World Bank Reprint Series: Number Ninety-one

Dean T. Jamison

Radio Educationand Student Repetitionin Nicaragua

Reprinted from The Radio Ma/llicinatics Project: Nicnragua, 1976-1977,Patrick Suppes, Barbara Searle, and Jamesine Friend, eds. (StanfordUniversity, Institute for Mathematical Studies in the Social Sciences,1978), pp. 199-221

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Chapter 7

RADIO EDUCATION AND STUDENT REPETITION

IN NICARAGUA

DEA N 'F. JAMNISON

7'TIe World Bank

IN MOST low-income countrties, studenits Nwlho have repeale(l onie or

imiore grades occupy a substantial portion of the availabl e

elemeni taryv-school pla;ices. In ad(diLi(,nI to the lpsNc1iolobgical andperhaps ecornomic cost to the chlild that this rel)p lioll enltails, thlere isa penalty to the school systo.um: (lass sizes tend(i to iciicrc;seC, S(10 \oI

l)Lclglets rise. and access to anyv schiooling at, all cxtemltts 1iTio slowly to

hitherto excitlded Imptilatit ins. It is thuis stm plr ising thtat thle literal11 til

contains few stu(ies in(deed f the (l eteIllillants of stlidel ill tihre aml

r epetitioni' ancl that proj ect t ValltitOllS tail to rIeport Oil the impiw t ol

repetition of the iitervenitions thev aIssess.2 T2he literatture that is

The author is indebted to Marian Beard, Jinwesine Frienid, Edward G(eorge. Roger(;rawe, Robert Horinik, Emile k .\nian%. Kathleen M\f N,ls%. Francois O)rivel, Barbar'a

Searle, Anita Summers, and Patrick Suppes For helpt10 (tis(-cussions concerning aspectsof this clhapter, and to John Sheehan for computer programming. Earlier elrsions lof

this paper were presented at a Septenmber 1977 uLouleiet c. IF(lut anil and EconomicDevelopment in Latin America." sponsored bv the Program of Joint Sttu(lies of LatinAmerican Economic Integration IE(1 El.) and the Nationial Btureau of Economnic Re-searcl, and at a meeitng of the Comparative and Internationial Education Societv,M\exico Citv, March 1978. TIhe conclusiolns expresse(d here are ntOt ten (sc. il s thlose ofthe World Bank or the Agencyv f0oi International Development.

I use failure to deniote a stotleiit's not l)eing promoted to the next grade anii

u1eintlim to denote his both fiailinigt anid I evi id liig, the tbleqnent lil eal.

2 A special issue of the Butlletini of lile International Bureau 0/ Edluration (IBE, I 9W)1

contains an aninotatedl bibliograp.l c concerninig waqon c ill education; IWe term v 'ol 7 tu'includes b)oth dropout and rel)etition in an educational ssste m. Onilv a lfew of the booksand( articles that tlhe sp(e ial issue annotate(d (ealt in ants Ns ay with causes of repetitiotn; ofthe fewstudies (ited, most dealt with European (counitries I Belgimn tn, France, Gel Illanii,

Italv, and the UTSSR) and olnly a few witli low incomile cotuntries (India andcl 'I'haliland).WlAlT (1971) provides a more recent study o. odeterminiants of repetition with data 1romi

199

20() JAMISON

a\ a-iihible concerlinr repel itioi sulggests, lau)isibly Cenou.gh, that give-nl

a school system's promnotion polihc, a chii(i's per foroiiance and atten-

dance at school and the economnic (-llditi()ns of Iis baick'gruind plav

ilipora limt roles; this Iiltenitii i-c is more stiggesti%"e than definitkiic,

more (jtialitaitivc tlhatn (jia titative.Though little is known about the detcrminina uts of re)etition, a

good deal of sta.tistical infornmtion is available concerniing its extent(IBE, 1972; UNESCCO, 1974). To give a sense of the magnitude of theproblem, Table 1 shows recent rep'.tition figures for a number ofLatin American c')untries. The numbers there are high indeed,though typically only half as lhighi for the fourth grade as for the first.It is the magnitude of these numbers, and their imnportance for theeconomics of school systems, that suggests the importance of in-creased attention to understanding the causes of repetition and theimpact of educational interventions on its extent,

My purpose in this chapter is to analyze the impact of the RadioMathematics Project on repetition rates. This analysis provides in-formation not only on the project's effect oni repetition, but also onthe other determinaints of repetition and how to aissess themi. Toundertake the analvsis, I construct a statistical mo(lel that first p)re(lictsposttest performance and then uses posttest performiance with othervariibles to predict student fi'ilure, repetition, and reenrollment. Thechapter is organized as follows. Section 1 briefly sti ini ariizes previolus

evaluations of the Radio Mat'hemiatics Project. Section 2 then de-scribes the model that I use to assess the project and the data used inthe model. Section 3 contains the statistical results and Sectioni 4 dis-cusses their economic inmplicatioins. Section 5 pirovides a brief coluhl-sion.

1. PREVIOU-S EVALUATIONS

The Radio Mttheimatics Project eVillUtecl student cognitive per-formance at the first-grade level in both the 1975 and the 1976 schoolyears (Nicariigua ii school years run from February throughNovemnber). The 1975 ev-aluiation was prelim-iinary: TIhliere wtas no

ca undoni assigninient of clissr-oons to radio versuis co ntlol, the radiocurriculum was still being developed, the samniple size wals relatively

B1 ,iil. I lwe (Y ot il(lie's on detcrnillioiallts ot pt p itiotl co ltrasts itht.111 *o cteltsivelitel'atuir'e otl (dtetm'nin.ntn o torlropping out, 00('1 ht ofvhiidi is annotated in the 13BEbiblihg ig *'I'' a.l(l a ell sulllniarizedl ill Beir'ni, Kinwsy'V *andI Mt ( ;inin l9)2j. Jallade (19177.1111d jamisorl l Iand L X, clpll. 8) latv' et)1i(t'(l ediden(e that thle e'ofloillicconmlepueC8e of rep)etitioln are suhstantial: theji Nvatk N; gg!ts thiat I hr internal late ofretuirni to investmnenit ill schooling tend, to he highilv sensitive to tie revpetition rate.

