Interpretation of chi-square test in SPSS for 2 way table Video Lecture

hello everyone this is phil from
statistics mentor.com in this video I'm
going to give you a gentle introduction
to the cross tabs otherwise known as
cross tabulation otherwise known as a
chi-square test now is a test so being a
test we've got to know what the null and
alternative Stroke experimental
hypothesis is the null is there is no
association between two attributes
another way of saying it is there is no
association between two attributes and
yet another way of saying that is
attributes say a and B are independent
okay so the words independent no
Association no relationship means the
same thing and the alternative of the
experimental hypothesis is there is a
relationship or there they are dependent
those two attributes or there is
Association depending on the words you
used for the null the idea of
Association is similar to correlation
recall with correlation we're looking to
see if there is a relationship as well
but for quantitative variables crosstabs
is for qualitative variables qualitative
we mean that the variable is either
nominal or ordinal okay now in crosstabs
crosstabs
the basic crosstabs you've seen if
there's a relationship or no
relationship between two qualitative
variables alright so these two
qualitative variables may be either both
nominal both ordinal or the mix one is
ordinal one is nominal
now this crosstabs is quite a common
method that is employed when you're
dealing with survey type data all right
now I've got an example here I'm trying
to see if there's a relationship between
smoking and lung cancer suppose I have
no idea that whether these variables are
quantitative qualitative how what kind
of clue can I get from that well if you
go to variable view smoke it is where
the person smokes yes or no it will
click on the values there that's coded
smoker or nonsmoker if it's coded
something like this then that means it's
qualitative in this case it's nominal
cancer
is coded again yes so again this tells
us it is qualitative so if we were to
see if looking to see if there's a
relationship between smoking and cancer
then correlation will is not the
appropriate method that the test
Association or cross tabs this crosstabs
analysis is and then we look at we've
got another two variables here which
we're not going to use the data just to
show you the age you can see it's not
coded the values there nothing there so
that tells us that age is most likely to
be quantitative those numbers actually
and means something they're not codes
okay only then the first few they're for
you so in that case if au is involved
then cross tabs would not be appropriate
but since our hypothesis trying to test
the see if there's a relationship
between smoking and cancer in both those
are qualitative cross tabs is the way
okay first of all been an introduction
let's take things real slow let's first
of all bring up the counts so to do that
go to analyze descriptives and we go to
cross tabs
we've got rows and columns it doesn't
matter really which one you put put one
in rows put one in columns I put smoking
rose put cancer in columns and just then
say okay she give us a table of the
counts alright this two tables first one
is not of interested just telling us
that we've got a sample of 100 people no
missing data there it's all there okay
the next one the cross tabs table all
right reading it we can see that smoking
is split into two categories smoker and
nonsmoker and cancer is split into
cancer and did not get cancer
and then we've got totals the row totals
and the column totals so were to read
this table this tells us that this
number here 30 says that 30 people were
smokers and had lung cancer this number
5 here says that five people were
smokers and did not get lung cancer hope
you get the idea let's go down to this
one what does that say that says that
the five people were non-smokers
and got lung cancer and this one here 60
60 people non-smokers did not get lung
cancer how many people we know there's
100 people out of a hundred people how
many people altogether got lung cancer
35 because you add up the this is the
column of people got count lung cancer
30 plus 5 is 35 that's why this total is
doing is cutting up the totting up these
column there I really hate this double
click to activate thing that keeps
popping up in SPSS very annoying right
how many people did not get lung cancer
65 okay similarly how many people in my
sample smokers smokers go to the column
Oh 30 plus 535 how many people of my
hundred were non-smokers 65 in this row
here we add up five 60 65 all right and
then if you look at the sum of the total
that's one hundred and some-odd total
there comes the hundred book which is as
it should be okay
just looking at this it gives us an idea
that smokers tended to have lung cancer
and
smokers okay but because the total
number of smokers and non-smokers are
different those is actually easy to
compare make comparisons in percentage
terms so to do it in percentage terms go
to analyze again where is it descriptive
stats cross tabs and now we click on
cells percentages
let's get row column total okay okay now
slightly bigger table but you can see
SEM is the first one because you still
got the numbers there look lung cancer
