Interpreting 2x2 and 2x3 chi-square - some reassurance please!

[underpressure]

Greetings from Ireland all. I am currently working on my master's thesis due in about a month. It looks in part at alcohol use amongst college students in a university, for which I distributed a survey. Most of what the survey examines is descriptive data and was easy to generate in SPSS. However I wanted to briefly examine via chi-square test for independence whether age and gender were related to a measure called the audit-c which basically classifies whether a student is at no risk/at risk of harm from alcohol. I would like your help in interpreting in particular the 2x3 and your reassurance that my interpretation of 2x2 is correct. I have read loads of stats books and looked online but still not getting it, as stats is not my strong point!

1)Output is as follows for the 2x2 table:



Sorry about poor quality, best I could do - for some reason if you zoom in a bit attachments become clearer. My interpretations as follows:
Table x reveals that 74.7% of students emerged as at risk of harm from alcohol.
There was a significant difference in positive AUDIT-C scores between males and females (81.9% versus 70.6%, p<0.0001).

_______________________________________________________________________________________
2)This is where it becomes more tricky. Below is 2x3 table - have i interpreted it correctly? As follows:
Table x demonstrates that 26.8% of students are at risk of serious harm from alcohol, and 38.1% are at severe risk. Although females scored marginally higher than males in the “At risk” and “High risk” categories, males scored far higher in the severe risk category (55.4% versus 28.4%) whilst the opposite was true for females in the “Not at risk/Low risk” category (29.4% versus 18.1%). This difference was significant at P<0.0001 as reflected in table x.




_________________________________________________________________________________________
3)
This examines age and the audit-c measure (whether a student is at no risk/risk). Again unsure if I have interpreted it correctly but here it goes: While there does not appear to be a difference amongst the younger categories (18-20 years and 21-24 years) in terms of a decreasing AUDIT-C score with age, those aged 25 years and above appear to enjoy this benefit. Table x demonstrates that this is a significant finding.






Overall question: Am i correct in assumming that in 2x3 tables or larger that it is not possible to examine specific differences between variables with this measure, only to say that a finding is significant or not (i.e. that there is some form of a difference or not?), where is in 2x2 you can say what this difference appears to be?

Really appreciate anyone who can help me out. Thanks so much
Tom

[John F Hall]



Tom

 

Left it a bit late, haven't you?  How do you know your sample is representative of the population from which it is drawn?  If not, there's no point at all in using inferential statistics.  Why bother with grouped scores when you can use a t-test (or analysis of variance if you're comparing more than one group) on the raw ones?  Who is you supervisor?  Send him/her off for re-training and tell him/her to ease off on the booze!  Mind you, N = 1700+ is a nice big "sample" to play with.

 

John Hall

 

One-time External Examiner for Ulster Polytechnic CNAA Masters' degrees (and I said the same then, but more about the standards than the stats.  My 2nd year undergrads did better stuff, but I got bollocked by the other Examiner, Prof Rcichard Brown, Durham, for being too honest in my report to CNAA, which I stand by to this day.  Needless to say, I resigned from CNAA duities as soon as my 3-year tour of duty was over: who wants to work a 14-hour day via the Heathrow Shuttle for peanuts, you get stopped by armed patrols, and the only cheese you get in the restaurant is Cheddar?  Decent wine?  Forget it, unless things have changed since.)

 

----- Original Message -----

From: [hidden email]

To: [hidden email]

Sent: Thursday, July 29, 2010 11:47 AM

Subject: Interpreting 2x2 and 2x3 chi-square - some reassurance please!

Greetings from Ireland all. I am currently working on my master's thesis due
in about a month. It looks in part at alcohol use amongst college students
in a university, for which I distributed a survey. Most of what the survey
examines is descriptive data and was easy to generate in SPSS. However I
wanted to briefly examine via chi-square test for independence whether age
and gender were related to a measure called the audit-c which basically
classifies whether a student is at no risk/at risk of harm from alcohol. I
would like your help in interpreting in particular the 2x3 and your
reassurance that my interpretation of 2x2 is correct. I have read loads of
stats books and looked online but still not getting it, as stats is not my
strong point!