STUDENT REPETIT ION 201

TrAB'L,E 1

Repetition Rates in Latin American(

Countries Year Grade 1 Grade 4

CF N I R.tI. ANIFRICA \Nt) CARIBBFAN

Costa Rica 1972 11 4C(uba 1971 41 27Dominican Republic 1969 33 11El Salvador 1972 16 5Nicaragua 1971 15 8Panama 1972 21 10

SmuiI{ A1EFRICA

Argentina 1969 23 9Chile 1972 13 8Colonibia 1972 22 10Ecuador 1972 16 10Guvana 1971 17 7Paraguav 1968 26 9PerC 1970 25 12Uraguay 1972 30 14Venezuela 1965 24 14

Note. From L'NESCO Statistical Yearbook (1974, pp. 203-204),"The enitries in the table are repetition rates, expressed in percent, where repetiton is

calculated by dividing the number of repeaters by the enrollment for the same vear.

small, and, for some of the schools, the occasional presence of projectpersonnel for formative evaluation may have affected the results.Nonetheless, reasonably good data were collected, and Searle, Friend,and Suppes (1976, chap. 9) report on an analysis of the effect ofexposure to radio on mathematics achievement. They found thatstudents who had had radio lessons scored about 67% correct on .heend-of-year test, while students who had had no radio lessons scoredonly about 55%; this cliffer-ence is highly statistically significant andreflects a difference of about half a standard deviatioln.

The evaluation of the project based on the 1976 data (reported inchap. 3 of this book) provides more conclusive results than do evalua-tions based on the 1975 data, The sample size was larger, the stucdentswvere randomly assigned to treatmnent and control groups, and,pelhaps most imlipolrtant1, a tested and revised version of the cur-riculum was in use. Table 2 (reprintedl from chap. 3) contains some ofthe more important results. Perhaps because the curriculum had been

Student- ,TiL 11 1characieristics

Age Matriematics Dropped out Maihemalics FNiled Reenrolled

Sex pretest Attendance within year potetfrt+March 1976 I

F'arents' occupation scr ae(0, 1) Nv:9 (1) (0, 1) I

Distance from school March 1975No195( )

Number of previous repeats -

School characteristics

Exposure to radioTeacner characteristicsClass size, etc.

FIGURE 1. Causal modiel of radio's effect on learninig, dlropout prIoCellsity. and flailure pwopcy sity.

STIU'DENT REPETITION 203

TABLE 2

Results of 1976 First-gradle Po,ittc(sin \hithemiutic >

EXI) I ilIVIIAl olltl ol(radio)

Number of classes 30 23Number of students 571 438Number of test items 84 84Meati item score-' 65.6 40.6Stanidard deviation 19.9 18.9

" Percent correct.

improved, the results showv a larger difference in favor of the radiostudents than was found in the 1975 data. On the posttest, the radiostudents performed at a level a full 1.26 standard deviations higherthan the controls; thev anse ered half agaiin as maniy (ueistioins correct-

In this chapter I extend the scope of the ev'al uations just describedby examiningi, the effect of the project on students' propensity torepeat or drop out. At the time of writing, data on these outcomeswvere unavailable for the 1976 school year; I therefore use data from1975, when the effect of the project on achievement test scores wasless pronounced.

2. THE MODEL AND DATA

The Model

Figure 1 diagi-anis the basic structure of the model I use to assessthe impact of radio on the various dependent variables of interest.The two large boxes, labeled "ctudent characteristics" and "schoolcharacteristics," contain the exogenous variables of the model; the sixsmaller boxes containi the six endogenous variables arranged as arecursive system. With six endogenous variables there are six regres-sion equationis in the model, and the arrows leading into each boxcontaining an endogenous variable inclicate the independent variablesto be used in the equation to predict that en(logelnous var-iable. Notethat the recuirsive structure of the model allows one to estimate indi-rect as well a,, direct effects of one variable on another. For example,the diagram iidicates that radio may influence posttest score directly,or indirectly through whatever influence it has on attendanice rate and

204 JAMISON

the subsequent direct infl Uencc of attendance rate on posttest. Sihnilarchains of indirect and direct influencea llow estimi ti C...n of the ef'fect ofradio on failure and r eeiirollriient.

Economists label analysis of the deteriniiaits of t(hievelncilt testscores "eCCILcational piod(lction ftitictioIi" Stitdies; Lau (1978) pro-vides an excellent discussion of the intliods tIse( in (dl1icati(jilidproduction-functioni analvsis and observes that miiost such a nalvscs.assume a single output. The regressioni indicated in Figuric 1 inwhich posttest score is the (de 1)eplndewi variable is an examiiple of tlradli-tional educatinial pod uction-f inctioii analysis; lhove er, the llmodelas presented in fact has two i ndic:ators of Studllt IperfOrmaf'ICe-his

posttest score and whether h.e f;iled first grade--and is thlUs properlyconsidered a multiple-output production model. Viewed fil l a pro-duction perspective, however, the model differs from)ii standarldmultiple-output models in that one output, posttest score, is both afinal output and an inteirmiediaite outptut because of its effect onpropensitv for failure.

Three of the dependent drlliales-ms'ithin-vca I ('l)io t, failure,

and reenrollment-are dichotomous, that is, they can take on1 onlyv

one of twvo possible values (indicated in Fig. I as 0 or 1). Spec(ialstatistical tech niquLLc, are required to hancdle regressions withdichotomous clepenilenit variables, ancl before I (liscuss further thevariables in the model, I shall describe the regression specificationsthat will be used.

The regressions with cont;lu ouis (dependenit variables-those forpretest and posttest scores andl the one for attendanice-are sp)ecifiedin the standlar-d way:

F = bh ± \ 1! N .

wvhere Y is the depeimdent variable, the X1 s 1 i-c l inlldllndellt vlli-ables, and the b, s are paranmeters to be e'tiiiiatedl (by oidill1 i leastsquarell aisstuinig iidpepn(ldei( c of tlhe error tcl lls in the (Iullatiolnsof the nmodel).

