Power analysis with Categorical Independent variable and Binary Outcomes help

[Michael Lanni]

I am using stata and I think the right command is "powercal." It takes 4 variables and calculates a 5th. they are the sample size, power, alpha (0.8), delta (meaningful difference), and standard deviation. I am trying to caluclate power of my study with n=40 surgical patients and 5 categories (surgical site) in my independent variable. But since my outcomes (complications) are just "yes" or "no" how do I define delta? background: this is a surgical study, independent variable is where we did the surgery (arm, leg, ect). dependent is y/n presence of wound healing complications. I am using logistic regression (logistic) and would like to do a power analysis to make sure our findings of no difference in complications depending on surgical site is true or just due to small sample size. Do I use the odds ratios from my logistic regression for delta or something?

[Michael Lanni]

This is what I have been playing with:

locationgroup is the surgical site. whc is wound healing complications.



summarize ageatoperation bmikgm2

Variable | Obs Mean Std. Dev. Min Max
-------------+--------------------------------------------------------
ageatopera~n | 40 54.4 15.68243 26 94
bmikgm2 | 40 30.2415 6.444009 20.8 53.5

. tab locationgroup

Location |
Group | Freq. Percent Cum.
------------+-----------------------------------
1 | 8 20.00 20.00
2 | 11 27.50 47.50
3 | 4 10.00 57.50
4 | 17 42.50 100.00
------------+-----------------------------------
Total | 40 100.00

. tab whc

WHC | Freq. Percent Cum.
------------+-----------------------------------
0 | 27 67.50 67.50
1 | 13 32.50 100.00
------------+-----------------------------------
Total | 40 100.00

. tab whc locationgroup

| Location Group
WHC | 1 2 3 4 | Total
-----------+--------------------------------------------+----------
0 | 5 10 3 9 | 27
1 | 3 1 1 8 | 13
-----------+--------------------------------------------+----------
Total | 8 11 4 17 | 40


. logit whc ageatoperation bmikgm2 i.locationgroup

Iteration 0: log likelihood = -25.223241
Iteration 1: log likelihood = -22.11904
Iteration 2: log likelihood = -21.970601
Iteration 3: log likelihood = -21.969743
Iteration 4: log likelihood = -21.969743

Logistic regression Number of obs = 40
LR chi2(5) = 6.51
Prob > chi2 = 0.2600
Log likelihood = -21.969743 Pseudo R2 = 0.1290

--------------------------------------------------------------------------------
whc | Coef. Std. Err. z P>|z| [95% Conf. Interval]
---------------+----------------------------------------------------------------
ageatoperation | .0168503 .0236308 0.71 0.476 -.0294652 .0631658
bmikgm2 | .057588 .0622451 0.93 0.355 -.0644101 .179586
|
locationgroup |
2 | -2.119003 1.366914 -1.55 0.121 -4.798105 .5600992
3 | -.2899529 1.415507 -0.20 0.838 -3.064296 2.48439
4 | .3354671 .8925478 0.38 0.707 -1.413894 2.084829
|
_cons | -3.116928 2.42583 -1.28 0.199 -7.871467 1.637611
--------------------------------------------------------------------------------

. margins locationgroup

Predictive margins Number of obs = 40
Model VCE : OIM

Expression : Pr(whc), predict()

-------------------------------------------------------------------------------
| Delta-method
| Margin Std. Err. z P>|z| [95% Conf. Interval]
--------------+----------------------------------------------------------------
locationgroup |
1 | .391054 .1685024 2.32 0.020 .0607953 .7213127
2 | .0769216 .0757145 1.02 0.310 -.0714761 .2253192
3 | .3275266 .2560628 1.28 0.201 -.1743472 .8294004
4 | .4692803 .1199323 3.91 0.000 .2342174 .7043432
-------------------------------------------------------------------------------

. graph display Graph

. graph drop Graph

. margins locationgroup, at( ageatoperation=generate(26(1)94))
unknown function 26()
r(133);

. margins locationgroup

Predictive margins Number of obs = 40
Model VCE : OIM

Expression : Pr(whc), predict()

-------------------------------------------------------------------------------
| Delta-method
| Margin Std. Err. z P>|z| [95% Conf. Interval]
--------------+----------------------------------------------------------------
locationgroup |
1 | .391054 .1685024 2.32 0.020 .0607953 .7213127
2 | .0769216 .0757145 1.02 0.310 -.0714761 .2253192
3 | .3275266 .2560628 1.28 0.201 -.1743472 .8294004
4 | .4692803 .1199323 3.91 0.000 .2342174 .7043432
-------------------------------------------------------------------------------

marginsplot

Variables that uniquely identify margins: locationgroup

logistic whc ageatoperation

Logistic regression Number of obs = 40
LR chi2(1) = 0.79
Prob > chi2 = 0.3746
Log likelihood = -24.829132 Pseudo R2 = 0.0156

--------------------------------------------------------------------------------
whc | Odds Ratio Std. Err. z P>|z| [95% Conf. Interval]
---------------+----------------------------------------------------------------
ageatoperation | 1.01957 .022442 0.88 0.379 .97652 1.064518
_cons | .165272 .2109791 -1.41 0.158 .0135392 2.017468
--------------------------------------------------------------------------------


. powercal powerage, n(40) a(0.05) d(0.008417) s(15.68)
Result to be calculated is power in variable: powerage


and my power is 0.02519908

[Steve Samuels]

Please read FAQ 12 and present code and results between CODE delimiters. And you are also asked to give the author and source of unofficial commands. powercal, by Roger Newson, is available at SSC.


The test of category differences after logistic or any other single outcome regression command is:

mtest i.locationgroup.1 = i.locationgroup.2 = i.locationgroup.3 = i.locationgroup.4, mtest(sidak)

(See example below. The mtest() option is needed to correct for multiple tests of pairwise differences)

The overall test is the "all" test Example, which will have 3 degrees of freedom for the null hypothesis of no difference between the four groups. . This is analogous to the F test in a four-group ANOVA. You have done the calculation for a one parameter test of the effect of a different variable. Power calculations for the overall 3 d.f. test require 1) that you guess response proportions in each category: and 2) that you form what is known as the non-centrality parameter. However this second calculation requires expert knowledge. I suggest that you do the power calculations for each of the pairs of categories (1 vs 2, 1 vs 3, 1 vs 4, 2 vs 3, 2 vs 4, 3 vs 4. It's probably easier to use Stata's power twoprop than it is use powercal. If you have continuous covariates, then estimate proportions at the covariate means


However, since you've already done this analysis, then a post-hoc calculation can be misleading. Just to state one paradox: if you find that one of the pairwise calculations (say \(p_1\) and \(p_4)\) is significant at p=0.05 (with or without correction for multiple tests), it will turn out that the pre-study power of detecting the observed difference was about 50%. Instead of such a post-hoc test, I recommend that you examine confidence intervals.