1)Output is as follows for the 2x2 table:

http://spssx-discussion.1045642.n5.nabble.com/file/n2256717/image002.gif
http://spssx-discussion.1045642.n5.nabble.com/file/n2256717/image004.gif
Sorry about poor quality, best I could do - for some reason if you zoom in a
bit attachments become clearer. My interpretations as follows:
Table x reveals that 74.7% of students emerged as at risk of harm from
alcohol.
There was a significant difference in positive AUDIT-C scores between males
and females (81.9% versus 70.6%, p<0.0001).

_______________________________________________________________________________________
2)This is where it becomes more tricky. Below is 2x3 table - have i
interpreted it correctly? As follows:
Table x demonstrates that 26.8% of students are at risk of serious harm from
alcohol, and 38.1% are at severe risk. Although females scored marginally
higher than males in the “At risk” and “High risk” categories, males scored
far higher in the severe risk category (55.4% versus 28.4%) whilst the
opposite was true for females in the “Not at risk/Low risk” category (29.4%
versus 18.1%). This difference was significant at P<0.0001 as reflected in
table x.

http://spssx-discussion.1045642.n5.nabble.com/file/n2256717/image006.gif
http://spssx-discussion.1045642.n5.nabble.com/file/n2256717/image008.gif

_________________________________________________________________________________________
3)
This examines age and the audit-c measure (whether a student is at no
risk/risk). Again unsure if I have interpreted it correctly but here it
goes: While there does not appear to be a difference amongst the younger
categories (18-20 years and 21-24 years) in terms of a decreasing AUDIT-C
score with age, those aged 25 years and above appear to enjoy this benefit.
Table x demonstrates that this is a significant finding.


http://spssx-discussion.1045642.n5.nabble.com/file/n2256717/image010.gif
http://spssx-discussion.1045642.n5.nabble.com/file/n2256717/image012.gif


Overall question: Am i correct in assumming that in 2x3 tables or larger
that it is not possible to examine specific differences between variables
with this measure, only to say that a finding is significant or not (i.e.
that there is some form of a difference or not?), where is in 2x2 you can
say what this difference appears to be?

Really appreciate anyone who can help me out. Thanks so much
Tom
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[Bruce Weaver]

SPSSassasin wrote

Greetings from Ireland all. I am currently working on my master's thesis due in about a month. It looks in part at alcohol use amongst college students in a university, for which I distributed a survey. Most of what the survey examines is descriptive data and was easy to generate in SPSS. However I wanted to briefly examine via chi-square test for independence whether age and gender were related to a measure called the audit-c which basically classifies whether a student is at no risk/at risk of harm from alcohol. I would like your help in interpreting in particular the 2x3 and your reassurance that my interpretation of 2x2 is correct. I have read loads of stats books and looked online but still not getting it, as stats is not my strong point!

--- snip the rest ---

Tom, I am not familiar with audit-c, but it appears to yield a score from 0-12, with higher scores indicating higher risk, is that right?  Is it fair to assume that it has at least approximate interval scale properties?  I.e., does a one-point increase indicate approximately the same change in risk at any point along the scale?  And would it be reasonable to use means & SDs descriptively for the audit-c?  If the answer is YES to both questions, then I wonder why you are not treating it as a continuous variable in your analyses.  Why are you not running a linear regression model with both age (as continuous) and sex as predictors, and perhaps their interaction?  Your sample size certainly looks large enough to support this kind of model.

HTH.

[underpressure]

Hi Bruce, thanks for your reply. You are correct in that the minimum someone can score is 0 points and 12 the maximum. However it is not scaled (if that is correct term) in that a one point increase does not equal the same change in risk. For the sake of ease in the basic 2x2 (and because several irish studies have done similar), someone scoring between 0-4 has a no to low risk of alcohol harm, where as someone getting 5 or above is at risk. However someone getting say a 4 is not twice as much at risk as someone getting a 2, they just fall under that category (hope this makes sense). Internationally it is agreed however that people scoring between 6-7 are at high risk and those scoring 8-12 at severe risk but some who gets 12 does not have double the risk of 6.