For the endgnotiOus \vari;lbt-s tlhait aIr c di hotmuin ni,s the 1nnmlelsl)ecifies a fiiict iom)ial formi, the p. ir lmeterls of ( whlch arc to b)(' esti-inated, that gives the ((111( iti( ii0i.il l)i()l )dl)ililt tiht the \allw ()to the

depemid(lnt variabl)le is 1, given the Aa(ucls of the ii(ledl)eiidel111 Vxllri-

ables. Ihle nmno dcl ws(1 ass u im ics that it a sci glit e st1 un of the illdi-)end(lct var ijal)les, K'bX, eNx (Ct(ls (ii uk m iiown) (ciili cal \viall C.. thell,

3 WUells's 1 97 1 .(I). S8 sttil 01 of ' ) e dlte IllillitItso (ii S I alt dI (lilIl(IionS of ( Oi)-

prehension ot ecoinomic(s is onie previous Stll(u\ ol edla.ltiolal pioduttioll iin uwhimulltiple olltpUts wert w\fli(id i considered.

S I'l )FN'I' R F 1) lI''H'l(F1O N 20) 5

1 1: othelrlwise I = 0. It aSl11('5c , C to l)he i'll(lOillIv (list i'il)LIC(d, andtifliigh (liff'erenlt III()dcIN fl i 'rolll difTerelIt aISsLIptiJonlS about the(lisi il ibioi for ('; iIn this papei' I use wh}latt is pcilhaps tlue illost('0111110ll aIssUtillp)tioi, thailt C fo6llows, the I iili( dis i'ihmioil. 'Theresultinl Ilo(lel for pi cdic !ill, the depenldenlt varliable is knlownt as thelogit il(lel. (ric CI the I c tltitlc il l fi) of1 th FIe logisNi dish il h ( i iio, it('ca be shlo()wn that

I/ll + e\p)( - ' b,X,)]'

TIlle )arallieteltsi of- the olmdel, the bi. c(.n be ctillinited v 1 1w' ilsimilrl-

likt,lillon)l mIlllI)(ls. ias call cNtilliatc' of their staiNittical sigilifi(imcec..As witlh o dilla 1\ regressin anllal'sis, the larger the valli cof f',, thle)I eh.1e(r1 will l)e the f irge ill this case) in the })I'obal)ilitv of' Y forl agiven' h.alige ill Xt.

7The Data

As p)ueviiuIIISI' iwfiched, the data lare hi'onii the 1975 scolol vearaniid omei firom s( hoo(kI in Masava I)Depi,nu.-eirt Ni.aragura, whl;ichi isabout 3() kilHO,ICUll's solithi m"f aLIMIr1a. Ille lf;),i(iiI)!hiiIg sCh1oolsrepresent a range (f enviro'()nmlentS-tr'on urlli)IMn to (qllitC ru l--1 il

the Itidenlt.s aItItelding thtemn iaIre likewiNe (diveise. While the allocatiollof'r-tadio lessons to 'liassiooiiis was iiiomiaiidomi, the stnd(leiits receivingid(lio lessotns (diUite(i only sliglitlv f'romii the controls. However, i-adiostudenlhs were mutch iiore likelv to ( MiR, frotl an agricultuilral faiiiilVthiaIn wNere noniriadio stiudcit's; inll. ddition. the% hail 1.ii',ci1 class sizes

and lower, pretest scorCes. iThe 1975 school NCa;11' waIs aI dlepeliulitall

periold that etwailed fiC(tLICIIt ViSitS bw Vlc jI stalf' to the pali(ticpati rig

r'adio sclhools. Plausiblv, tliei-'ew'e, a Hawthorlne ef'fect could haveaIcu'li ted for thle superio -pc uni011l(Ce of thle radio t((ldel(ts; how-cvel, the p1)1(1l piu widcd radio lesNmii withi no (lii'ect super-visionwhatever to aI fcw Nsch s in thle adji l( ciit Depa V-t it-it of Grallada,an1dl srlidelits ill those schools also peit hirimcld much better thaii didtthe (c(mitli us. Scailc et al. (1976) (hi5(1i5 these and other aspe. ts of the(data in mIulcih mor'e (detail.

Table 3 lists and (definlcs the va 1i'lhIcs used in this a mialv'sis. p)i'tesc'isthleiri aI111 c ll ad( Shlal (ild dcX'iat it[Is, gives Oic cu'ieals fol'0r thc radtEio.arid o lolonrdiclio Srbgio ip'is and shows the u111111ber of' stiudenits f'0m

'Koliii t19T lir j)1O' irte Ides a 1,a bc (' i(" *at c' 1>1 .111(I I ('tedtCd aj itpi nices to('%timlaltionl ot illo(lets to p1 (-(t' I ( iOi(t' i )lOtcp lrtailities l tt tisi l iIluillaIte' .1 liii (li9(l ett'ets ot outtomlils.

206 JAXIS 0 N

TABiLE 3

fe±ans and !.Stnd-in d Deviations of the VariatNks

Sulbsample mneanls

Variable N' Mean StandarddtLvimitjoI Ra(ldio Nonl(radio

groul) group

Stiullelnt ( larc mel Ii c,

MALE 1 for male stttdenits.0 for female 943 .50(1 .5(0 .487 .525

AGE Age of stucdent,in vears 853 8.54 1.64 8.151 8,60

AGOCC 1 if stucdenit's familtis emploved inagriculture 926 .I 98 .398 .257 .085

DIST D)istance in kiloniwtei Nof studenit frotmi sclhool 863 .75 9 876 .82 ; .596