sysuse auto, clear
recode rep78 1/2=5
logistic foreign i.rep78 turn
test 3.rep78 =4.rep78=5.rep78, mtest(sidak)

with results

. logistic foreign i.rep78 turn

Logistic regression                             Number of obs     =         69
                                                LR chi2(3)        =      47.27
                                                Prob > chi2       =     0.0000
Log likelihood = -18.767412                     Pseudo R2         =     0.5574

------------------------------------------------------------------------------
     foreign | Odds Ratio   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       rep78 |
          4  |    9.93192   11.37761     2.00   0.045     1.051794    93.78554
          5  |   8.681175   9.171395     2.05   0.041     1.094738    68.84094
             |
        turn |   .5438822    .085999    -3.85   0.000     .3989444    .7414764
       _cons |   1.07e+09   6.09e+09     3.64   0.000     14683.46    7.75e+13
------------------------------------------------------------------------------

. test 3.rep78 =4.rep78=5.rep78, mtest(sidak)

 ( 1)  [foreign]3b.rep78 - [foreign]4.rep78 = 0
 ( 2)  [foreign]3b.rep78 - [foreign]5.rep78 = 0

---------------------------------------
       |        chi2     df       p
-------+-------------------------------
  (1)  |        4.02      1     0.0881 #
  (2)  |        4.18      1     0.0799 #
-------+-------------------------------
  all  |        5.13      2     0.0770
---------------------------------------
              # Sidak-adjusted p-values

[Michael Lanni]

Hey there,

Sorry for my breech of etiquette, I have since read the FAQ's. As a new guy, I appreciate the guidance and am trying to correct format here for the first time (I hope it works).

I really appreciate your help. I have been struggling with this for over a week now. I will use the confidence intervals as shown in the example picture. Here is how I got it:

Input Code:

logistic whc i.locationgrouplogistic whc i.locationgroup
test 1.locationgroup = 2.locationgroup = 3.locationgroup = 4.locationgroup, mtest(sidak)
margins locationgroup
marginsplot, xdimension(locationgroup)

Results Code:

Logistic regression            Number of obs   =    40
            LR chi2(3)      =    5.15
            Prob > chi2     =    0.1610
Log likelihood = -22.646917            Pseudo R2       =    0.1021

                
whc  Odds Ratio    Std. Err.    z    P>z     [95% Conf.    Interval]
                
locationgroup 
2     .1666667    .2130032    -1.40    0.161     .0136143    2.040332
3     .5555556    .7590334    -0.43    0.667     .0381737    8.085189
4     1.481481    1.299526    0.45    0.654     .2654846    8.267097
              
_cons          .6    .438178    -0.70    0.484     .1433909    2.51062
                

( 1)    [whc]1b.locationgroup -    [whc]2.locationgroup    =    0
( 2)    [whc]1b.locationgroup -    [whc]3.locationgroup    =    0
( 3)    [whc]1b.locationgroup -    [whc]4.locationgroup    =    0

        
    chi2     df    p
        
(1)    1.97      1    0.4092 #
(2)    0.19      1    0.9631 #
(3)    0.20      1    0.9586 #
        
all    3.81      3    0.2826
        
    # Sidak-adjusted    p-values

Adjusted predictions        Number    of obs   =    40
Model VCE    : OIM

Expression   : Pr(whc), predict()

                
Delta-method
Margin   Std. Err.    z    P>z    [95% Conf.    Interval]
                
locationgroup 
1         .375   .1711633    2.19    0.028    .0395261    .7104739
2     .0909091   .0866784    1.05    0.294    -.0789775    .2607957
3          .25   .2165064    1.15    0.248    -.1743447    .6743447
4     .4705882   .1210578    3.89    0.000    .2333193    .7078572
                
 Variables that uniquely identify margins: locationgroup

On another note, I am a student in Albany. What are the odds? No wait, no need to answer that, it is just an expression. No more stats questions from me for a while. Thanks again.

[Steve Samuels]

Glad it helped. Unfortunately there' s no evidence of a difference in proportions. Since you have no other covariates, the marginal proportions should be the same as the crude proportions, which I don't think you've shown:

proportion wbc, over(locationgroup)

Note that the confidence interval endpoints for margins extend beyond the [0,1] bounds for a proportion. You can get CIs without this problem as follows: Download transform_margins by Jeff PItblado ("findit transform_margins") and install. Then run:

logit wbc i.locationgroup, vce(robust)
margins locationgroup, predict(xb)
transform_margins invlogit(xb)

[Steve Samuels]

Correction: the transform_margins command is:

transform_margins invlogit(@)

[Michael Lanni]

Hello again,

At the risk of looking like a toddler, I included all the tests I ran after reading your first message. I had to break the results up into multiple posts due to the character limit. No evidence of a difference in proportions is not unfortunate. We are trying to show that this flap can be used anywhere on the body without increased risk for WHC or SSI, so I was hoping for no difference. We do have other covariates of interest, but I was trying to keep my question simple. We are looking at patient Age, BMI, Surgical Site, and Flap size (Flap size as a categorical variable; 1-50 cm^2 = small, 51-100 cm^2=medium, etc.) I also have data for comorbidities (like Smoker/nonsmoker) that I was going to just test for relationship with WHC.SSI using Chi^2. Graphs are linked (the website only lets me post 5). For the SSI (Surgical Site Infection), they are divided up into Major(1 event) and minor (3 events). I think I got an error here due to lack of events so switched to Fischer's Exact or Chi^2. Major and Minor wound healing complications (WHC) are still being defined and I will have to do the stats after we finish the chart review. So I still need to go back and do the transform_margins invlogit@ command by Jeff PItblado.

