 no observations. The estimates given
by exact logistic regression do not depend on asymptotic results.

Please note: The purpose of this page is to show how to use various data
analysis commands. It does not cover all aspects of the research process which
researchers are expected to do. In particular, it does not cover data
cleaning and checking, verification of assumptions, model diagnostics or
potential follow-up analyses.

Example

Suppose that we are interested in the factors
that influence whether or not a high school senior is admitted into a very competitive
engineering school. The
outcome variable is binary (0/1): admit or not admit.
The predictor variables of interest include student gender and whether or not the
student took Advanced Placement calculus in high school. Because the response variable is binary, we need
to use a model that handles 0/1 outcome variables correctly. Also, because of the number of students
involved is small, we will need a procedure that can perform the estimation with
a small sample size.

Description of the data

The data for this exact logistic data analysis include the number of students admitted, the total
number of applicants broken down by gender (the variable female), and whether or not
they had taken AP calculus (the variable apcalc). Since the dataset
is so small, we will read it in directly.

The tables reveal that 30 students applied for the Engineering program. Of
those, 15 were admitted and 15 were denied admission. There were 18 male and 12
female applicants. Sixteen of the applicants had taken AP calculus and 14 had
not. Note that all of the females who took AP calculus were admitted, versus only
about half the males.

Analysis methods you might consider

Below is a list of some analysis methods you may have
encountered. Some of the methods listed are quite reasonable, while others have
either fallen out of favor or have limitations.

Exact logistic regression - This technique is appropriate because
the outcome variable is binary, the sample size is small, and some cells are
empty.

Regular logistic regression - Due to the small sample size and the presence of
cells with no subjects, regular logistic regression is not advisable, and it
might not even be estimable.

Two-way contingency tables - You may need to use the fisher or exact
with proc freq option to
get the Fisher's exact test due to small
no observations. The estimates given 
 by exact logistic arrested development do not count on asymptotic resultant role. 

 Please note: The function of this page is to testify how to use various datum 
 analysis commands. It does not cover all aspect of the research process which 
 research worker are expected to do. In particular, it does not cover datum 
 cleaning and checking, verification of assumptions, exemplar diagnostics or 
 potential follow - up analysis. 

 Example 

 Suppose that we are interested in the factors 
 that influence whether or not a gamey school senior is admitted into a very competitive 
 engineering school. The 
 outcome variable star is binary (0/1 ): admit or not admit. 
 The forecaster variables of interest include student sex and whether or not the 
 student took Advanced Placement calculus in high school. Because the response variable is binary, we need 
 to use a model that handles 0/1 outcome variables correctly. Also, because of the number of students 
 involved is small, we will necessitate a procedure that can perform the estimate with 
 a humble sample size. 

 Description of the data 

 The data for this accurate logistic data psychoanalysis include the number of students accommodate, the total 
 number of applicants broken down by gender (the variable female), and whether or not 
 they had taken AP calculus (the variable apcalc). Since the dataset 
 is so small, we will understand it in directly. 

 The table reveal that 30 students applied for the Engineering program. Of 
 those, 15 were admitted and 15 were deny admission. There were 18 male and 12 
 female applicants. Sixteen of the applicant had taken AP tartar and 14 had 
 not. Note that all of the females who took AP calculus were admit, versus only 
 about half the male. 

 Analysis method you might consider 

 Below is a tilt of some analysis methods you may have 
 run into. Some of the methods listed are quite fair, while others have 
 either fallen out of favor or have limitations. 

 Exact logistic regression - This technique is appropriate because 
 the outcome variable is binary, the sample size is small, and some cells are 
 empty. 

 even logistic regression - Due to the small sample distribution size and the presence of 
 cells with no subjects, regular logistic regression is not advisable, and it 
 might not even be estimable. 

 Two - way eventuality tables - You may need to use the fisher or exact 
 with proc freq option to 
 get the Fisher's exact trial due to little
 no observations. The estimaues given
by exact logistmc regrsssion du not depend on asymptotic rxsulrs.

