Unintended Pregnancy in College-aged Women Yi Su and Zhe Zhao

May 3, 2010

Survey Data

•2008 subjects•65 questions -Age (range from 18-35) -Race -High School Class Size -Year in

College -History of Sexuality (Hx Sex) -Use of Emergency Contraception (EC) -Questions involving Knowledge of EC -Questions involving Accessibility to EC

Client’s Goal

•Obtain frequency tables for certain variables

•Find relationship between knowledge of EC and given variables

•Find relationship between accessibility of EC and given variables

Before Analysis…• Eight columns involving race should be

represented by one variable showing all levels

--Race variable SAS Code

• Variable should be created to summarize subject’s knowledge of EC, level of accessibility to EC

--Knowledge_index, Access_indicator, Access_index SAS Code

all subjects

Hx sex Yes Hx sex No

EC use Yes EC use No

Frequency Tables

Frequency Tables (continued)• Create, customize and manage output via SAS

ODS

• Code

ods listing close;ods html body='C:\Consulting for Melissa\OUTPUT\all_freq.xls'

style=Minimal;ods NOPROCTITLE;proc freq data = mydata.Survey_V03;

……Ods html close;

• Output Excel

Relationship between Knowledge Index and Race

•Knowledge Index: [0,1)

•Race: Eight different races

Initial Try: ANOVA on original data

proc glm data=mydata.survey_final;class Race_Coded;model Knowledge_Index=Race_Coded;lsmeans Race_Coded/adjust=Tukey pdiff;

output out=o p=pred r=resid;run;

Test Results Least Squares Means for effect Race_Coded Pr > |t| for H0: LSMean(i)=LSMean(j)

Dependent Variable: Knowledge_Index

i/j 1 2 3 4 5 6 7 8

1 0.9970 0.9917 0.9954 0.2634 0.9995 1.0000 1.0000 2 0.9970 0.9999 0.9494 <.0001 1.0000 0.9993 0.9885 3 0.9917 0.9999 0.9311 0.1671 0.9999 0.9971 0.9790 4 0.9954 0.9494 0.9311 0.5436 0.9654 0.9927 0.9917 5 0.2634 <.0001 0.1671 0.5436 0.0828 0.3404 0.0395 6 0.9995 1.0000 0.9999 0.9654 0.0828 0.9999 0.9992 7 1.0000 0.9993 0.9971 0.9927 0.3404 0.9999 1.0000 8 1.0000 0.9885 0.9790 0.9917 0.0395 0.9992 1.0000

Model Diagnostics

Model Diagnostics

Tests for Normality

Test --Statistic--- -----p Value------

Shapiro-Wilk W 0.81658 Pr < W <0.0001 Kolmogorov-Smirnov D 0.189102 Pr > D <0.0100 Cramer-von Mises W-Sq 17.61803 Pr > W-Sq <0.0050

Anderson-Darling A-Sq 104.3814 Pr > A-Sq <0.0050

Model Diagnostics

Conclusion

•Non-normality

•Non-constant variance

Second Try

•Box-Cox transformation for ANOVA

proc transreg data=mydata.survey_final;Model boxcox(Knowledge_Index/parameter=0.00001)=class(Race_Coded);

run;

Box Cox transformation result• The TRANSREG Procedure

• Transformation Information• for BoxCox(Knowledge_Index)• Lambda R-Square Log Like• -3.00 0.00 -58498.8• -2.75 0.00 -53051.7• -2.50 0.00 -47621.1• …………………………………………………………………………………………………….• 1.75 0.02 3953.4• 2.00 0.02 3989.9• 2.25 0.01 4018.2• 2.50 0.01 4039.6• 2.75 0.01 4055.2• 3.00 + 0.01 4065.8 <• < - Best Lambda

ANOVA with cube transformationproc glm data=a;class Race_Coded;model Knowledgetr=Race_Coded;lsmeans Race_Coded/adjust=Tukey pdiff;

output out=o p=pred r=resid;run;

Pairwise Comparison Result• Least Squares Means for effect Race_Coded• Pr > |t| for H0: LSMean(i)=LSMean(j)

