Date:         Sun, 29 Jul 2001 11:25:30 -0300
Reply-To:     hmaletta@fibertel.com.ar
Sender:       "SPSSX(r) Discussion" <SPSSX-L@LISTSERV.UGA.EDU>
From:         Hector Maletta <hmaletta@FIBERTEL.COM.AR>
Subject:      Re: reading risk tables
Content-Type: text/plain; charset=us-ascii

Bill Gottdiener wrote:
> Could anyone help me understand how to read the following relative risk
> table? I don't understand what the different odds ratios refer to. Does the
> first one mean that males are 1.6 times more likely to be married than
> females? If so, then what do the other two odds ratios mean. I'd appreciate
> any help with this.
> Bill
>                                                          95% CONF.INTERVAL
> Respondent's Sex                              Value    Lower  Upper
> Odds Ratio for SEX (1 Male / 2 Female)        1.617    1.314  1.989
> For cohort MARRIED Married ? = 1.00 yes       1.248    1.136  1.371
> For cohort MARRIED Married ? = 2.00 no         .772     .688   .865
> N of Valid Cases    1499

Bill:
Look first at the first line. The value 1.617 says that the odds ratio
of being married (for males relative to females) is 1.617. This number
is the ratio of two odds:
Odds of a male being married = Married males/Unmarried males.
Odds of a female being married = Married females/Unmarried females.

The ratio 1.617 says that the odds of a male being married are 1.617
times as large as the odds of a female to be married.
Now for the other two lines. They give you two alternative ways of
looking at your data. If you consider that "being married" is the event
to be observed, look at the second line. The value 1.248 is the ratio of
the following:
Married males / Total males
Married females / Total females.

The third line does the same but based on unmarried people, obtaining
the result 0.772.

>From the former (1.248) you can conclude that males are roughly 25% more
likely to be married than women. The confidence intervale in this case
goes from 1.136 to 1.371, so you can reject (with 95% confidence) the
null hypothesis that the two proportions (% married males and % married
females) are the same, i.e. the null hypothesis that both genders are
equally likely to be married.
>From the latter (0.772) you may conclude that males are roughly 23% less
likely to be unmarried than females, and again you can reject the null
hypothesis that both genders are equally likely to be unmarried.

These two values (1.248 and 0.772) are called Estimates of Relative
Risk, whilst the former is called the Odds Ratio.

Hope this helps.

Hector Maletta
Universidad del Salvador
Buenos Aires, Argentina