smoke is 35 560 those numbers are still
there but now we've got percentages
right so if we read along where it says
a hundred here means that's out of all
people who smoke have all people of
smoke eighty five point seven percent
get to lung cancer and out of everyone
who smokes 14.3% do not get lung cancer
and those two percentages add up to 104
non-smokers within whose smoke comes 100
so how does it is that hundred split up
with between the lung cancer no long
cancer will happen on some smokers seven
point seven percent have lung cancer
that's five which represent which is
five out of 65 which is seven point
seven percent and ninety two point three
percent do not look like lung cancer who
are the people who are non-smokers
that's 60 divided by sixty five that's
60 out of sixty five of me make is
ninety two point three percent okay so
now you can see that relationship is
reversed for smokers and have a higher
probability or higher chance of getting
lung cancer
than non-smokers non-smokers people who
are non-smokers that the pattern is
reversed most do not get lung cancer all
right so what I'm saying is their
relationship between a and B with by
relationship we're looking for a pattern
you know in this case is peers from our
data that those people who do not smoke
have less of a chance of getting lung
cancer than those who did all right now
we analysis doesn't stop there we're not
actually done any cross tabs are all you
have we because we have not done a test
well now we're ready for the test
because what we've done so far is we've
looked to see if there's a relationship
just by looking at the counts and
percentages but these counts and
percentages this apparent pattern what
we've noted could just be due to
sampling error all right so we need to
test formally whether such a
relationship holds yes or no if it
doesn't then the pattern that we've just
looked at here is just due to randomness
in the data it's not actually there so
that is why we need to do the test so
now let's go ahead and do it it's pretty
much the same buttons again analyze the
script of stats cross tabs this time we
click on statistics and we request the
chi-square there let's say okay and then
we okay now you see the first two tables
are the same as what we've seen
previously there's an additional table
this is the chi-square test table recall
that the null is well you can chant it
out tell me what it is yes I the null is
that there is no relationship between
smoking
and non-cancer we read off the top one
here forget all the other ones Pearson
chi-square the test statistic is sixty
point eight seven for one degree of
freedom but to be honest that doesn't
interest us those numbers the test
statistic and degree of freedom
ultimately to get the p-value which is
comes under this what they call
asymptotic significance two-sided
alright right there
zero now recall that if the p-value is
low we reject the null and the Dickey to
remember is if P is low nor must go now
P is low lower than not point naught 5
indeed it's lower even than not point
not one so what do we do is low so the
null must go ie we reject null in favor
of the alternative so we conclude that
there is a relationship that is there is
evidence to support a relationship
between smoking and lung cancer once
we've done that we can report it we can
report it like this in the report there
is very strong evidence of a
relationship between smoking and death
due to lung cancer open bracket and then
write down the chi-square comment the
degree freedom comma the p-value less
than naught point naught naught 1 it
even it's really tiny or you can replace
that if you are not comfortable nor
point naught 5 ok
so let's just look back at what we've
done let's look at the sky square so
this carry square test is the test
whether there's an association between
two qualitative variables which may be
nominal or was it nominal or ordinal or
mix of all and nominal we run the
chi-square test and we look at the PSN
sky square and the null is there is no
relationship between the two things all
right if we do not reject the null then
the analysis stops and say there is no
evidence that there is a relationship
between a and B . done but if we reject
the null that is a relationship and then
we report what that relationship is by
going to this table of Council and then
looking and reporting a pattern like
with or like we did earlier okay so
that's only time that this comes into
place when we find that is evidence of a
relationship now what I want to make
clear is basically finish now I want to
conclude by pointing out a few things
because this has been a very gentle
introduction there's obviously lots of
things we've missed out but for a first
first pass through this topic is
sufficient all we've done right now I
get students saying that saying that
because the p-value here is less it's
very very tiny degrees basically less
than not but not one that there is a
they say that there is a very strong
relationship there is a very strong
relationship between smoking and death
due to lung cancer now why is that not
correct it's not correct because the
lower the p-value it does not mean the
stronger the relationship you know the
test this is only test to see whether
there's evidence of a relationship or
