SPSS for newbies: Cochran-Mantel-Haenszel Test for 2x2xK tables Video Lecture | SPSS: For Beginners - Data & Analytics

hey hi Phil from Statistics Metacom
today we're looking at the cochran
mantle
Hansol test the 2 by 2 by K tables this
test is often known as the mantle Hansol
test because many of you have said that
my videos are a bit on the long side I'm
starting off with an example here and
that means that once you see how I run
the test then we're done but I'm adding
on a few other things because you know
when you watch an demo being done and
then try to do it on your data set you
often find that their various issues
that I'm not being covered in a video
all right so in real life there's loads
of kind of things so at the newbie level
I'm just touching upon a few things that
will I can tell you about but don't have
to go too deeply into ok so let start
off with the example to worker
satisfaction data i anderson 1985 so
what we've got is got a data set and we
are interested in is a relationship
between this about company companies
worker satisfaction and supervisor
satisfaction what we do first what i've
done first is a related test is the test
of Association
so one let's see if there's a test so a
relationship between worker satisfaction
and supervisors active action each of
these variables are categorical and they
are rated low and high we look at the
PSA and we see that the p-value for the
test is less than naught point naught 1
so we conclude that is very strong
evidence to reject the null hypothesis
the null hypothesis in the test of
Association is that there is no
association between those two
qualitative variables so here we
conclude there's very strong evidence
association between the worker
satisfaction and supervisor satisfaction
ok now this is the stepping stone to the
Cochrane mental test Cochrane mental
Heinsohn test sorry
you see when you do this kind of a test
you find that there is a evidence of
relation between the two variables you
have to think about okay is that a
direct is this at
relationship or isn't it so often is the
case if we think about correlation or
just leaving two quantitative variables
you find there is correlation between
two things it doesn't mean though those
correlations are meaningful and it's the
same here for example I'll give you one
about the European folklore about stocks
bringing babies to households okay you
find that for any given year there over
years there's correlation a positive
correlation between the population of
stocks in the countries and the number
of births of babies it doesn't mean that
storks bring babies just because the
book is a positive correlation and
that's what we're talking about here so
we've got to think about is there any
other kind of variable or variables that
could explain this association so here
we think about some things and then
we've got the data here for the
management the company management good
and bad so let's look at that okay so
this is where the video really begins so
we've got worker set words we're still
interested is that a relationship
between worker satisfaction and
supervisor satisfaction but this time
now we're controlling for a third
variable for variable being the
management good bad management now why
this is called the 2 by 2 by K test is
because we're looking at the if there is
a evidence of a relation between two
variables each of which are dichotomous
ie are broken down to two bits like
worker satisfaction low and high so suck
so if so supervisor satisfaction low and
high so that explains a two by two bit
times k now this K is for the third
variable in the K stands for the number
of sub groups is broken down to and the
jargon they use is strata or so here
we've got band management and good
management so that's makes this table
two by two by two table all right
all right so to run the test what we
want to do is we go to look at our data
set first I saw that table that I just
showed you I got it from this original
data okay this is group data so first I
need to tell SPSS that so I go to data
and then I go to weight cases and get on
the screen so go to data weights cases
and then I make sure that I click on
weight cases here in transfer management
in - I mean sorry frequency into this
box okay which I had so it's just set up
again so it looks like this when you
first go into it I click on weight cases
by frequency because they contain the
actual counts but each cell take it over
I go okay now I'm ready to run this test
so I go to analyze descriptive
statistics reset this as well right so
first I want to take the two variables
which I'm interested that there's a so
station between in two rows and columns
it doesn't matter which kind of order
the management that is the controlling
variable that is the K bit that's the
conditioning variable you'll take that
into voices layer then we'll go to
statistics and now here we go
all the way down here and says Cochran
this test so we click on to check that
where it's this test a common odds ratio
equals one leave that one and now go
okay
now when we do that we're going to see 1
2 3 4 1 2 4 tables so this is the
breakdown of natural numbers which I
just showed you before I did the example
that I showed you how I got these
numbers and first thing first didn't
this table test of homogeneity of odds
ratio so this is the condition in laymen
terms what just test is doing is its
testing that there is an association the