Input:

logistic whc ageatoperation
test ageatoperation , mtest(sidak)
margins, at( ageatoperation=(20(10)90))
marginsplot, xdimension(at(ageatoperation))
logistic ssi ageatoperation
margins, at( ageatoperation=(20(10)90))
marginsplot, xdimension(at(ageatoperation))
logistic ssimn ageatoperation
test ageatoperation , mtest(sidak)
margins, at( ageatoperation=(20(10)90))
marginsplot, xdimension(at(ageatoperation))
logistic ssimj ageatoperation
 test ageatoperation , mtest(sidak)
margins, at( ageatoperation=(20(10)90))
marginsplot, xdimension(at(ageatoperation))
logistic whc bmikgm2
test bmikgm2 , mtest(sidak)
margins, at( bmikgm2 =(20(5)50))
marginsplot, xdimension(bmikgm2 )
logistic ssi bmikgm2
test bmikgm2 , mtest(sidak)
margins, at( bmikgm2 =(20(5)55))
marginsplot, xdimension(bmikgm2 )
logistic ssimn bmikgm2
test bmikgm2 , mtest(sidak)
margins, at( bmikgm2 =(20(5)55))
marginsplot, xdimension(bmikgm2 )
logistic ssimj bmikgm2
test bmikgm2 , mtest(sidak)
margins, at( bmikgm2 =(20(5)55))
logistic whc i.locationgroup
*To Be Continued
test 1.locationgroup = 2.locationgroup = 3.locationgroup = 4.locationgroup, mtest(sidak)
margins locationgroup
marginsplot, xdimension(locationgroup)
logistic ssi i.locationgroup
tabulate locationgroup ssi, exact
margins locationgroup
tabulate locationgroup ssimn, exact
logistic ssimn i.locationgroup
margins locationgroup
marginsplot, xdimension(locationgroup)
*I know there is only one variable. I did this graph for completeness I guess.
logistic ssimj i.locationgroup
margins locationgroup
marginsplot, xdimension(locationgroup)
logistic whc i.flapsizegroup
tabulate flapsizegroup whc, exact
tabulate flapsizegroup whc, chi2
margins flapsizegroup
marginsplot, xdimension(flapsizegroup)
logistic ssi i.flapsizegroup
tabulate flapsizegroup ssi, exact
margins flapsizegroup
marginsplot, xdimension(flapsizegroup)
logistic ssimn i.flapsizegroup
tabulate flapsizegroup ssimn, exact
margins flapsizegroup
marginsplot, xdimension(flapsizegroup)
logistic ssimj i.flapsizegroup
tabulate flapsizegroup ssimj, exact
margins flapsizegroup
marginsplot, xdimension(flapsizegroup)

I repeat this


Output:

. logistic whc ageatoperation

Logistic regression                               Number of obs   =         40
                                                  LR chi2(1)      =       0.79
                                                  Prob > chi2     =     0.3746
Log likelihood = -24.829132                       Pseudo R2       =     0.0156

--------------------------------------------------------------------------------
           whc | Odds Ratio   Std. Err.      z    P>|z|     [95% Conf. Interval]
---------------+----------------------------------------------------------------
ageatoperation |    1.01957    .022442     0.88   0.379       .97652    1.064518
         _cons |    .165272   .2109791    -1.41   0.158     .0135392    2.017468
--------------------------------------------------------------------------------

. test ageatoperation , mtest(sidak)

 ( 1)  [whc]ageatoperation = 0

---------------------------------------
       |        chi2     df       p
-------+-------------------------------
  (1)  |        0.78      1     0.3786 #
-------+-------------------------------
  all  |        0.78      1     0.3786
---------------------------------------
              # Sidak-adjusted p-values

. margins, at( ageatoperation=(20(10)90))

Adjusted predictions                              Number of obs   =         40
Model VCE    : OIM

Expression   : Pr(whc), predict()

1._at        : ageatopera~n    =          20

2._at        : ageatopera~n    =          30

3._at        : ageatopera~n    =          40

4._at        : ageatopera~n    =          50

5._at        : ageatopera~n    =          60

6._at        : ageatopera~n    =          70

7._at        : ageatopera~n    =          80

8._at        : ageatopera~n    =          90

------------------------------------------------------------------------------
             |            Delta-method
             |     Margin   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         _at |
          1  |   .1958334   .1354984     1.45   0.148    -.0697385    .4614053
          2  |   .2281598   .1169441     1.95   0.051    -.0010465     .457366
          3  |   .2640699   .0949227     2.78   0.005     .0780248     .450115
          4  |   .3034103   .0770983     3.94   0.000     .1523003    .4545202
          5  |   .3458571   .0798143     4.33   0.000     .1894239    .5022902
          6  |   .3909097   .1098219     3.56   0.000     .1756627    .6061567
          7  |   .4379024   .1552722     2.82   0.005     .1335744    .7422304
          8  |   .4860364   .2059972     2.36   0.018     .0822893    .8897834
------------------------------------------------------------------------------

. marginsplot, xdimension(at(ageatoperation))

  Variables that uniquely identify margins: ageatoperation

. logistic ssi ageatoperation

Logistic regression                               Number of obs   =         40
                                                  LR chi2(1)      =       0.00
                                                  Prob > chi2     =     0.9565
Log likelihood = -13.001832                       Pseudo R2       =     0.0001

--------------------------------------------------------------------------------
           ssi | Odds Ratio   Std. Err.      z    P>|z|     [95% Conf. Interval]
---------------+----------------------------------------------------------------
ageatoperation |   .9981398   .0341298    -0.05   0.957     .9334388    1.067325
         _cons |   .1229147   .2361982    -1.09   0.275     .0028438    5.312637
--------------------------------------------------------------------------------

. margins, at( ageatoperation=(20(10)90))

Adjusted predictions                              Number of obs   =         40
Model VCE    : OIM

Expression   : Pr(ssi), predict()

1._at        : ageatopera~n    =          20

2._at        : ageatopera~n    =          30

3._at        : ageatopera~n    =          40

4._at        : ageatopera~n    =          50

5._at        : ageatopera~n    =          60

6._at        : ageatopera~n    =          70

7._at        : ageatopera~n    =          80

8._at        : ageatopera~n    =          90

------------------------------------------------------------------------------
             |            Delta-method
             |     Margin   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         _at |
          1  |   .1058828   .1209755     0.88   0.381    -.1312248    .3429903
          2  |   .1041329   .0911052     1.14   0.253    -.0744299    .2826957
          3  |   .1024086   .0655419     1.56   0.118    -.0260512    .2308685
          4  |   .1007097   .0493504     2.04   0.041     .0039847    .1974347
          5  |   .0990359   .0504175     1.96   0.049     .0002193    .1978524
          6  |   .0973868   .0666825     1.46   0.144    -.0333085    .2280821
          7  |   .0957623   .0893827     1.07   0.284    -.0794245    .2709492
          8  |   .0941621   .1140975     0.83   0.409    -.1294649    .3177891
------------------------------------------------------------------------------

. marginsplot, xdimension(at(ageatoperation))

  Variables that uniquely identify margins: ageatoperation

. logistic ssimn ageatoperation

Logistic regression                               Number of obs   =         40
                                                  LR chi2(1)      =       0.32
                                                  Prob > chi2     =     0.5737
Log likelihood = -10.497152                       Pseudo R2       =     0.0148

--------------------------------------------------------------------------------
         ssimn | Odds Ratio   Std. Err.      z    P>|z|     [95% Conf. Interval]
---------------+----------------------------------------------------------------
ageatoperation |   .9774102   .0407941    -0.55   0.584     .9006381    1.060726
         _cons |   .2670126    .580296    -0.61   0.543     .0037725    18.89905
--------------------------------------------------------------------------------