NRPT Number of tines studenitrepeated first gra(le 951 .480( .63t1() 1(;"2 .512

School characteristics

RURAL 1 if studlenit attell(le(lrural school 950 .361 .A8(8 .4-10 .792

USH 1 if stu(dent attendedlurban school wvithslhifts 95( .537 .199 .56( .J!1

UNOSH" I if stud(lent attendedUrhan sclhool witholt"hill r 950 .102 .3(13 .298

CLSIZ stidcimt-r,-t%em lie],

ratio in sludent\sclassroom 951) 46.7 12.0 49.() 42.2

RADIO 1 if studlent's classreceived r'il(liOillstcll(ctitl ! 15( .657 .f1751)

TAGE Age of stru(leiit'steacher, ill Nears 950 32.0 8.57 31.3 3:1.-I

TED Education of' student'sti-.nhe (I . inl Aars 950( 11.2 1.38 11.7 10.5

TEXP Teaching experience ofstldetit's teva her.in lal s 951) 11.5 8.16 11.() 12.5

'I't'lI) EN'I' R IE P IT'11ON 207

I IB IABE 3, (contj)

S1bsamnple inieianis

tlesviatioIn R.lutio .Notii tstlio

gi(l)p group

1'.tdogelgollus '.riai)les

PRE StudlenIt pretest s"oreill ilatlielltiatics 2( * .3 4.65 19.8 21.2

POST Student prosttest s(ot tin 111 r lihcdLil > I s122 s5.8 1:3.5 5 9.2 50. 2

ATTAV Srd(et'iit's .rventgeatten(Iirt e ill (Wsprt onltl 911 1 .1 23.3 14.3 15.1

DROP 1 if stitulent dlropp)edouit (urinig school vear 665 .140 .3 4 7 .173 .074

FAIL I il stud(elit lailedtgrade S.S5 .53 A498 .462 .438

RENRL I it sttr(ideit itemol)lIedlin sulbsequnent st liol

s.s 78. .A09 .803 .763

.VNte. All *altues ate repotted it) thiee sigififinilm dligits.'N.V is the numberol)t stofudelnts fol whoin inimhinmtion 011 the indlicatedl vniialhie was .isrillhlc) As thlere *ser r' no IUx.rl s ltriuls shmuiltiple sessions or shits, edi sttlent has .1lUe ot I fIOI

ex\P 1- onie (if the Naoiabhles RURAL, LSH1,1 and L'NOSH.

wvhom informiation is available on the p)articlIIar item. It is evidentfrom Table 3 that there is a substa ntia.l \,liati(i in the nuiniber ofst i(lenits for whoiTi each pa rtictlar itelli of infI ormiati on is a vaillbble.For this reason the analvses reported in the next section were alsoundertaken witlh the subsample of students for- whomn all data wereava ilal)le. as well as other sLsl)Saipi)les. The broal pattern of restultsreported in Section 3 reillainUs mi liluiiged.

3. RESULTS

I divi(de the (Iiscuissioii of the r esuilts of this .1111;lN sis ilnto tvo pal ts.Thie first part (list ui.scs the (Idcterminanilts of' si ld(llt Pvefi))rmaice: ticdependent vai iables (considctic(l in that pall are p)rtets'>t Scotrt', positesscore, zand li li t' j)i'(iuc )p'o5sit V. 'Ihets S IM'('(i i)aI't (liSCtIIS.Wt. (lt0ei'IiIiLi: ills

of demand folr schooilg;5 the i clcv'aint (dc'l)ptidelt vwiabl1es are s1chool

-l1jaisl5) .uid M?NaldIv (19 7 r)x ided .pr o\ilied mrtr.d- anasis of the tdemiland(i fot( hooliing in Ni(mag.ir I ,thI data gi liii cld a.s t baselinte otr' (s\ uation of thie RId(Iio

\tMr111cm. it i ;P-oject. See'lec 'lrct-r'lrr.1O (;on/de .t-rd (o; ge (io hdip. 8 of this olII1e)providle aI more (detailedi anal :,is of, these haselilne (dIataI and .l 111oliii rogh 1(dl' I pIrlr of'the process antii prrirer nrs of stil(lelnt flows ill \ u. .,gli.rr. schools.

208 JANIISN

attendance rate, within-year d.ropout )ropernsity, and propensity toreenroll for the subsequent school year.

Determinants of .StudSent Perft rmlance

There is by now an extensive liter-atuire on flactors cleterniiningstudent perforniance as measured by sta(ldardized cliiev cnhmt tests.Lau (1978) provides an excellent overview of tie (Iocel)ttLial andltechnical methods and problems of this "educational prod.(iction"literatur-e; Jarnisorn, Suppes. and Wells (1974, pp. 1-67) and Simmonsand Alexander (1976) review its empirical Findings. However, as Iindicated in the introductory paragraphs of this chapter, almost noresearch has been undertaken in wvhich the nicas tire of perfornianceis whether the student passes or fails. One r eaison fo)r this is that mostresearch on educational production has been undertaken witlh datafrom high-inicomiie countries wshere promotion is virmtall ' t a niatic;another reason, perhaps, is that the subjective nature of a teaclher'sdecision. to fail a student may seem to provide a less valid dependentmeasure than an (o)bjective test scoi e. For whatever rIeaIsonI, the litera-ture is scant on the (letermi-ia nlts of failtir e dlespite the majOr,economic imprtan011lce of failure rattes in eduicational planni tig.

This part cointaiins estimalltionls of' three edtLicatioial produtitionfunctions, in which the perforniance neasuires are the studenlt's pre-test score, hiis posttest score, and whether he rFiled first gi aide.Figure 1 shows these variables in their proper causal seqtuence in themodel.

Pretest score. Table 4 shows the estiniateol regression coefficientsfor the deternminants of pretest score in inatlheinatics. Only tvow of the

'IA ABL.E 41

Rcg,gvcssioi Dortmm illmat'. of' Pretest Scores

Variab)le Susampl C(oetfhficit t vallte

MA1 J .512 L 3U9 . .30 .69AGE 8.6 1 .752) 7.5AGOCC 222 -. 422 .6DIST .79)l _. I31 .rzNRPT .5 16 .75 5.7

(CorSt.ai 131

N'vote. Dep)en(lent variahle - PRE; utibs)niple XicWatkPREj = 20.1; subsaimple SID ;PREi t 1 i; stisa>inplesiue -- 473; multiple R2 - .17. All values are repotte(l. tothree significant digits.