The other reason I am using this method is that it is a taught master's thesis (so this thesis makes up about 35-40% of overall masters as modules make up rest) and the fact that there is a large qualitative component that examines the health services on campus, as well as other questions aimed at students such as their agreement with various statements, level of drink-driving, open-ended questions etc. and all this with only a 10,000 word count so limited in terms of space. One of the main things I wanted to do anyway was just to see what proportion of the population actually met the Audit-C criteria which I have done. I just wanted to use chi-square to examine briefly any potential associations.

Thanks
Tom

On Thu, Jul 29, 2010 at 1:44 PM, Bruce Weaver [via SPSSX Discussion] <[hidden email]> wrote:

SPSSassasin wrote:

Greetings from Ireland all. I am currently working on my master's thesis due in about a month. It looks in part at alcohol use amongst college students in a university, for which I distributed a survey. Most of what the survey examines is descriptive data and was easy to generate in SPSS. However I wanted to briefly examine via chi-square test for independence whether age and gender were related to a measure called the audit-c which basically classifies whether a student is at no risk/at risk of harm from alcohol. I would like your help in interpreting in particular the 2x3 and your reassurance that my interpretation of 2x2 is correct. I have read loads of stats books and looked online but still not getting it, as stats is not my strong point!

--- snip the rest ---

Tom, I am not familiar with audit-c, but it appears to yield a score from 0-12, with higher scores indicating higher risk, is that right?  Is it fair to assume that it has at least approximate interval scale properties?  I.e., does a one-point increase indicate approximately the same change in risk at any point along the scale?  And would it be reasonable to use means & SDs descriptively for the audit-c?  If the answer is YES to both questions, then I wonder why you are not treating it as a continuous variable in your analyses.  Why are you not running a linear regression model with both age (as continuous) and sex as predictors, and perhaps their interaction?  Your sample size certainly looks large enough to support this kind of model.

HTH.

--
Bruce Weaver
[hidden email]
http://sites.google.com/a/lakeheadu.ca/bweaver/

"When all else fails, RTFM."

NOTE: My Hotmail account is not monitored regularly.
To send me an e-mail, please use the address shown above.

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[Bruce Weaver]

SPSSassasin wrote

Hi Bruce, thanks for your reply. You are correct in that the minimum someone
can score is 0 points and 12 the maximum. However it is not scaled (if that
is correct term) in that a one point increase does not equal the same change
in risk. For the sake of ease in the basic 2x2 (and because several irish
studies have done similar), someone scoring between 0-4 has a no to low risk
of alcohol harm, where as someone getting 5 or above is at risk. However
someone getting say a 4 is not twice as much at risk as someone getting a 2,
they just fall under that category (hope this makes sense). Internationally
it is agreed however that people scoring between 6-7 are at high risk and
those scoring 8-12 at severe risk but some who gets 12 does not have double
the risk of 6.

To say that 12 reflects twice as much risk (or twice as much whatever) would require a ratio scale--i.e., a scale with a true 0.  Interval scales only require that a change of x units reflects the same amount of change in risk (or whatever) at any point along the scale.  But from what you've said, Audit-c does not even meet that criterion.

SPSSassasin wrote

The other reason I am using this method is that it is a taught master's
thesis (so this thesis makes up about 35-40% of overall masters as modules
make up rest) and the fact that there is a large qualitative component that
examines the health services on campus, as well as other questions aimed at
students such as their agreement with various statements, level of
drink-driving, open-ended questions etc. and all this with only a 10,000
word count so limited in terms of space. One of the main things I wanted to
do anyway was just to see what proportion of the population actually met the
Audit-C criteria which I have done. I just wanted to use chi-square to
examine briefly any potential associations.