association between the two things were
looking at worker and was it worker and
supervisors satisfaction are the same
across each strata so good management
and bad management are the same
relationship here as here okay that's
that layman's terms technically speaking
it's like saying that the partial odds
ratio so the odds ratio for each strata
is the same we look now this is more
popular a lot to test you to look up in
this top top one is a more popular one
very slow day and you don't need to make
a meal of this you can see they're both
pointing the fact the same numbers very
slow day this is the p-value and to
remember the rule if the p-value is
bigger than not point naught 5 is pretty
much young do not reject the null
so here it's point seven nine nine so
there's no evidence to reject the null
in other words we we our condition is
satisfied we do not reject the null so
then that's good that we go on to the
test itself now test itself test of
conditional independence right the null
hypothesis here we can put it in loads
of different ways it's a bit like the
test of Association here except for now
we've got a third variable the null
hypothesis is we can say express it as
no partial association between the two
variables given a third variable here no
partial association between the
satisfaction of the worker and the
supervisor given the management all we
can say that similar express it as
conditional independence of the two
variables given the third variable or we
can express it as all the conditional
odds ratio is equal to one that last one
is a very is more technical one but kind
of links back to this text of
homogeneity where this says that they
all equal now this one is saying like
that not that they're all equal that all
equal to one right anyway let's look
we're doing this CMH or MH test the
chi-square this is what we'll report
will report at four point nine six is
the glue your freedom one and this test
under the null hypothesis follow a chi
square distribution and we just report
that associated p-value it is point zero
two six that is less than naught point
naught 5 so we conclude that is evidence
to reject the null I have evidence to
support the alternative here that there
is association between this satisfaction
that satisfaction given the management
ok
and then there's one more thing to do
because we managed to reject the null we
say that there's evidence of Association
so then we can go one step further what
is the nature of that Association well
then you report guys you report the all
common odds ratio the estimate here is
one point four seven so that's what your
report or you can report the 95 percent
confidence interval for a common odds
ratio the lower bound is one point zero
six and the upper bound is two point
zero three eight okay I don't know how
long that took me but that's done the
test okay next thing right now I'm going
to do stuff that you might not be
bothered about but I think this one you
do need to be bothered about really how
the common odds ratio well this kind of
video is a bit slightly after soom that
you know a bit more I have to assume you
know about odds right odds and odds
ratios which I've covered in another
video
now this 1.47 what is it saying okay
well I'll tell you what it says first
and I'll tell you how I know it says
that that 1.7 may be interpreted as
follows that's the odds of happy worker
given say a happy supervisor is one
point four seven times higher than the
odds of failure an unhappy worker given
an unhappy supervisor so I'm just here
using happy instead of a high
satisfaction I'm happy to represent low
satisfaction all right so how do I know
it says that well guys this is the thing
when you're coding what is doing is just
look at each of these tables okay of a
worker satisfaction and supervisor
satisfaction there's actually one two
well as three tables but forget about
the total there are two tables because
there's a table for these two
satisfactions associated linked to each
strata of management one for bad
management one for good management so
these two tables one for bad management
one for good management each table is
what caught partial table in other words
ISM it's a part of the whole thing
because it's broken down by here
management type of management now what
the odds ratio what it does is comparing
the odds of whatever is to the top right
here here is a high worker satisfaction
given whatever is on the bottom of this
partial table it's also high supervisor
satisfaction hence I was talking about
odds of a happy worker or they say a
happy worker given given
a happy say supervisor now when app how
did this table why'd you get low and
height low and high well it's how we
coded it up we coded low right this is
just boring technical bit now so it's up
looks not really statistics but I have
to show you otherwise it doesn't I what
I've done with supervisor and workers
guys is I've coded one for low and two
for high and what the table what SPSS
does automatically even though these
numbers don't mean anything they're just
labels whatever the lowest number is
it'll put that first so here one is low
so it's going to put that first two is
high so it follows you know next how do
i coded a low to be two and high to be
one these two things with a swap round
and that would have you know altered
that your interpretation of the odds
ratio so that's very important to look
out for just in case you don't believe