S'I'l I) 1:,.N I RE P ETITI O N 209

variables examined affect the pr-etest score-the sttident's age ani(1 thenumber of times he has repeate(d first grade. Older students perf'or mbetter, as do those wvho have repeate(l. Prior exposure to the miatlhe-niatics C.LIIu 1( ni11 would seem to niore thain compeisalte for the

(pr-esumaly'N) lower ability of the lepe;itets, a fi i(iiig sO -niewcit;at atod(ls wvith that of' (arno!v, Sack, andcl Thias (1977) whlo fotlidl thienumber of pi ima'ry-school 1 repeats tob)e ncga,i1tive1 v elaite to tse oiiiLii. -

school perforii' I' lice.Posttest score. Table 5 showNs the estilmlte(l pi 1 lictioIl f'uiction

f'or prol-rnI Ml;imiCC on the liiatlieiiatit.hs Imottest. Since the pr'eteSt StOvCis contrlolle(l for ani(d all data are available on1 an i viiditlua,il-sn:ntll)dsis. this data set allowvs letter es-ti inatioll of' the cf fe ts of' v'ariotusteacher and school xarlial)les tlhani do mIIost cl(ucit Ic m )lp(i (1lctici-

f'uinctioIi studies. In contrast to the resuilts oIn dfptrliilil: ll'h of' pretestscore, the number of' times the stuidenit has repeate(l is Hio longersigni fi( a ii, and( the st tlCeit's age is onilv mairginally so. Piretest s(core isa powerftl (letelluuiii;nt of posttest pei'f'oviiimce , as all previous iye-

t'1;(1 Ch on the mattel wvotuld( swest. d .1 i -el (class sizes r estult ill bc'ilb'st ttdeiii pei'f 1 ini ti(e. wvhiclh, tlhotuglh oicin Ic iiitimui6vc is (oiwit temli

wvithi a imixee(l tlernli of' fill(lirig , in the literature (Ja litism niet al., 1974; Haddad. 1977), As onle wNsouild( expect, ilnore f (c'lll ut

Nt it dCit a IRLI e(1.MC IntrsultS in better pecru ci c tm .lie m's ed(ltal-tioii level and( Cx)eriClicc are illisig ilifical it, ;111(1. controlling for cx-)e'ietnce olli' teahliei's lhave lowver pchforinmice. Studenlts froill 'uralfarming families do less well.

Perhaps the most strikinig aspect of Table 5 is the niiiglitim(le andsig iiicaiice of the coefficient for the effect of rad(io. Exposlle to theradio nmathematits lessons cani fari nre tlili coim pemsmte f'r at child'sagrictultural origins and can more than compenisate fol' his pel'for-mance fallimg one and a half stan(dard deviations behind on thepretest. The radio lessons appear to have no differential benefit foireither good or poor students, as the regressioni coefficient for theintei.dctiori between piretest score and exposurie to radio ';as inisig-nificant (in a regression not repoi-ted he-'e).

Failure propensity. Table 6 shows the inaixiiumii-likelilhowl esli-mates of the coefficients in the logit equation to p)l'efict end-of'-yalvfailu're. Each child's teacheir deternimiies wvhetheir the clhil(l p);sses orWflils, b)aIsedl oIn the chil(d's pCl0forniaice on cud-o e I' tests lpl('tl)llc(lby the teachllel in five subjects, one of wvhiclh is Illnlle1llati(s. Ill ilnel-pretinog the regressic ui results it slioui(Id be ionre in mi(l th;at tlte

Zti egltel 1 92 8) leview('d an i1id e xLtLItl ede c I x w otk olI t'ne in)poI taut II( c o I .I i 'nd.IIIc t

iII dO C I i n linIi IIg ILttI(eIiII pertOrniance, anlId(, mmitIh nime oic' i'(t WltNx -\\it 97 h7 I and Wilexsaid Hiarnistifteger ci 974) ieenmp)hasized th'e inmpo taltuc' ot aitte'Id(ldi(u t ith .allut)beempuict andl idolicv stutdies.

210 JAMISON

TABLE 5

Regressioni Determiiinants of Posttest Scores

Varial)Ie Subisample Coefficielnt t valuemean

Studenit characteristics

MALE .537 .866 .6()AGE 8.57 .788 1.9AGOCC .185 -5.32 -2.6DIST .696 -. 323 -. 39NRPT .522 .782 .54

Sichool characteristics

USH .641 -1 .26 -. 53UNOSH .0444 -. 453 .09CLSIZ 44.3 .232 2.4RADIO .752 1(.1 6.4TAGE 31.5 -. 474 2.0TED 11.2 --.82(6 -. 95TEXP 11.1 .297 1.5

PRE 20.4 1.21 8.6POSTATTAV 15.2 .687 3.0DROPFAILRENRL

Constant 20.0

Note. Dependent variable = POST; subsample mean(POST) = 57,8; subsample SD (POST) = 12.2; subsamplesize = 270: multiple R 2 =.40. All values are reported tothlee significant digits.

teacher was inaWaire of the child's score on the project-aidnihiisteledmathematics test, wvhich is the test score used in the analysis here.Table 6 clearly indicates that the student's posttest score is a strongdeterminant of likelihood to fail; it can be computed that, other thingsbeing equal, a student scorinig 5 points higher than the mean on theposttest will have his probability of FailUtre decreased by .11 from whatit would be had he scored at the miean. The table also suLggests sexdiscrimination: Male students are l1ss likely to fail than are females.