. test ageatoperation , mtest(sidak)

 ( 1)  [ssimn]ageatoperation = 0

---------------------------------------
       |        chi2     df       p
-------+-------------------------------
  (1)  |        0.30      1     0.5841 #
-------+-------------------------------
  all  |        0.30      1     0.5841
---------------------------------------
              # Sidak-adjusted p-values

. margins, at( ageatoperation=(20(10)90))

Adjusted predictions                              Number of obs   =         40
Model VCE    : OIM

Expression   : Pr(ssimn), predict()

1._at        : ageatopera~n    =          20

2._at        : ageatopera~n    =          30

3._at        : ageatopera~n    =          40

4._at        : ageatopera~n    =          50

5._at        : ageatopera~n    =          60

6._at        : ageatopera~n    =          70

7._at        : ageatopera~n    =          80

8._at        : ageatopera~n    =          90

------------------------------------------------------------------------------
             |            Delta-method
             |     Margin   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         _at |
          1  |   .1446199   .1720353     0.84   0.401     -.192563    .4818028
          2  |   .1185822    .107713     1.10   0.271    -.0925314    .3296958
          3  |   .0967023   .0640958     1.51   0.131    -.0289231    .2223277
          4  |   .0785001   .0435961     1.80   0.072    -.0069468    .1639469
          5  |   .0634832   .0435432     1.46   0.145      -.02186    .1488264
          6  |   .0511795   .0499483     1.02   0.306    -.0467173    .1490763
          7  |   .0411556   .0547932     0.75   0.453    -.0662371    .1485482
          8  |   .0330266   .0566475     0.58   0.560    -.0780005    .1440536
------------------------------------------------------------------------------

. marginsplot, xdimension(at(ageatoperation))

  Variables that uniquely identify margins: ageatoperation

. logistic ssimj ageatoperation

Logistic regression                               Number of obs   =         40
                                                  LR chi2(1)      =       0.63
                                                  Prob > chi2     =     0.4262
Log likelihood = -4.3597458                       Pseudo R2       =     0.0677

--------------------------------------------------------------------------------
         ssimj | Odds Ratio   Std. Err.      z    P>|z|     [95% Conf. Interval]
---------------+----------------------------------------------------------------
ageatoperation |   1.050554   .0650702     0.80   0.426     .9304559    1.186153
         _cons |   .0013069   .0055416    -1.57   0.117     3.21e-07    5.316385
--------------------------------------------------------------------------------

. test ageatoperation , mtest(sidak)

 ( 1)  [ssimj]ageatoperation = 0

---------------------------------------
       |        chi2     df       p
-------+-------------------------------
  (1)  |        0.63      1     0.4259 #
-------+-------------------------------
  all  |        0.63      1     0.4259
---------------------------------------
              # Sidak-adjusted p-values

. margins, at( ageatoperation=(20(10)90))

Adjusted predictions                              Number of obs   =         40
Model VCE    : OIM

Expression   : Pr(ssimj), predict()

1._at        : ageatopera~n    =          20

2._at        : ageatopera~n    =          30

3._at        : ageatopera~n    =          40

4._at        : ageatopera~n    =          50

5._at        : ageatopera~n    =          60

6._at        : ageatopera~n    =          70

7._at        : ageatopera~n    =          80

8._at        : ageatopera~n    =          90

------------------------------------------------------------------------------
             |            Delta-method
             |     Margin   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         _at |
          1  |    .003492   .0106235     0.33   0.742    -.0173296    .0243137
          2  |   .0057055   .0140579     0.41   0.685    -.0218474    .0332584
          3  |   .0093089   .0178081     0.52   0.601    -.0255942    .0442121
          4  |   .0151535    .021544     0.70   0.482     -.027072     .057379
          5  |   .0245766   .0263317     0.93   0.351    -.0270327    .0761858
          6  |   .0396234   .0398444     0.99   0.320    -.0384701     .117717
          7  |    .063285   .0784977     0.81   0.420    -.0905677    .2171377
          8  |   .0996108    .159884     0.62   0.533    -.2137561    .4129777
------------------------------------------------------------------------------

. marginsplot, xdimension(at(ageatoperation))

  Variables that uniquely identify margins: ageatoperation

. logistic whc bmikgm2

Logistic regression                               Number of obs   =         40
                                                  LR chi2(1)      =       0.09
                                                  Prob > chi2     =     0.7645
Log likelihood = -25.178368                       Pseudo R2       =     0.0018

------------------------------------------------------------------------------
         whc | Odds Ratio   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
     bmikgm2 |   1.015739   .0525884     0.30   0.763     .9177246    1.124221
       _cons |   .2997612   .4831833    -0.75   0.455     .0127271    7.060282
------------------------------------------------------------------------------

. test bmikgm2 , mtest(sidak)

 ( 1)  [whc]bmikgm2 = 0

---------------------------------------
       |        chi2     df       p
-------+-------------------------------
  (1)  |        0.09      1     0.7629 #
-------+-------------------------------
  all  |        0.09      1     0.7629
---------------------------------------
              # Sidak-adjusted p-values

. margins, at( bmikgm2 =(20(5)50))

Adjusted predictions                              Number of obs   =         40
Model VCE    : OIM

Expression   : Pr(whc), predict()

1._at        : bmikgm2         =          20

2._at        : bmikgm2         =          25

3._at        : bmikgm2         =          30

4._at        : bmikgm2         =          35

5._at        : bmikgm2         =          40

6._at        : bmikgm2         =          45

7._at        : bmikgm2         =          50

------------------------------------------------------------------------------
             |            Delta-method
             |     Margin   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         _at |
          1  |    .290606   .1314325     2.21   0.027      .033003    .5482089
          2  |   .3069619   .0936018     3.28   0.001     .1235057    .4904181
          3  |   .3238182   .0741702     4.37   0.000     .1784472    .4691892
          4  |   .3411445   .0926516     3.68   0.000     .1595506    .5227384
          5  |   .3589058   .1378875     2.60   0.009     .0886512    .6291603
          6  |   .3770626    .194027     1.94   0.052    -.0032234    .7573485
          7  |   .3955711    .255239     1.55   0.121    -.1046881    .8958303
------------------------------------------------------------------------------

. marginsplot, xdimension(bmikgm2 )

  Variables that uniquely identify margins: bmikgm2

. logistic ssi bmikgm2

Logistic regression                               Number of obs   =         40
                                                  LR chi2(1)      =       0.27
                                                  Prob > chi2     =     0.6051
Log likelihood = -12.869658                       Pseudo R2       =     0.0103

