see a quote
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significant difference unquote just by
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random chance so five times in 100 or
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one time in 20 if I run 20 analyses and
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I use 0.05 as my Criterion in theory one
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of them will probably be a false
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positive now the thing is that if you're
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doing a lot of these tests then you
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should use a lower level of p p being
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the probability of getting a false
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positive so uh what some people do is
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they just go down to 0.01 as their P so
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they won't take anything that's not less
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than .001 and other people use What's
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called the bonon technique and that
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means that you take your p and you
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divide it by the number of analysis that
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you're doing which in a casee like this
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would mean that we have P = 05 we divide
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it by 2 we get p =
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025 but um if you're doing 100 analyses
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it gets a little tough you look at the F
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test if the F test is significant then
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you use this second line here and you
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look at the significance for the T Test
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or you look at the significance for the
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T Test and you say well I'd reject this
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no matter what and I'd accept this no
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matter what so it doesn't really matter
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what the f test says unless these two
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lines are saying different things so if
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the significance was 0.02 for one of
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them and2 for another then you'd have to
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go through the work of doing the F test
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so that's basically the T Test and the T
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Test is a very very handy thing to know
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it's very often handy to compare two
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groups against each other
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