S I't'l)E N'1l R E1F I Il I I 0N 211

(Observations in the classrooms also indicated teacher favoritism formale students.) More regular attendance decr,.'ises a child's piolbiil-ity of failure, though the coefficieiu is statislically iiisigilificalvit. Expo-sure to radio in itself has no signiificanit effect oni the likelihood that achild will fil; the effect of ijir(lio is, iil,tcald. illdilc0-tliiol,gil itsimiipact oni aicIuievciieiit anid achievement's ,til scqtici i impact oni fail-tire pro)peflsity. Despite this cmcl(Ilisic)i1 that poor it( licv(tlictlit is an

Regression Deteriiiiiiatits ofl(ld-of'-vearl F:ailulre

Striaibbsample A.f syllAp)otitV ariable C.oef ficentmean t value

Sttudent characteristics

MALE .539 -1.39 -3.7AGE 8.57 .041 ..3AGOCC .182 .455 .77DIST .6 97 .063 .39NRPT .5,2 i l -.687 -2.1

School Characteristics

USH .643 .503 .75UNOSH .0)446 2.82 2.0CLSIZ 44.2 .(11 .38RADIO .751 .484 .72TAGE 3 1.6 -.201 -2.3TED 11.2 .256i 1.1TEXP 11.1 .177 2.3

E'ndogenious variables

PRE 20(.4 -.(19 -. 42POST 57.8 -.114 -5.5ATTAV 15.2 -.1(H) -1.2DROPFAILRENRL

Constant 7.940 1.57

Note. i)epentidentt vlahle -- FAIL, sulhsample inetii(FAIL)- .271 ; su,s,iample SI) FAIL) - 44; sutbsainiplesize = 269. Regressiorn chau(teristfis: l)chotot)mouis depenilenitvarialble, logit >pe i .io imuc, mIw6i\inlikclilioudl estntiintiuo.Chi-square of estimate (8 (degrees of fteedonw - 94.2. All N.tiltesreported to thiee significanit digits.

212 JAMISON

important determinant of failure, it is nonetheless possible, as Robin-son (1977) has suggested, that lack of places in higher grades cancause teachers to fail students and that relative achievement is thescreening mechanism. 7

We shall return in Section 4 to lisCLssionl of the overall milgnlitUdeof radio's impact (both direct and indirect) oii failure anld othervariables.

Determinan ts of f)cDm Pd1 fior vSrI wiolig

This stibsection exa min tie the (determin antts of thiee inudicaltors ofstudenits' demiandi foi- .rclooliiig in NicaraguaLlii-theil rate of attell-

lance in s1l1 their propensity to drop out during the sch00] year,ancd, given that they- completed the y-ear, tlheiri propensity to reenlrollthe subse(qUent schlool year.8

Attendance. As previously noted, attendance is itself an ipGp(xl ltatdeterminant of student learning; Table 7 reports on the factorsinfluencing attendance riate, here clefined as the number of days permonth that the child attended schliool averaged over that portion of'the school Year during which the child was emlrolledl. The talble ideni-tifies a number of variables that significantly affect attendance; ;InIoIlgschool variables, both teacher expeirience and enrlollmentll in a single-shift urban school increase attendaince Lates, while large class sizesdecrease them. Being from an agricultural family tends to increaseattendance, a finding that differs from results of early research in theUnited States on dsterminants of attendance (Folks, 1920;Reavis, 1920); more recent studies with U.S. data (Maynard & Mur-name, 1978) also indicate that imprtoving the eCon1o0mic elnvironniewil

of the home improves attendance rates.Within-year dropout propensity. Table 8 shows the deter-minants

of within-year dropout propensity as estim; ted from these data. Thecoefficient of attendance is highly significant at standard levels; how-ever, more frequent attendance increases the likelihoodi that a childwould drop out. contrary to nafti r.l expectations. Students wvithhigher pretest scores are less likely to drop out, thliogh this effect is

LRegressioI)n allnahNses ot tile (etetflnillants f eni(I-of-vetll tfailit, e Nwere also midertak-ell to the radio al(l control "OI JtS separately. ior both grotlps. postlest score 1ha1(d aOtI ()IIL illti statisticaillv iglifi(i(do IM tIllact oJI 1 cdm iln' i .1oi,l.ilct propen SiytV, h)ut tinc ll)ag-

nito(de of the effect eits higher s'ithlin the ral(gio t roiip. No other de'termilinanits of.tiIiii 1' Wvere stlatisti(ciiV %iL.lihiO Ot 11llin tllt contit l gropll), tllough a SOl)stalnltiMl nlnlbel,

partictilarlN teacher characteristics, were signill(wiat Ifo 1tic rad(lio grotlpl).

EatIli of the regressions reported in tlhi siibse( tiOII stffsl' Si ronti thle defect that thesamlple is onlilx of uhildol ci h)o enterled s hlool; 1tic results fbr' dropolit .otti rteenioll-Jlte?nt p)I'op(ensitv are thlis contilngent otnc he llilol's 111i1i.1Y havitng eniolled. Shino Tlidg(c(tio daite), ill a valuab)le stud( tvt school attendance inl tolrah India, uses a logit mlodel totestimate the potitoijolit' that a (thil(i attends school at all.

ST'VI)E N'I R EPE'I'1 IFI ON 213

TABLE 7

Regressioni Determiniralts of'Attenldance Rate

Variable Subsample Coefficielit t valuemeanl

Stud(lent cha.racteristics

MALE .5(9 .313 1.0AGE 8.64 .103 1.0AGOCC .230 2.4') 4.5DIST .806 .264 1,6NRPT .504 .717 4.9

School chariacteristics

USH .605 -1.12 -1.3UNOSH .055 5.(8 4.4CLSIZ 45.4 -. 1141 --1.()RADIO .765 .032 1.5TAGE 31.8 --.1 93 - 1.6TED 11.3 --.552 -1 .7TEXP 11.3 .067 1.1

Endlogellotts Variables

PRE 20.1 .007 .20POSTATTAVDROPFAILRENRL

Constant 27.7

Note. Depenident variable = ATTAV; subsamplemean (ATTAVI = 14.87; subsample SD (ATTAV) = 3.49;subsample size = 456; multiple R = .26. All values are re-pm ied to three %ignific.ini digits.

only marginally) signiificaiit. StuLdenits from agricultural families aremore likely to drop out, though, contr-olling for that, students in rurallschools are more likely to stay through the year.