• Dependent Variable: knowledgetr

• i/j 1 2 3 4 5 6 7 8

• 1 0.9974 0.9922 0.9791 0.3095 0.9996 1.0000 1.0000• 2 0.9974 0.9998 0.8736 <.0001 1.0000 0.9988 0.9743• 3 0.9922 0.9998 0.8427 0.2235 0.9999 0.9954 0.9606• 4 0.9791 0.8736 0.8427 0.4110 0.9052 0.9750 0.9735• 5 0.3095 <.0001 0.2235 0.4110 0.1135 0.3510 0.0368• 6 0.9996 1.0000 0.9999 0.9052 0.1135 0.9998 0.9976• 7 1.0000 0.9988 0.9954 0.9750 0.3510 0.9998 1.0000• 8 1.0000 0.9743 0.9606 0.9735 0.0368 0.9976 1.0000

Model Diagnostics

Model Diagnostics

Conclusion

Non-constant variance problem was fixed but still

has problem with non-normality

Third Try: Non-parametric test

•Wilcoxon two sample test---- The Wilcoxon-Mann-Whitney test is a

non-parametric analog to the independent samples t-test and can be used when you do not assume that the dependent variable is a normally distributed variable

•Kruskal-Wallis Test----

The Kruskal Wallis test is used when you have one independent variable with two or more levels. In other words, it is the non-parametric version of ANOVA. It is also a generalized form of the Mann-Whitney test method, as it permits two or more groups.

•Kruskal-Wallis Test---- This test is an alternative to the

independent group ANOVA, when the assumption of normality or equality of variance is not met. This, like many non-parametric tests, uses the ranks of the data rather than their raw values to calculate the statistic. Since this test does not make a distributional assumption, it is not as powerful as the ANOVA.

SAS code for Kruskal-Wallis Testproc npar1waydata=mydata.survey_final wilcoxon;class Race_Coded;var Knowledge_Index;run;

Test Result

Kruskal-Wallis Test

Chi-Square 27.4365 DF 7 Pr > Chi-Square 0.0003

Pairwise Comparison

•Not provided by proc npar1way

Solutions

•1) Carry out all tests one by one, be careful of controlling for family error rate

•2) SAS macro

Pairwise Comparison P-value• 0 and 1 0.4739 0 and 2 0.4692 0 and 3 0.2810 0 and 4 0.0371• 0 and 5 0.6427 0 and 6 0.9011 0 and 7 0.9637• 1 and 2 0.7909 1 and 3 0.1200 1 and 4 <.0001 1 and 5

0.7874• 1 and 6 0.4259 1 and 7 0.2596• 2 and 3 0.1546 2 and 4 0.0234 2 and 5 0.7117 2 and 6

0.4199• 2 and 7 0.3096 3 and 4 0.0518 3 and 5 0.1860 3 and 6

0.3709• 3 and 7 0.2524 • 4 and 5 0.0148 4 and 6 0.0469 4 and 7 0.0038• 5 and 6 0.5720 5 and 7 0.5267• 6 and 7 0.9816

•Compare P-value with 0.05/21=0.00238

SAS Macro (1)• ODS OUTPUT WilcoxonScores=wlx(drop=variable);

• ODS EXCLUDE wilcoxonScores;

• proc npar1way data=mydata.survey_final wilcoxon;

• class Race_Coded;

• var Knowledge_Index;

• run;

• PROC PRINT DATA=wlx NOObs ;

• run;

• * macro var k == number of groups;

• DATA _null_ ; SET wlx nobs=nobs; CALL SYMPUT("k",LEFT(nobs)); run;

• %put &k.;

• PROC TRANSPOSE DATA =wlx OUT=cnts(drop=_name_ _label_) prefix=_n; var n;

• ID class; run;

• PROC TRANSPOSE DATA =wlx OUT=mns(drop=_name_ _label_) prefix=_mn; var

• meanscore; ID class; run;

• proc print data=cnts; RUN;

• proc print data=mns; RUN;

• %LET alpha=.05; * familywise pvalue ;

• DATA results; SET cnts; SET mns; DROP nn _n1-_n&k. _mn1-_mn&k.;

• LENGTH reject $2; RETAIN reject ' ';