Pleqse note: The purpose ow this pahe is to shox how to use varmkus data
analyals coknands. It does kot cover anl aspects of dhd xesearch process which
researchers arq expecyef to do. In parjiculsw, it does not cover data
cleaning and cgecking, verification of assumptions, model diagjostlcs or
potential foplow-up analiaes.

Qzample

Supposd that we are interestgd in the factors
that influence dhethzr or not a hugh vchool seniir is admitted inbp a vesy comprtitive
engineeving vchiol. The
outcome variabne is binary (0/1): admij or not agmnt.
The predictor variavlws of intaresg inzluse sfudent geider and whsther or nor the
student took Acvwbced Placemenf calctlts in high school. Because the response narizble is binary, we need
ti use a model that hajdles 0/1 ouecome variables correctly. Also, because of the numter oh rtubckts
ivcopved is small, we will need a procedure that cwh kernorm the estimatlon with
a small sakppe fize.

Descriptiun of cge data

The data for hhis exwct ligistic dwta snalysis include the number of students qdmitted, the total
uumber of ap'licanjs brolen down by gender (the rariabme female), ajd whethed or not
they had gakvn A[ calculus (the variable apsalc). Sincx the dataseg
is xo smajl, we will read it in directly.

The habled seveal thah 30 students applied for the Engmieering progrsm. Of
nhose, 15 wexe admltted and 15 were denied admissnon. Therz were 18 male and 12
female applicants. Sixteen of tvg applicants iad taken AP xalcylus ana 14 had
not. Note yhat all of the femqles who took AP celcuuhs were admitteb, cersus only
abouy hxlf tje mwnes.

Analysis kethuds uou mkght considcr

Bdlow is a list of some atalyais methods you mau mave
encoubtered. Sjme of the meyhods listed are qkite ceasoneble, wnilg others have
either fallen out kf favor lr mave limitatijns.

Ewact logistic xegression - This technique is appropriatx because
the outcome vaeiable is binary, thg ssmple size ms smajl, and soke cells are
empty.

Regylar logistic regvession - Due to the smzll sakple dize and the presence of
cells with no subjects, regular logistic regressiob is not advisable, and it
michc npt eveg be xstimable.

Two-way cpntingency tables - You may need to use dhz fisher or exact
with proc frrq option to
get the Fisher's exact test sue to skall
no observations. The estimates given by exact do depend on results. Please note: is show how to various data analysis It does not cover all aspects the research process which researchers are expected to do. In particular, it does cover data cleaning and checking, verification of assumptions, model diagnostics or potential follow-up Example that are in the factors that influence whether or not a high school senior is admitted into a competitive engineering school. The outcome variable is binary admit or not admit. predictor variables of interest include gender whether or the took Placement calculus in school. Because the response variable is binary, we need to use a model that handles 0/1 outcome correctly. Also, the number students is we will need that can perform the estimation with size. Description of the data The data for exact logistic analysis include the number of students the total number of applicants broken down by (the variable female), and whether or not they had taken AP calculus (the variable apcalc). dataset is so small, will read it directly. tables that students applied the Engineering program. Of those, 15 were admitted and 15 were admission. There were 18 male and 12 female applicants. Sixteen applicants taken AP calculus 14 had not. Note all the females who took were versus the Analysis you might consider Below a list of some analysis you may have encountered. are quite reasonable, while others have either fallen of favor or have limitations. Exact logistic - This technique is appropriate because the outcome variable is binary, the size is some cells are empty. Regular logistic regression - to the small sample and the presence of cells with no subjects, regular regression not advisable, it might not be estimable. Two-way tables - You to use fisher exact option to get the Fisher's exact due small
 no observations. The estimateS given
by exAct loGisTic ReGresSion Do not depend on aSYmptOtic results.

Please note: THe purPoSE of tHIs Page iS to show HOw TO Use VaRiOus DaTA
aNalysIs cOmmands. it does not cOveR aLl aspects of tHE rEsearch proCesS which
researCheRs are eXpEctED to do. in pArticUlar, it DOes not Cover data
ClEAning aND checkiNG, VeRifiCation of assumptioNS, mODel diagnostics Or
poteNtIAl FOLloW-up Analyses.