------------------------------------------------------------------------------
         ssi | Odds Ratio   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
     bmikgm2 |   .9510494   .1004031    -0.48   0.634     .7732874    1.169675
       _cons |   .4889687   1.514016    -0.23   0.817     .0011315    211.2979
------------------------------------------------------------------------------

. test bmikgm2 , mtest(sidak)

 ( 1)  [ssi]bmikgm2 = 0

---------------------------------------
       |        chi2     df       p
-------+-------------------------------
  (1)  |        0.23      1     0.6345 #
-------+-------------------------------
  all  |        0.23      1     0.6345
---------------------------------------
              # Sidak-adjusted p-values

. margins, at( bmikgm2 =(20(5)55))

Adjusted predictions                              Number of obs   =         40
Model VCE    : OIM

Expression   : Pr(ssi), predict()

1._at        : bmikgm2         =          20

2._at        : bmikgm2         =          25

3._at        : bmikgm2         =          30

4._at        : bmikgm2         =          35

5._at        : bmikgm2         =          40

6._at        : bmikgm2         =          45

7._at        : bmikgm2         =          50

8._at        : bmikgm2         =          55

------------------------------------------------------------------------------
             |            Delta-method
             |     Margin   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         _at |
          1  |   .1519687   .1389244     1.09   0.274    -.1203182    .4242556
          2  |   .1223685   .0719525     1.70   0.089    -.0186557    .2633928
          3  |   .0978684   .0477881     2.05   0.041     .0042055    .1915313
          4  |   .0778386   .0598107     1.30   0.193    -.0393882    .1950654
          5  |    .061628   .0743497     0.83   0.407    -.0840947    .2073507
          6  |   .0486155   .0823336     0.59   0.555    -.1127555    .2099864
          7  |   .0382385   .0842003     0.45   0.650     -.126791    .2032681
          8  |   .0300067   .0816653     0.37   0.713    -.1300544    .1900677
------------------------------------------------------------------------------

. marginsplot, xdimension(bmikgm2 )

  Variables that uniquely identify margins: bmikgm2

. logistic ssimn bmikgm2

Logistic regression                               Number of obs   =         40
                                                  LR chi2(1)      =       0.04
                                                  Prob > chi2     =     0.8350
Log likelihood = -10.633672                       Pseudo R2       =     0.0020

------------------------------------------------------------------------------
       ssimn | Odds Ratio   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
     bmikgm2 |   .9791328   .1027661    -0.20   0.841     .7970813    1.202764
       _cons |   .1523166   .4816012    -0.60   0.552       .00031    74.83646
------------------------------------------------------------------------------

. test bmikgm2 , mtest(sidak)

 ( 1)  [ssimn]bmikgm2 = 0

---------------------------------------
       |        chi2     df       p
-------+-------------------------------
  (1)  |        0.04      1     0.8408 #
-------+-------------------------------
  all  |        0.04      1     0.8408
---------------------------------------
              # Sidak-adjusted p-values

. margins, at( bmikgm2 =(20(5)55))

Adjusted predictions                              Number of obs   =         40
Model VCE    : OIM

Expression   : Pr(ssimn), predict()

1._at        : bmikgm2         =          20

2._at        : bmikgm2         =          25

3._at        : bmikgm2         =          30

4._at        : bmikgm2         =          35

5._at        : bmikgm2         =          40

6._at        : bmikgm2         =          45

7._at        : bmikgm2         =          50

8._at        : bmikgm2         =          55

------------------------------------------------------------------------------
             |            Delta-method
             |     Margin   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         _at |
          1  |    .090829   .0966936     0.94   0.348    -.0986869     .280345
          2  |   .0824894   .0582077     1.42   0.156    -.0315955    .1965744
          3  |   .0748525   .0417054     1.79   0.073    -.0068885    .1565935
          4  |   .0678703   .0523492     1.30   0.195    -.0347322    .1704727
          5  |   .0614961   .0720276     0.85   0.393    -.0796755    .2026676
          6  |   .0556847   .0907908     0.61   0.540     -.122262    .2336314
          7  |   .0503931   .1065266     0.47   0.636    -.1583952    .2591814
          8  |     .04558   .1189828     0.38   0.702     -.187622    .2787821
------------------------------------------------------------------------------

. marginsplot, xdimension(bmikgm2 )

  Variables that uniquely identify margins: bmikgm2

. logistic ssimj bmikgm2

Logistic regression                               Number of obs   =         40
                                                  LR chi2(1)      =       0.56
                                                  Prob > chi2     =     0.4544
Log likelihood = -4.3964785                       Pseudo R2       =     0.0598

------------------------------------------------------------------------------
       ssimj | Odds Ratio   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
     bmikgm2 |   .8167698   .2668607    -0.62   0.536     .4305159    1.549566
       _cons |   7.413841   64.98746     0.23   0.819     2.56e-07    2.14e+08
------------------------------------------------------------------------------

. test bmikgm2 , mtest(sidak)

 ( 1)  [ssimj]bmikgm2 = 0

---------------------------------------
       |        chi2     df       p
-------+-------------------------------
  (1)  |        0.38      1     0.5356 #
-------+-------------------------------
  all  |        0.38      1     0.5356
---------------------------------------
              # Sidak-adjusted p-values

. margins, at( bmikgm2 =(20(5)55))

Adjusted predictions                              Number of obs   =         40
Model VCE    : OIM

Expression   : Pr(ssimj), predict()

1._at        : bmikgm2         =          20

2._at        : bmikgm2         =          25

3._at        : bmikgm2         =          30

4._at        : bmikgm2         =          35

5._at        : bmikgm2         =          40

6._at        : bmikgm2         =          45

7._at        : bmikgm2         =          50

8._at        : bmikgm2         =          55

------------------------------------------------------------------------------
             |            Delta-method
             |     Margin   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         _at |
          1  |   .1145981    .243437     0.47   0.638    -.3625297     .591726
          2  |   .0449334   .0494864     0.91   0.364    -.0520582    .1419249
          3  |   .0168139    .024746     0.68   0.497    -.0316873    .0653152
          4  |   .0061779    .017889     0.35   0.730    -.0288839    .0412398
          5  |   .0022545   .0100787     0.22   0.823    -.0174993    .0220083
          6  |   .0008207   .0049878     0.16   0.869    -.0089553    .0105966
          7  |   .0002985   .0022969     0.13   0.897    -.0042035    .0048004
          8  |   .0001085   .0010112     0.11   0.915    -.0018734    .0020904
------------------------------------------------------------------------------

. marginsplot, xdimension(bmikgm2 )

  Variables that uniquely identify margins: bmikgm2

. logistic whc i.locationgroup

Logistic regression                               Number of obs   =         40
                                                  LR chi2(3)      =       5.15
                                                  Prob > chi2     =     0.1610
Log likelihood = -22.646917                       Pseudo R2       =     0.1021

-------------------------------------------------------------------------------
          whc | Odds Ratio   Std. Err.      z    P>|z|     [95% Conf. Interval]
--------------+----------------------------------------------------------------
locationgroup |
           2  |   .1666667   .2130032    -1.40   0.161     .0136143    2.040332
           3  |   .5555556   .7590334    -0.43   0.667     .0381737    8.085189
           4  |   1.481481   1.299526     0.45   0.654     .2654846    8.267097
              |
        _cons |         .6    .438178    -0.70   0.484     .1433909     2.51062
-------------------------------------------------------------------------------

*To Be Continued

I hope my attempts at statistics didn't make you too upset. I'm still a beginner.