me I actually did one earlier should do
it together okay I don't make this thing
last for ages but let's say let's get
you to try it I'll just show you one
that I actually did recall that the
common code ratio was one point four
seven when we did it now look if I kind
of code the thing okay so now just
change those labels around for
supervisor satisfaction just look at my
previous example just reverse the video
and you'll see okay you see that the
odds ratio exactly the same but now the
interpretation is different because now
before this was supervisor this was high
and that was low but now it's reverse so
now my interpretation will be different
it will be that the odds of a happy
worker given a not happy supervisor is
one point four seven times higher and
for a happy worker so you see that the
coding day matters so as you understand
that we're comparing this given that so
odds of this given that all right let's
see you next one what is the homogeneous
Association condition is not met so
often you see a basic example they'll
give you a nice one where the
assumptions are all satisfied but what
happens when the assumptions are not
satisfied talk about this one let's test
of homogeneity all right well if this
test is not satisfied this condition is
not met sorry we can do we can think of
some other things one job in the out
pose second is that we could look at
some other test that does not require
this assumption for example we can use a
log linear model if we can say that one
of the variables such as the workers
satisfaction level is like the dependent
variable and the other ones could be
thought of as an independent variable so
you think about like some kind of like a
causality thing going on there we could
use like a logistic regression otherwise
you've got a large sample size we can
use a Pearson chi-square the thing if we
this is an important statement I'm
making here we just step back a bit
about this test the entorhinal test is
that it tests for a specific type of
relationship partial relationship and
that is that each of the partial odds
ratios across each strata are the same
now it could be that there is a
relationship but those partial and odds
ratios are not the same and they are
different to one that's the same as
saying there's a relationship between
these two things but they differ as you
go across the strata another way of
saying that the partial odds ratios yeah
I just said already okay different as
you're going across the strata well that
kind of thing is what can call a
three-way Association and that's
something that a log linear model could
pick up
next often you read like on the web
forums people saying I will get so
worried about what is the difference
being a Cochrane and the CMH test and
they talk about less about this Pearson
chi-square right well all three can do
this test let's just say that all of
these three they are what we call large
sample tests in other words they to work
well they need large sample sizes now
why this test is often these days are
called the mantle Hensel but Cochran was
the first guy who came up with this test
and the mantle Heinz Doyle came up with
this test based on this set of different
assumptions but asymptotically eyeing
large samples to our equivalent by this
bloke and these two guys so hence if we
link it if we call this testicle Michael
Hines that's more fair to this guy
though Cochran and this mantle high Sol
asymptotically large samples there's
nothing to differentiate them so don't
worry because this test is the large
sample test anyway right Pearson
chi-square my Pearson chi-square is I
think it's the first test you of a test
of Association you do you certainly do
this before you ever touch these two
okay so that's why we're more free of
this now this can also do this kind of
stuff but and it's also a lot of samples
and said but the thing about it is you
heard of this thing called the cell
count must be greater than the five rule
cause it's been kind of it's been shown
in some papers that if you've got like
more than 20% of your cell counts or
expect it cell counts talk about these
guys he expected cell counts less than
five then the test doesn't work that
well
this we don't have such a drawback with
sorry don't have such a drawback with
the mantle hangs up test so what we're
doing to get two by two by K and that's
why they focus on these two rather than
the PS and chi-square even divisor one
of the things you've learned first okay
finally I'm not going to touch on this
because this is not a newbie level but
there are generalizations to larger
table so in other words I've got here 2
by 2 by K but we don't have to have 2 by
2 can have these as any other number
like 3 by 5 by 6 or something like that
ok these two numbers don't have to be 2
by 2 in when when we see such kind of
tables then we have to we can choose the
test depending on the type of nature of
these two variables that we are seeing
whether or not this Association whether
the nominal or ordinal the two by two
case we don't have to make such a
distinction between whether they're
nominal ordinal we can play this test so
long I say categorical and broken out
into two level each this just the verbal
stratifying against that variable
doesn't matter where that's ordinal or
ordinal well okay guys that's another
long-winded video from me see what your
comments are haven't made a video for
ages so I think I'm a bit rusty all
right
I know it's hope that is helped you