ExAmPle

SuPPose thaT We ARE IntERested in the faCtors
that inFLueNce wheThEr oR Not a hiGh schOoL SenIor is admittEd inTo a very coMpetitIVe
enginEEring scHool. ThE
ouTcoMe vaRIaBlE is BiNAry (0/1): ADmIt oR Not Admit.
The PrEdIctor VariABLES of iNteRest IncluDe student gendEr aNd whETheR or noT the
sTudeNt Took ADvanceD PlacEmEnt calculus in hiGh scHool. BecauSe tHe ResPoNse vaRIable iS biNarY, we need
To use a mODel ThAT HAnDles 0/1 outcome variablEs CORrEctly. AlsO, becauSE oF tHE number oF sTudEnts
INVolveD is sMAlL, we will nEed a prOCeDuRe that cAn PerforM tHe eStiMatioN With
A small Sample siZe.

DesCRiption of the daTA

The data for thIS eXACt LOgisTic Data analysiS incLUde tHe nuMBeR of STudenTs admItTEd, THe total
number of applIcAnts brOken dOwn by gender (thE variable fEMALe), and wheTher OR nOT
they had taken Ap calcUlus (the varIAble apcaLc). SinCe the datAset
is so sMALl, we will ReaD it In dIreCTLy.

the tables reveAL That 30 StUdents aPplIed for tHe ENgiNeeRinG pRogram. Of
tHose, 15 were AdMiTtEd And 15 Were dENied admiSsIon. thEre Were 18 mALe and 12
fEmale ApplIcAnTS. SiXteen of THe APPlicAnTs Had tAkeN Ap calcUlus ANd 14 hAd
not. NoTe that all Of tHE femAlEs Who took aP calculus werE aDmitted, verSuS onLy
abouT HAlf the maLes.

Analysis methods you miGHt consiDer

below Is a lIst of some AnaLysis mEthODs you mAy have
EncouNtEreD. sOme of THE mEthOdS listed are QUIte ReasoNaBle, wHile othErs have
either falleN Out Of favor or have LimItatIONs.

exaCT lOGisTiC RegRESsion - This techniQue is approPrIAtE because
thE OutCoMe variaBle is biNary, tHE sample Size is smaLl, and some CeLls aRE
EmpTy.

Regular lOgistic rEgression - dUe to tHE sMall sAmpLe size AnD thE presEnce of
CEllS with No subjEcTs, reguLar loGiStic regrEssion is not advisable, and It
mighT not eVen Be estimabLe.

TWO-waY contingeNcy tAbles - You maY neEd tO use tHe fISher oR exaCT
wIth PRoc frEq opTIon to
get tHE FIshER'S eXact test due TO SMalL
 no observations. The esti mates give n
byexa ctlo gist ic r egression do n o t de pend on asymptotic res ults. 
P leas e  n ote:The pur p os e ofth is  pa ge is  to s how  how to  use vario usda ta
analysisc om mands. Itdoe s not coverall  aspec ts  of the r ese archproces s  which 
research er s  are e x pectedt o  d o. I n particular, itd oe s  not cover dat a
clea ni n ga n d c hec king, veri fi catio n  of ass u mp t i o ns, model diagnos tics or
pot e nti al fol lo w-u p  analy ses.
E x amp le

Suppose  tha t we areintere s ted int he fact ors
th atinf luen c ewh eth er orn ot  ah igh  schoolse ni or is  adm i t t e d in toa ve ry co mpetitive
eng ine erin g  sc hool.  Theoutc om e var iableis bi na ry (0/1): admit  ornot admit .
T he  pr ed ictor variab les  of  intere st incl u dest u d e nt  gender and whethe ro r  n ot the
s tudent to ok Advanced  P lac emen t calcu lusi nhigh sch ool. B e ca us e the r es ponseva ria ble  is b i nary , we n eed
to u se am odel that hand l es 0/1 outcom e  v a r ia b lescor rectly. Als o, b e caus e of th e n u mberof st ud e nt s 
involved is small,  w e will  need  a procedurethat can p e r f orm theesti m at i on with
a smal l sam ple size.Descript ion o f the da ta

The d a t a for th isexa ctlog i s ti c data analys i s  inc lu de thenum ber ofstu den tsadm it ted, thetotal
nu mb er  o fapp lican t s broken  d own  b y g ender (the v ariab le f em al e ),and whe t he r or n ot 
t heyhad  t akenAP c a lcu lus (th e variabl e a p calc ).  S ince th e dataset
isso  small, we  w ill  readi t  in dire ctly.