[Michael Lanni]

Output Part 2:

 test 1.locationgroup = 2.locationgroup = 3.locationgroup = 4.locationgroup, mtest(sidak)

 ( 1)  [whc]1b.locationgroup - [whc]2.locationgroup = 0
 ( 2)  [whc]1b.locationgroup - [whc]3.locationgroup = 0
 ( 3)  [whc]1b.locationgroup - [whc]4.locationgroup = 0

---------------------------------------
       |        chi2     df       p
-------+-------------------------------
  (1)  |        1.97      1     0.4092 #
  (2)  |        0.19      1     0.9631 #
  (3)  |        0.20      1     0.9586 #
-------+-------------------------------
  all  |        3.81      3     0.2826
---------------------------------------
              # Sidak-adjusted p-values

. 
. margins locationgroup

Adjusted predictions                              Number of obs   =         40
Model VCE    : OIM

Expression   : Pr(whc), predict()

-------------------------------------------------------------------------------
              |            Delta-method
              |     Margin   Std. Err.      z    P>|z|     [95% Conf. Interval]
--------------+----------------------------------------------------------------
locationgroup |
           1  |       .375   .1711633     2.19   0.028     .0395261    .7104739
           2  |   .0909091   .0866784     1.05   0.294    -.0789775    .2607957
           3  |        .25   .2165064     1.15   0.248    -.1743447    .6743447
           4  |   .4705882   .1210578     3.89   0.000     .2333193    .7078572
-------------------------------------------------------------------------------

. 
. marginsplot, xdimension(locationgroup)

  Variables that uniquely identify margins: locationgroup

. 
. logistic ssi i.locationgroup
note: 1.locationgroup != 0 predicts failure perfectly
      1.locationgroup dropped and 8 obs not used

note: 2.locationgroup != 0 predicts failure perfectly
      2.locationgroup dropped and 11 obs not used

note: 3.locationgroup != 0 predicts failure perfectly
      3.locationgroup dropped and 4 obs not used

note: 4.locationgroup omitted because of collinearity

Logistic regression                               Number of obs   =         17
                                                  LR chi2(0)      =       0.00
                                                  Prob > chi2     =          .
Log likelihood = -9.2751078                       Pseudo R2       =     0.0000

-------------------------------------------------------------------------------
          ssi | Odds Ratio   Std. Err.      z    P>|z|     [95% Conf. Interval]
--------------+----------------------------------------------------------------
locationgroup |
           1  |          1  (empty)
           2  |          1  (empty)
           3  |          1  (empty)
           4  |          1  (omitted)
              |
        _cons |   .3076923   .1759298    -2.06   0.039     .1003283    .9436474
-------------------------------------------------------------------------------

. 
. tabulate locationgroup ssi, exact

Enumerating sample-space combinations:
stage 4:  enumerations = 1
stage 3:  enumerations = 2
stage 2:  enumerations = 5
stage 1:  enumerations = 0

  Location |          SSI
     Group |         0          1 |     Total
-----------+----------------------+----------
         1 |         8          0 |         8 
         2 |        11          0 |        11 
         3 |         4          0 |         4 
         4 |        13          4 |        17 
-----------+----------------------+----------
     Total |        36          4 |        40 

           Fisher's exact =                 0.185

. 
. margins locationgroup
Warning: prediction constant over observations.

Adjusted predictions                              Number of obs   =         17
Model VCE    : OIM

Expression   : Pr(ssi), predict()

---------------------------------------------------------------------------------
                |            Delta-method
                |     Margin   Std. Err.      z    P>|z|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
4.locationgroup |   .2352941   .1028794     2.29   0.022     .0336543     .436934
---------------------------------------------------------------------------------

. 
. tabulate locationgroup ssimn, exact

Enumerating sample-space combinations:
stage 4:  enumerations = 1
stage 3:  enumerations = 2
stage 2:  enumerations = 3
stage 1:  enumerations = 0

  Location |       SSI Minor
     Group |         0          1 |     Total
-----------+----------------------+----------
         1 |         8          0 |         8 
         2 |        11          0 |        11 
         3 |         4          0 |         4 
         4 |        14          3 |        17 
-----------+----------------------+----------
     Total |        37          3 |        40 

           Fisher's exact =                 0.417

. 
. logistic ssimn i.locationgroup
note: 1.locationgroup != 0 predicts failure perfectly
      1.locationgroup dropped and 8 obs not used

note: 2.locationgroup != 0 predicts failure perfectly
      2.locationgroup dropped and 11 obs not used

note: 3.locationgroup != 0 predicts failure perfectly
      3.locationgroup dropped and 4 obs not used

note: 4.locationgroup omitted because of collinearity

Logistic regression                               Number of obs   =         17
                                                  LR chi2(0)      =       0.00
                                                  Prob > chi2     =          .
Log likelihood = -7.9219874                       Pseudo R2       =     0.0000

-------------------------------------------------------------------------------
        ssimn | Odds Ratio   Std. Err.      z    P>|z|     [95% Conf. Interval]
--------------+----------------------------------------------------------------
locationgroup |
           1  |          1  (empty)
           2  |          1  (empty)
           3  |          1  (empty)
           4  |          1  (omitted)
              |
        _cons |   .2142857   .1363305    -2.42   0.015     .0615816    .7456505
-------------------------------------------------------------------------------

. 
. margins locationgroup
Warning: prediction constant over observations.

Adjusted predictions                              Number of obs   =         17
Model VCE    : OIM

Expression   : Pr(ssimn), predict()

---------------------------------------------------------------------------------
                |            Delta-method
                |     Margin   Std. Err.      z    P>|z|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
4.locationgroup |   .1764706   .0924594     1.91   0.056    -.0047466    .3576878
---------------------------------------------------------------------------------

. 
. marginsplot, xdimension(locationgroup)

  Variables that uniquely identify margins:

. 
. *I know there is only one variable. I did this graph for completeness I guess.