Thanks
Tom

OK then, so you have several categories of risk, and they are ordered (from lowest to highest).  You also have a large sample.  Your explanatory variables are sex and age.  Again, the age categories are ordered.  So one option is to take advantage of the ordinal nature of your categories by looking at the test of linear-by-linear association you get in the table of chi-square output.  You can read about it here:

   http://www.uvm.edu/~dhowell/methods7/Supplements/OrdinalChiSq.html

The title says something about missing data, but that is just a typo.

HTH.

[Art Kendall]

I would suggest 1) do exploratory graphics as if the data were continuous, i.e., boxplots for all SES * SES variable groups, and for� � values on each of the marginal SES variables, and for all cases. Try a 3D scatterplot, you can use color to add a fourth variable.
2) see how an ordinary regression looks with the SES variables as predictors
4) use� categorical regression with the SES variables as predictors with a 0-12 value DV. See if measurement level (ordinal vs interval) is important.
5) use categorical regression on a coarsened dv (0 to 4 =1) etc. See if measurement level (ordinal vs interval) is important.

If the unusual happens and coarsening the DV does not distort the picture, go ahead with the coarsened DV. Mention that more refined measurement did not change the substantive conclusions.

Art Kendall
Social Research Consultants


On 7/29/2010 8:53 AM, SPSSassasin wrote:

Hi Bruce, thanks for your reply. You are correct in that the minimum someone can score is 0 points and 12 the maximum. However it is not scaled (if that is correct term) in that a one point increase does not equal the same change in risk. For the sake of ease in the basic 2x2 (and because several irish studies have done similar), someone scoring between 0-4 has a no to low risk of alcohol harm, where as someone getting 5 or above is at risk. However someone getting say a 4 is not twice as much at risk as someone getting a 2, they just fall under that category (hope this makes sense). Internationally it is agreed however that people scoring between 6-7 are at high risk and those scoring 8-12 at severe risk but some who gets 12 does not have double the risk of 6.

The other reason I am using this method is that it is a taught master's thesis (so this thesis makes up about 35-40% of overall masters as modules make up rest) and the fact that there is a large qualitative component that examines the health services on campus, as well as other questions aimed at students such as their agreement with various statements, level of drink-driving, open-ended questions etc. and all this with only a 10,000 word count so limited in terms of space. One of the main things I wanted to do anyway was just to see what proportion of the population actually met the Audit-C criteria which I have done. I just wanted to use chi-square to examine briefly any potential associations.

Thanks
Tom

On Thu, Jul 29, 2010 at 1:44 PM, Bruce Weaver [via SPSSX Discussion] <[hidden email]> wrote:

SPSSassasin wrote:

Greetings from Ireland all. I am currently working on my master's thesis due in about a month. It looks in part at alcohol use amongst college students in a university, for which I distributed a survey. Most of what the survey examines is descriptive data and was easy to generate in SPSS. However I wanted to briefly examine via chi-square test for independence whether age and gender were related to a measure called the audit-c which basically classifies whether a student is at no risk/at risk of harm from alcohol. I would like your help in interpreting in particular the 2x3 and your reassurance that my interpretation of 2x2 is correct. I have read loads of stats books and looked online but still not getting it, as stats is not my strong point!

--- snip the rest ---

Tom, I am not familiar with audit-c, but it appears to yield a score from 0-12, with higher scores indicating higher risk, is that right? � Is it fair to assume that it has at least approximate interval scale properties? � I.e., does a one-point increase indicate approximately the same change in risk at any point along the scale? � And would it be reasonable to use means & SDs descriptively for the audit-c? � If the answer is YES to both questions, then I wonder why you are not treating it as a continuous variable in your analyses. � Why are you not running a linear regression model with both age (as continuous) and sex as predictors, and perhaps their interaction? � Your sample size certainly looks large enough to support this kind of model.

HTH.

--
Bruce Weaver
[hidden email]
http://sites.google.com/a/lakeheadu.ca/bweaver/

"When all else fails, RTFM."

NOTE: My Hotmail account is not monitored regularly.
To send me an e-mail, please use the address shown above.

---

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