The tables revea l  that 3 0 s tuden ts a pplied fo r t he Eng ine e ring p rogram . Ofth ose , 15 we r e  a dmi tt ed and 15w e redenie dadmi ssion.There were 18 male and  12
female ap pli cant s .  S ixt e en ofth e  ap p l icants had take n AP calcu lu s  a nd 14 hadn ot.  N ote tha t all o f the females  who took  AP calcu lu s we r e  ad mitted, ve rsus onl y
about h a lf th e  m ales. 

A nalysi smet hodsyou mi g htconsi der

B el ow isa lis tof someanalysis methods you ma y have 
enco unt ered. Som e o f  th e methods  lis ted are qu ite  re asona ble ,  whil e ot h er s h a ve
ei ther fallen ou t  o f f a v or  or have li m i t ati ons.
Ex a ct log isti c regression - Th i s technique is  app r o pri ate beca us e
the outcomevar ia b l e is bin ar y, the samp le sizeis small , andsome c ells ar e em p ty.

R egul arlogisticreg re s sion -Du et o thesmal lsample  sizea nd t h e  presence of
cel ls wi t h  no s u bje cts,re gular l o gist ic regress ion is notadvisa ble,  andit
migh tnot ev enbe  estimable . 

Two-way  cont ingency  t able s -  You m ay n e e d touseth e f isher ore x ac t 
w it h  pr oc f req o pt ionto
get th e  Fisher' s e x act tes tdue t o smal l 
 no_observations. The_estimates given
by exact logistic_regression do_not_depend on_asymptotic_results.

Please note: The_purpose of this_page is to show_how to use_various_data
analysis commands. It does not cover all aspects of the research process which
researchers are_expected_to do._In_particular,_it does not cover data
cleaning_and checking, verification of assumptions,_model diagnostics_or
potential follow-up analyses.

Example

Suppose that we are interested in_the_factors
that influence whether_or not a high school senior is admitted into_a very competitive
engineering school. The
outcome variable_is binary (0/1):_admit_or_not admit.
The predictor variables_of interest include student gender and_whether or not the
student took Advanced_Placement calculus in high school. Because the_response variable is binary, we need
to_use a model that handles_0/1 outcome_variables correctly. Also, because of_the number of_students
involved is_small, we will_need a procedure that can perform_the estimation with
a_small sample size.

Description of the data

The_data_for this exact_logistic_data_analysis include_the number of_students_admitted, the_total
number_of applicants broken down by gender_(the_variable female), and whether or not
they had_taken AP calculus (the_variable_apcalc). Since the dataset
is_so small, we will read_it in directly.

The tables reveal that_30 students_applied for_the Engineering program. Of
those, 15 were admitted and 15 were denied_admission. There were 18 male and_12
female applicants. Sixteen of_the applicants_had_taken AP calculus_and_14 had
not._Note that all of the females who_took AP_calculus were admitted, versus only
about half_the males.

Analysis methods you_might_consider

Below is a list of some_analysis methods you may have
encountered. Some_of the methods listed are_quite_reasonable,_while others have
either fallen out_of favor or have limitations.

Exact logistic_regression - This_technique is appropriate because
the outcome variable is_binary,_the sample size is small, and_some_cells are
empty.

Regular logistic regression - Due_to_the_small sample size and the_presence of
cells with no subjects, regular_logistic regression is not advisable, and it
might not even_be estimable.

Two-way contingency_tables - You may need_to_use_the fisher or exact
with proc freq option to
get the Fisher's_exact test_due to small