. 
. logistic ssimj i.locationgroup
note: 1.locationgroup != 0 predicts failure perfectly
      1.locationgroup dropped and 8 obs not used

note: 2.locationgroup != 0 predicts failure perfectly
      2.locationgroup dropped and 11 obs not used

note: 3.locationgroup != 0 predicts failure perfectly
      3.locationgroup dropped and 4 obs not used

note: 4.locationgroup omitted because of collinearity

Logistic regression                               Number of obs   =         17
                                                  LR chi2(0)      =       0.00
                                                  Prob > chi2     =          .
Log likelihood = -3.8032073                       Pseudo R2       =     0.0000

-------------------------------------------------------------------------------
        ssimj | Odds Ratio   Std. Err.      z    P>|z|     [95% Conf. Interval]
--------------+----------------------------------------------------------------
locationgroup |
           1  |          1  (empty)
           2  |          1  (empty)
           3  |          1  (empty)
           4  |          1  (omitted)
              |
        _cons |      .0625   .0644235    -2.69   0.007     .0082886    .4712794
-------------------------------------------------------------------------------

. 
. margins locationgroup
Warning: prediction constant over observations.

Adjusted predictions                              Number of obs   =         17
Model VCE    : OIM

Expression   : Pr(ssimj), predict()

---------------------------------------------------------------------------------
                |            Delta-method
                |     Margin   Std. Err.      z    P>|z|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
4.locationgroup |   .0588235   .0570672     1.03   0.303    -.0530261    .1706732
---------------------------------------------------------------------------------

. 
. marginsplot, xdimension(locationgroup)

  Variables that uniquely identify margins:

. 
. logistic whc i.flapsizegroup

Logistic regression                               Number of obs   =         40
                                                  LR chi2(4)      =       1.82
                                                  Prob > chi2     =     0.7680
Log likelihood = -24.310957                       Pseudo R2       =     0.0362

-------------------------------------------------------------------------------
          whc | Odds Ratio   Std. Err.      z    P>|z|     [95% Conf. Interval]
--------------+----------------------------------------------------------------
flapsizegroup |
           2  |   .4285715   .5207083    -0.70   0.486     .0396119    4.636829
           3  |      .5625   .6392898    -0.51   0.613     .0606344    5.218263
           4  |        1.5   1.732051     0.35   0.725     .1560301    14.42029
           5  |         .6    .742967    -0.41   0.680     .0529818    6.794785
              |
        _cons |   .6666667   .6085806    -0.44   0.657     .1113965    3.989752
-------------------------------------------------------------------------------

. 
. tabulate flapsizegroup whc, exact

Enumerating sample-space combinations:
stage 5:  enumerations = 1
stage 4:  enumerations = 2
stage 3:  enumerations = 5
stage 2:  enumerations = 8
stage 1:  enumerations = 0

 Flap Size |          WHC
     Group |         0          1 |     Total
-----------+----------------------+----------
         1 |         3          2 |         5 
         2 |         7          2 |         9 
         3 |         8          3 |        11 
         4 |         4          4 |         8 
         5 |         5          2 |         7 
-----------+----------------------+----------
     Total |        27         13 |        40 

           Fisher's exact =                 0.795

. 
. tabulate flapsizegroup whc, chi2

 Flap Size |          WHC
     Group |         0          1 |     Total
-----------+----------------------+----------
         1 |         3          2 |         5 
         2 |         7          2 |         9 
         3 |         8          3 |        11 
         4 |         4          4 |         8 
         5 |         5          2 |         7 
-----------+----------------------+----------
     Total |        27         13 |        40 

          Pearson chi2(4) =   1.8646   Pr = 0.761

. 
. margins flapsizegroup

Adjusted predictions                              Number of obs   =         40
Model VCE    : OIM

Expression   : Pr(whc), predict()

-------------------------------------------------------------------------------
              |            Delta-method
              |     Margin   Std. Err.      z    P>|z|     [95% Conf. Interval]
--------------+----------------------------------------------------------------
flapsizegroup |
           1  |         .4    .219089     1.83   0.068    -.0294066    .8294066
           2  |   .2222223   .1385799     1.60   0.109    -.0493894    .4938339
           3  |   .2727273   .1342816     2.03   0.042     .0095401    .5359144
           4  |         .5   .1767767     2.83   0.005      .153524     .846476
           5  |   .2857143   .1707469     1.67   0.094    -.0489436    .6203721
-------------------------------------------------------------------------------

. 
. marginsplot, xdimension(flapsizegroup)

  Variables that uniquely identify margins: flapsizegroup

. 
. logistic ssi i.flapsizegroup
note: 1.flapsizegroup != 0 predicts failure perfectly
      1.flapsizegroup dropped and 5 obs not used

note: 2.flapsizegroup != 0 predicts failure perfectly
      2.flapsizegroup dropped and 9 obs not used

note: 5.flapsizegroup omitted because of collinearity

Logistic regression                               Number of obs   =         26
                                                  LR chi2(2)      =       1.22
                                                  Prob > chi2     =     0.5437
Log likelihood = -10.553045                       Pseudo R2       =     0.0546

-------------------------------------------------------------------------------
          ssi | Odds Ratio   Std. Err.      z    P>|z|     [95% Conf. Interval]
--------------+----------------------------------------------------------------
flapsizegroup |
           1  |          1  (empty)
           2  |          1  (empty)
           3  |        .25   .3354102    -1.03   0.301     .0180274    3.466943
           4  |   .3571429   .4848281    -0.76   0.448     .0249643    5.109331
           5  |          1  (omitted)
              |
        _cons |         .4    .334664    -1.10   0.273     .0776057    2.061704
-------------------------------------------------------------------------------

. 
. tabulate flapsizegroup ssi, exact

Enumerating sample-space combinations:
stage 5:  enumerations = 1
stage 4:  enumerations = 2
stage 3:  enumerations = 5
stage 2:  enumerations = 9
stage 1:  enumerations = 0

 Flap Size |          SSI
     Group |         0          1 |     Total
-----------+----------------------+----------
         1 |         5          0 |         5 
         2 |         9          0 |         9 
         3 |        10          1 |        11 
         4 |         7          1 |         8 
         5 |         5          2 |         7 
-----------+----------------------+----------
     Total |        36          4 |        40 

           Fisher's exact =                 0.403

. 
. margins flapsizegroup

Adjusted predictions                              Number of obs   =         26
Model VCE    : OIM

Expression   : Pr(ssi), predict()