Reenrollment. Table 9 shows the dleterin-ilianits of stLudenit reen-rollment. Students who fail are significantly less likely to reenroll thanare those who pass, a result supportive at the micr o-level ofLevy's (1971) finding that coutrWies with higher failure rates hadhigher dropout rates. Controlling for failure, higher posttest scores

214 J AXMiTS(VN

'fABL.E 8

Regression Detcimill.1iit1s ofWiulhi"-v!''; DiropoUt

Sariable Subsample (:oefficient Asvmp toticmean t value

Stutlent characteristics

MALE .513 -. 261 -. 65AGE 8.61 -. o74 -.54AGOCC .26() 1.(9 2.1DIST .782 .299 1.5NRPT .504 .015 -. 049

Sciool characteriistics

USH .580 2.3() 2.3UNOSH .0,560 3.21 1.8CLSIZ 15.6 .03:3 .86RADIO .759 .653 .66TAGE 31,5 -.0A33 -:23TED 11,2 .153 .455TEXP 10.8 .019 .19

Endogenous %ariables

PRE 20.0 -. I)05 -1.63POSTATTAV 15.3 .237 3.75,rDROPFAILRENRL

C onstant -10(.2

Note. Depenident variable= DROP; subsample mean(DROP) = .126; subsample S) (DROP) - .33, subsamplesize = 357. Regression characteristics: ihl)ito[mIItIbn dc'tpendeitivariable. logit specification, nlu.%ki\niiri-likl;ilio nl estimlatioln.Ghi-square of estimate (12 degrees of freedom) = 71.". A11 Niml-ties reported to three significant dligits

STUI)ENT REPETITION 215

TABI.E 9

Regression Determinants ofReenrolinient SubsequLenit Yeai

riale Subsample o Asvynptoticnmean t value

Student (h;lrctLerkistics

MALE .527 -. 380) -. 799AGE 8.58 -. 172 -1.13AGOCC .187 1.10 1.11DIST .697 .220 .541NRPT .523 -.248 -.640

Schoo. tracteristics

USH .633 -.111 -.12UNOSH'CLSIZ 44.3 .08() 1.7RADIO .744 -. 525 -. 75TAGE 31.7 -. 065 -. 78TED 11.2 .181 .50TEXP 11.2 .074 .82

Enclogenous variables

PRE 20.4 -.126 -1.9POST 57.9 .047 2.2ATTAV 15.2 .022 .23DROPFAIL .275 -1.26 -2.5RENRL

Constant .302 .45

Note. Dependent variable =RENRL; subsample mean(RENRL) =.897: subsample SD (RENRL) .304; uh.ts.aniplesize = 262. Regression cdharacteristics: Dichotomous dependentvariable, logit >pecifi(anon,. niaxinmum-likelihood estimation.(:Aii-quiire ot e:nmtLe (15 (legiees of freedom) = 29.2. All val-ues are reporte(d it) thriee signilicant (ligits.

a UNOSH was eliminated from the regression because of itsnoljinvairit with the dependtenit variable.

216 JAMISON

lead to higher probabilities of reenrollment; but, initerestinlglyenough, higher pretest scores lead to a lower probability of reenlroli-ment. This suggests that, lholding end-of-year pcr-forma.cc coll.mtailu.the more a child lihas gained dturing the year, the iiiotr likely he is toreenroll the next vear.

4. ECONOMIC IMPIICATIONS

My pr incipal purpose in this chapter has been to ;issecs- the impactof radio and other vairiablks on several i ndicaors of a studellt's s lool

performance, par-ticuklrly on the prohaiblfilit that he will fail the firstgrade. The preceding section piresentie(l the res;ults of this analysis.However, since failure and repetition rates have such iulportant im-plications for the cost of a "grad itate" from each gid(le or each cycle ofa school system, I feel it uworth including a preliminary aiialysi of theecon-tomic impact of the Radio Mahtlhemnatics Project thluough its effecton these variables.

The intro(lli(tioii of radio iecve,X;i til\ raises the (ost per "tIIdletltper veal aissuiii g nolituitamoitsH iCI)'l(';l ill cass si/c oir otherresource saving); hoe er. if illt I to(lICiL2 radio 1 ('( uo t'c thle pi hahil-ity of, a stildlent s [.tili ig, it liay wVell ed(l itc tlle cost per fil,s-grilh9gr;ad1iate' (wei th1oulgh it raisec the cost per studelnt. Let / he theprobhability that a child fails first gr alde. let C, be the (ost per ttildenltper vear, and let C,g be the cost )er grsaduiate. It is eas- to c(Oilpue thatCg = G(l -f ). In ordrer to c(ompla).re the cost per gi£t1(i a e ith rad(ioto the cost per gira nid te without ra(io it is, thelln ], icc'ca m;11 V to havevalues of C, and f witli and withlott ria(lio.

Cost. A recent aissess'meint of' the c(hi(atioiimi sector in Nit ar.igm

(Academv for EdulClatio uial Deveb )liltrcit, 1975) esti i mites the cost perprimary student per yea r to be . 5-4.0), Jniioiiom and McAnany (1978,(hap. 4) estimate the cost per sttudenit in the l)rQjt to he albuo w3.(tlper year ;isililg, ad1ssumi d 1rt( usage of' the system. (TIhle margrllaul costper student is abotut $1.65 per year, allowing scope folr tl)taittiilr-edlictiO l inl a\'vera[ge (cw& as uslge expa;ilsd.) We thills haveC, = $54.00 witlihott radio and S57. () with radio.

Effectiveness Fro estimiate the effect of the pi oject ot he probabil-ity that a student Faiis, one must take into accouit the dii rt! efFet amidall of the indivect effects indicated in Figure 1. TIhis ani) be doin,using the esti n-ated I-egressioIns of' Sectioll 3. (Given a dli Jriblitioll of'values for thie exogenouis N-aidlilcs, one can coti)p)llte the expectedvalues for the endogenouis "aiiiiiiibecs: First, the c(ef fictsis in TIalc 4allow coinp p t t;on of' the expected pretest scor'e; (ex t thte co f ficie its

STI'UDENT REPETITION 217

in Table 5, with the computed pretest value, allow computation of theexpected attendance rate; and so forth.