• LABEL compare='Critical Value' abs_diff='Absolute Difference in Mean

• Ranks';

SAS Macro (2)• c= ((&k.*(&k.-1))/2); * number of pairwise tests;

• z = PROBIT( (1- ((&alpha./2)/ c) ) ); * multiplier ;

• nn=SUM(of _n1-_n&k.); * total number of observations ;

• ARRAY nc{&k.} _n1 - _n&k.;

• ARRAY mn{&k.} _mn1 - _mn&k.;

• DO i = 1 to (&k.-1);

• DO j = (i+1) TO &k.;

• sc1 = mn{i}; sc2 = mn{j};

• ABS_diff = abs(sc1 - sc2);

• compare = z * SQRT( nn*(nn+1)/12 * ((1/nc{i}) + (1/nc{j})));

• IF abs_diff > compare then reject='**'; * the ** marker is to denote

• any significant differences ;

• OUTPUT results;

• reject=' '; * reset marker to missing ;

• END;

• END;

• RUN;

• proc print data=results NOobs label;

• var i j sc1 sc2 ABS_diff compare reject;

• FORMAT abs_diff 6.3 comp 6.2;

• run;

• Absolute• Difference Critical• i j sc1 sc2 in MeanRanks Value reject

• 1 2 1000.41 976.19 24.216 287.78• 1 3 1000.41 1605.50 605.09 1257.79• 1 4 1000.41 717.08 283.32 193.10 **• 1 5 1000.41 1026.73 26.318 322.07• 1 6 1000.41 1138.90 138.49 563.76• 1 7 1000.41 1136.55 136.14 390.23• 1 8 1000.41 . . .• 2 3 976.19 1605.50 629.31 1288.92• 2 4 976.19 717.08 259.11 341.40• 2 5 976.19 1026.73 50.533 427.78• 2 6 976.19 1138.90 162.71 630.15• 2 7 976.19 1136.55 160.36 481.19• 2 8 976.19 . . .• 3 4 1605.50 717.08 888.42 1271.13• 3 5 1605.50 1026.73 578.77 1297.00• 3 6 1605.50 1138.90 466.60 1377.07• 3 7 1605.50 1136.55 468.95 1315.59• 3 8 1605.50 . . .• 4 5 717.08 1026.73 309.64 370.76• 4 6 717.08 1138.90 421.82 592.93• 4 7 717.08 1136.55 419.46 431.29• 4 8 717.08 . . .• 5 6 1026.73 1138.90 112.17 646.53• 5 7 1026.73 1136.55 109.82 502.45• 5 8 1026.73 . . .• 6 7 1138.90 1136.55 2.352 683.05• 6 8 1138.90 . . .• 7 8 1136.55 . . .

Test Results for KnowledgeVar/Method

YearIn College

Size HSClass

Race Hx Sex

FalseAlarm

EC Use

BirthControl

Original ANOVA/Two Sample t-test

Freshman worse than Junior, Senior and Graduate

NotSignificant

WhiteBetter thanAsian_PI

Hx_Yes better than Hx_No

False Alarm Yes better than False Alarm No

EC Use Yes betterThan EC use No

Birth Control Yes better than Birth Control No

Transformed ANOVA

SameAsAbove

Not Significant

Multiracial and White are better than Asian_PI

Non-Parametric

Freshman worse than Junior and Graduate

Not Significant

White better than Asian_PI

Hx_Yes better than Hx_No

False Alarm Yes better than False Alarm No

EC Use Yes betterThan EC use No

Birth Control Yes better than Birth Control No

Test Results for AccessVar/Method

YearIn College

Size HSClass

Race Hx Sex FalseAlarm

BirthControl

Original ANOVA/Two Sample t-test

Freshman worse than Sophomore, Junior, Senior and Graduate

NotSignificant

WhiteBetter thanAsian_PI

Not Significant

Not Significant

Not Significant

Transformed ANOVA

Freshman worse than Graduate

Not Significant

WhiteBetter thanAsian_PI

Non-Parametric

Freshman worse than Graduate

Not Significant

White better than Asian_PI

Not Significant

Not Significant

Not Significant