-------------------------------------------------------------------------------
              |            Delta-method
              |     Margin   Std. Err.      z    P>|z|     [95% Conf. Interval]
--------------+----------------------------------------------------------------
flapsizegroup |
           3  |   .0909091   .0866784     1.05   0.294    -.0789775    .2607957
           4  |       .125   .1169268     1.07   0.285    -.1041723    .3541723
           5  |   .2857143   .1707469     1.67   0.094    -.0489436    .6203721
-------------------------------------------------------------------------------

. 
. marginsplot, xdimension(flapsizegroup)

  Variables that uniquely identify margins: flapsizegroup

. 
. logistic ssimn i.flapsizegroup
note: 1.flapsizegroup != 0 predicts failure perfectly
      1.flapsizegroup dropped and 5 obs not used

note: 2.flapsizegroup != 0 predicts failure perfectly
      2.flapsizegroup dropped and 9 obs not used

note: 5.flapsizegroup omitted because of collinearity

Logistic regression                               Number of obs   =         26
                                                  LR chi2(2)      =       0.12
                                                  Prob > chi2     =     0.9396
Log likelihood = -9.2359726                       Pseudo R2       =     0.0067

-------------------------------------------------------------------------------
        ssimn | Odds Ratio   Std. Err.      z    P>|z|     [95% Conf. Interval]
--------------+----------------------------------------------------------------
flapsizegroup |
           1  |          1  (empty)
           2  |          1  (empty)
           3  |         .6   .9033272    -0.34   0.734     .0313783    11.47291
           4  |   .8571428    1.30261    -0.10   0.919     .0435986    16.85133
           5  |          1  (omitted)
              |
        _cons |   .1666667   .1800206    -1.66   0.097     .0200653    1.384368
-------------------------------------------------------------------------------

. 
. tabulate flapsizegroup ssimn, exact

Enumerating sample-space combinations:
stage 5:  enumerations = 1
stage 4:  enumerations = 1
stage 3:  enumerations = 2
stage 2:  enumerations = 2
stage 1:  enumerations = 0

 Flap Size |       SSI Minor
     Group |         0          1 |     Total
-----------+----------------------+----------
         1 |         5          0 |         5 
         2 |         9          0 |         9 
         3 |        10          1 |        11 
         4 |         7          1 |         8 
         5 |         6          1 |         7 
-----------+----------------------+----------
     Total |        37          3 |        40 

           Fisher's exact =                 0.850

. 
. margins flapsizegroup

Adjusted predictions                              Number of obs   =         26
Model VCE    : OIM

Expression   : Pr(ssimn), predict()

-------------------------------------------------------------------------------
              |            Delta-method
              |     Margin   Std. Err.      z    P>|z|     [95% Conf. Interval]
--------------+----------------------------------------------------------------
flapsizegroup |
           3  |   .0909091   .0866784     1.05   0.294    -.0789775    .2607957
           4  |       .125   .1169268     1.07   0.285    -.1041723    .3541723
           5  |   .1428571     .13226     1.08   0.280    -.1163677     .402082
-------------------------------------------------------------------------------

. 
. marginsplot, xdimension(flapsizegroup)

  Variables that uniquely identify margins: flapsizegroup

. 
. logistic ssimj i.flapsizegroup
note: 1.flapsizegroup != 0 predicts failure perfectly
      1.flapsizegroup dropped and 5 obs not used

note: 2.flapsizegroup != 0 predicts failure perfectly
      2.flapsizegroup dropped and 9 obs not used

note: 3.flapsizegroup != 0 predicts failure perfectly
      3.flapsizegroup dropped and 11 obs not used

note: 4.flapsizegroup != 0 predicts failure perfectly
      4.flapsizegroup dropped and 8 obs not used

note: 5.flapsizegroup omitted because of collinearity

Logistic regression                               Number of obs   =          7
                                                  LR chi2(0)      =       0.00
                                                  Prob > chi2     =          .
Log likelihood = -2.8708142                       Pseudo R2       =     0.0000

-------------------------------------------------------------------------------
        ssimj | Odds Ratio   Std. Err.      z    P>|z|     [95% Conf. Interval]
--------------+----------------------------------------------------------------
flapsizegroup |
           1  |          1  (empty)
           2  |          1  (empty)
           3  |          1  (empty)
           4  |          1  (empty)
           5  |          1  (omitted)
              |
        _cons |   .1666667   .1800206    -1.66   0.097     .0200653    1.384368
-------------------------------------------------------------------------------

. 
. tabulate flapsizegroup ssimj, exact

Enumerating sample-space combinations:
stage 5:  enumerations = 1
stage 4:  enumerations = 1
stage 3:  enumerations = 0
stage 2:  enumerations = 0
stage 1:  enumerations = 0

 Flap Size |       SSI Major
     Group |         0          1 |     Total
-----------+----------------------+----------
         1 |         5          0 |         5 
         2 |         9          0 |         9 
         3 |        11          0 |        11 
         4 |         8          0 |         8 
         5 |         6          1 |         7 
-----------+----------------------+----------
     Total |        39          1 |        40 

           Fisher's exact =                 0.300

. 
. margins flapsizegroup
Warning: prediction constant over observations.

Adjusted predictions                              Number of obs   =          7
Model VCE    : OIM

Expression   : Pr(ssimj), predict()

---------------------------------------------------------------------------------
                |            Delta-method
                |     Margin   Std. Err.      z    P>|z|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
5.flapsizegroup |   .1428571     .13226     1.08   0.280    -.1163677     .402082
---------------------------------------------------------------------------------

. 
. marginsplot, xdimension(flapsizegroup)

  Variables that uniquely identify margins:

[Steve Samuels]

Now that I re-looked at your results, I wouldn't confidently declare that there are no differences: CIs are very wide, with ORs as high as 8 inside.
Thus the power to declare differences was quite low. For the rest of your posts, I'm not sure what your question is.

[Michael Lanni]

Ok. So i think our questions are:

1) Effect of age on Total/Major/Minor WHC/SSI.
2) Effect of BMI on Total/Major/Minor WHC/SSI.
3) Effect of surgical site on Total/Major/Minor WHC/SSI.
and possibly
4) Effect of Flap size (petite, small, medium, large, extra large) on Total/Major/Minor WHC/SSI.

And I was trying to use the 95% CI's to show if our results of no difference were true or due to small sample size, which seems to be the case, huh. Maybe I just have to report it like that? "Although we found no statistical difference between groups, we realize our results are limited by sample size as demonstrated in the wide 95% CI's."

What do you think?

And BTW, I realize you are a professor and a consulting statistician. Can I send you a thank-you gift or something because I realize you don't have to be helping me out and I greatly appreciate it?

[Steve Samuels]

Although we found no statistical difference between groups, we realize our results are limited by sample size as demonstrated in the wide 95% CI's.

That sounds okay.

I'm glad I was able to help you; the gratitude that you have already expressed is more than sufficient return. Good luck in the future.