there's no evidence and if there's
evidence how strong is the degree of
that evidence I think that's where
students get caught out
especially if their first language is
not English so if the p-value is very
low it does not mean that there is very
strong relationship it means that there
is very strong evidence evidence of a
relationship okay so let's say that
again low p-value means the low the
lower the p-value that means the
stronger the evidence of a relationship
it does not mean the stronger the
relationship that's first thing the
second thing is that look under this
chi-square test it says here zero cells
0% have expected cell count of less than
five okay now you will encounter
occasionally especially if you've got
some categories with a few number of
observations that some of the expected
cell values is less than five now if
that's the case this chi-square
proximation does not work so well and
then how do you get around that is by
collapsing groups you might have heard
about collapse in groups or combining
groups okay if you're still in a dark
there let's just run this thing but with
the expected to tell values and you'll
see what I mean
so we're go to analyze again and let's
see where is it
descriptive stats cross tabs and we want
expected not count what expected
now look at this table counts I've seen
previously well Scott under each cell
now expected count these expected counts
of the kind of the theoretical numbers
you would expect to see in the cell if
the null was not true
sorry if the null is true so we're this
is number 30 is it says we observe 30
people who smokers and had lung cancer
but if we expect them there to be no
relationship i if we expect the null to
be true we'd expect there to be actually
around around twelve point three people
with who are smokers and lung cancer why
say around this because obviously you
cannot get point three of a person all
right so the closer for each cell the
close to the count value to the expected
count that means the null is probably
you probably will not reject the null
either it's no relationship okay because
the expected counts are generated
assuming that the null is true I that
there is no relationship okay now we've
swipe around here twelve point three
twenty two point eight twenty two point
eight forty two point three all those
expected counts I just read out our
exceed five so we have no problem right
but I'm saying that four tables where
some of the numbers are less expected
cell cancer is less than five then we
would have to think about collapsing
cells if we can because you can't always
do it okay next thing write in terms of
so going back to the strength of
relationship we know the p-value cannot
give you the strength for relationship
but if we find that there is strength of
relation we want to if there is a
relationship we can kind of report the
relationships I'll do my DT very simply
if you want to do it more sophisticated
you would use something called the odds
and odds ratio which you can get from
this table again I'm not going to do
that in this video that would give you
the odds and odds ratio give you a idea
the strength of relationship the other
thing you can do is to report the whole
set of statistics
you to report the strength of relation
linear association so if we go back to
descriptive stats and cross tabs if we
click on statistics here can you see at
nominal and then ordinal under each
column you've got whole load of boxes
there these are basically options to
test for this coming not to test to
indicate the strength of association the
degree of Association by a weak or
medium or strong between your two your
two qualitative variables okay well this
is supposed to be gentle intro but I've
said quite a bit towards the end finally
also okay so based on this test it may
appear there is a strident between
smoking and lung cancer however as with
statistics isn't always as simple as
that because although that could appear
to be a relationship from the analysis
we have done this relationship could
disappear when we introduce one other or
one or more other variable into the
analysis ie if we condition on one or
more other variable sometimes this is
called the third variable problem so in
correlation the analogous thing to occur
in correlation to this is the partial
correlation so you know when you look at
correlations between a and B when
introduced see the correlation to it a
and B could disappear disappear because
a and B create there's no real a real
direct relation between a and B just
that they're PSB it relation between a
and B because each of a and B are
related by a C okay so similarly to here
but again that's what another that's
would be a bit more advanced than we're
doing today so let's stop there so in
this video just know that crosstabs is
the test for the relationship between
two qualitative variables and that we
use the chi-square
to do that and the null is there is no
relationship between two things a bee
the alternative is that there is a
relationship between a and B we look at
the chi-square value if we reject it
means that there is evidence of a
relationship then we go in to the table
of counts and report percentages look
for a pattern there okay right well I
hope that has been useful thanks for
watching