Table 10 shows the results of computing the values of the en-dogenous variables under the alternative assumptions that the systemuses and does not use radio. Note that the within-year dropout prob-ability is slightly highler for the radio students, but that their end-of-year failure probability is much lower, almost entirely because ofradio's effect on the posttest score and the subsequent effect of theposttest score on l'ailure probability. Notice, too, that Table 3 indicatesthat the mean failure rate in the radio group is slightly higher than forthe noniiad;lio group; this well illustrates the importance of disentan-gling the multiple determinants of failure through statistical analysis.Though the radio group differed only moderately from the nonradiogrouip in terms of mean values for most variables, the differences allfavored the nonradio group in terms of factors determining failurepropensity. A much higher fraction of the radio group came fromagricultural families, leading to lower posttest scores and, thereby,

TABI.E 10

Effect of Radio onthe Endlogenous Variables

Estimated expected valueVariable

WNithout radio With radio

PRE 20.0 20.0ATTAV 12.5 12.5DROP .013 .)25POST 47.8 58.0FAIL .45 .33RENRL .91 .92

Note. Ihis table showys the estimated expectedvalues of the endogenous variables in the svstemunlder the assumption that the vector of exogenousvariables (except radio) i distributed in the popula-tion1 in the same wav that it is dlistributed in thesubsample of our sample for which Nwe have corn-plete infor-mation on the exogenous variables. (Be-cause of the nonlinearitv of the logit transforma-tiOll, the expected values of' the vector' of en-doge-nous variables is not, of (ourse, the estimatedl func.tioin of the expected value of the exogenous vari-albles.) Ihe radio variable takes on the %Ilute ofeither I ("With radio" column) or 0 ("Withotitlildio'" (olmino). All values are reported to three

significant (igits.

218 JAMISON

higher failure probabilities. The radio group also had fewer repeatersand fewer males, and both factors caused it to have more failures.These factors are all systematically accounted for in the failure com-parison of Table 10, and we use those values in the cost-effectivenesscomparison.

It would be inappropriate, howvever, to take the valujes of thevariable FAIL in Table 10 for the values of:f to be use(d in (collIpUtiligcost per graduate. We need also to consider the (small) effect of'within-year dropouts. For the nonradio group, 5% of the students arepredicted to drop out and 36%,7e of those remniaininig fail; thus

f = 1 - (1 - .03)(l - .45) = .457.

For the radio group wve have

f = 1 - (1 - .025)(1 - .33) = .347.

Cost-effectiveness analysis. We are now in a position to calctilatethe cost per first-grade graduate for both the radio groups alld thenonradio groups. Using the simple formil:i at tihe lbegi ii i ig of' this

section we can compute that, for the nottradio group, the cost pergradtuate is given by

CF = $54/(l-.457) = $99.45.

For the radio group:

C = $57/(1-.347) = $87.29.

Even though introducing radio raises the cost per studclenit, Cs, by$3.00 per year, it reduces the cost per graduate by $12.16 or aboult12%. Another way of putting this is that, for a given total level ofexpenditure on first-grade education, about 12% more childrenwould graduate from first grade each year with the project in opeTa-tion than without it.9

These methods of coniipu cing cost-effectiveness can easily be cx-tended to cycles covering more than one grade (Jamnisoni & L.eslic,

9 An alternative way of iti dihikhig ab io the cost-efTec tiveness ol the p' ()il t- is to viewas wasted the resources spent on a stud(enit if he fails first grade. Wliile this itiethiodl^would give some insight iilto the niature of the udvantmage ol the prii cjt over traditionalinstruction, the metlhod of calcuhain ig cost-effectiveness (les( iibed in the text is prefer-able. The reason is that prodttction of gt.drac.tcs is a more appropriate criterion ofeffectiveness than is avoidance of wastage.

STt'DEN 'U REPF.ETITION 219

1977, pp. 114-150; Lethem, 1977, chap. 13): When the data be-come available from Nicaragua concerniiing the project's impact at thesecond- and third-grade levels, this will be done.

5. CONCLUSIONS

This analysis of data concerning 1975 firsl-grade students in.Nicaragua leads to four principal conclusion-ts:

1. 'Ilic Nicaia ga Radio Nfiatlheinitics Project canl, as previous evaluationshave already shown, signinlifilcatNl improve the mathemiatics perfor-mnance of first-gl-ade vccidciiis Students expo,,ed to the radio lessorsscoredl about thiree-fotiurths of a stiid;uird deviation lhighier oni standard-ized tests than did coiitrol studetnts.

2. In large part becatise of their inpio\ edl miathematics compelclcnc,tll(dIllts exNI)se( to Itli ) lessons were considerably less likely to fail

first grade than wvere controls. Tle estimatecl pihlability of failure ofstuclents expowld to r adio was .33; the estimated prol)blability for cointrolstu(lents wvas .45.

3. 1wrlodtlLicing project ra(lio lessonis wouldi acddabout $3.00 to the pesentcost of S54.00 per sttu(dernt per year of elenientarv edtliCation in)Nicarizigiimi. Howvever, pihi icipipllv because of tlhe inl)act project lessonlshave in redl i lig rcl)ctitii in rates, the cost per first-grade greiduiti, witlhproject les-mis wotild be abotit $12.16 less t0an the 99_.5() it wvould( bewithiout themn.

4. Ihrouglh its ef fect on achievementboth dlirectl'% aid iiidirectly' tlhrotughlthe effect of ;ichiex emuen t on failure propensitv, introduction of ra(lio(slightly) decreases between-year dr-opout propensitv, a fiii(lidi at theimicro-level coisistenlt wvitlh thatof Levy (1971) ata cr(oss-lziiti0u;il level.

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