Wilson - Critical Review of Menstrual Synchrony Research

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psychon~uroendocrinology. Vok 17. No. 6. pp. 565-591, 1992 0306-4530/92 $5.00+0.00Printed in Great Britain Pergamon Press I.~d.

A CRITICAL REVIEWOF MENSTRUAL SYNCHRONY RESEARCH

H. CLYDE WILS ONDepartment of Anthropology, University of Missouri - Colum bia, Columbia, Missouri, U.S.A.

(Received 23 July 1990; in final orm 25 July 1992)

S U M M A R YTw o expe rimen ts and three studies reported a s ignificant leve l of menstrual s ync hro ny aftersubjects had been treated with applications of axillary extract from a donor subject or after subjectshave spent time together. Fo ur studies failed to replicate these results. A com paris on of the studiesshows the on ly consistent difference is that those studies not finding men strual s ync hro ny reportedproblems with subjects who had irregular cycle lengths, while those finding menstrual synchronyreported no such problems. All experiments and studies were based on the me thod s and researchdesign introduced b y McClintock (1971). Thr ee errors are inherent in research base d on her model:(1) an implicit assumption that differences between menses onsets o f ran dom ly paired subjects va ryrandomly over consecu t ive onset s , (2 ) an incorrec t p rocedure fo r determin ing the in i t i a l onsetabsolute difference between subjects, and (3) exclusion of subjects or some onsets of subjects whodo not have the num ber of onsets specified by the research design. All of these errors increase theprobabil ity of f inding menstrual synchro ny in a sample. One o r more o f these errors occu rred in theexperiments and s tudies repo rt ing synchro ny; no s ignificant levels o f menstrual syn chro ny occu rwhen these errors are corrected. Menstrual sync hron y is not demonstrated in any of the experiments

or studies.

I N T R O D U C T I O NI N 1 9 71 M c C l i n t o c k p u b l i s h e d a n a r ti c le r e p o r t i n g m e n s t r u a l s y n c h r o n y i n p a i r s a n d g r o u p s o fc o l le g e w o m e n w h o s p e n t t im e t o g e t he r . B y 1 9 7 8 , t h e d a t e I b e g a n m e n s t r u a l s y n c h r o n yr e s e a r c h , M c C l i n t o c k ' s a r t i c le h a d b e e n c i te d o v e r 4 0 t i m e s i n th e s c i e n ti f ic l i t e ra t u r e a n d c o n -t in u e s t o b e c i t e d i n p r o f e s s i o n a l j o u r n a l s , l i t e ra t u re o n b i o l o g i c a l a n d p s y c h o l o g i c a l i s s u esr e g a r d i n g w o m e n , a n d t he p o p u l a r m e d i a ( e .g . , M o n m a n e y , 1 9 8 7 ) . T h e p o s s i b i l i ty t h a t o n ew o m a n m i g h t i n f lu e n c e t h e m e n s t r u a l c y c l e o f a n o t h e r h a s b o t h p r a c t i c a l a n d t h e o r e t i c a l i m p l i -c a t i o n s. T h e p r a c t i c a l i m p l i c a t i o n is t h e p o t e n t i a l o f a p h e r o m o n e o r s o m e o t h e r s i g n a li n f l u e n c i n g t h e ti m i n g o f o v u l a t i o n t h a t w o u l d a s s i st i n r e p r o d u c t i v e s c h e d u l i n g . T h e t h e o r e t i-c a l i m p l i c a t i o n i s u n d e r s t a n d i n g s y n c h r o n o u s o v u l a t i o n a s t h e p r o d u c t o f n a t u r a l s e l e c t i o n i nh u m a n b i o l o g i c a l e v o l u ti o n .

S e v e r a l t y p e s o f b e h a v i o r a r e k n o w n t o in f lu e n c e m e n s t r u a l c y c l e s a n d o v u l a t i o n i n h u m a n s :p r o l o n g e d a n d i n t e n s i v e b r e a s t f e e d i n g , l o ss o f b o d y f a t b e l o w c e r t a in l e v e l s , p s y c h o l o g i c a ls tr e ss , a n d i n g e s ti o n o r i n j e c t i o n o f h o r m o n e s . M c C l i n t o c k ' s r e s e a r c h r a i s e s t h e a d d e d p o s s i b i l-Address correspondence and reprint requests to: Dr. H. C. W ilson, Department of Anth ropo logy , Universityof Missouri - Columbia, 20 0 Swallow Hall , Columbia M O 65211, USA .

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566 H .C. Wtt.soNi ty o f p h e r o m o n a l c o n t r o l o f m e n s t r u a l c y c l e s a n d t h e ti m i n g o f o v u l a t io n . R o g e l ( 1 9 7 8 ) c i t e sM c C l i n t o c k i n h e r e x t e n s i v e r e v i e w , " A C r i t i c a l E v a l u a t i o n o f t h e P o s s i b i l i ty o f H i g h e r P r i m a t eR e p r o d u c t i v e a n d S e x u a l P h e r o m o n e s , " a n d s u g g e s ts :

From the research discussed in th is article, it seem s that the m ost prom ising area in w hich tosearch for pherom onal control of higher primate sexual and reprod uctive behavior is m enstrualsynchrony, a phenom enon that suggests the action of a primer pherom one. (p. 826)

B e n n e t t ( 1 9 7 4 ) p o i n t e d t o " th e c o n t r a c e p t i v e p o s s i b i l it i e s o f p h e r o m o n e s " a s o n e o f th er e s e a r c h a r e a s o n c h e m i c a l c o n t r a c e p t i v e s u n d e r s t u d y ( p p . 1 8 1 - 1 8 2 ) . C o n v i n c i n g e v i d e n c em e n s t r u a l s y n c h r o n y o c c u r s i n h u m a n s w o u l d j u s t i f y a m a j o r r e s e a r c h e f f o r t to i d e n t i fy th ep h e r o m o n e o r o t h e r p h e n o m e n o n r e s p o n s ib l e f o r t h is e f f e c t.

C o n f i r m i n g m e n s t r u a l s y n c h r o n y i n h u m a n s a ls o c o u l d c o n t r ib u t e t o t he e m e r g i n g b o d y o fe v i d e n c e t h at s tr e s s e s t he i m p o r t a n c e o f p r i m a t e f e m a l e s i n m a t e c h o i c e , g e s t a ti o n , a n d i n f a n tc a r e . U n t i l r e c e n tl y , t h e o r i e s in e v o l u t i o n a r y b i o l o g y h a v e c o n c e n t r a t e d o n t h e p r i m a t e m a l e ' sc h o i c e o f m a t e s ; t h e e s t r o u s f e m a l e s w e r e c o n s i d e r e d n e u t r a l o r p a s s i v e i n t h i s p r o c e s s ( H r d y ,1 9 8 1 , p p . 1 1 - 1 2 ) . H o w e v e r , fi e ld s t u d i e s o f p r i m a t e s r e p o r t d o m i n a n c e h i e r a r c h i e s a m o n gf e m a l e s i n m a n y s p e c i e s ( H r d y , 1 9 8 1 ). F u r t h e r, th e s e d o m i n a n t f e m a l e s f a v o r a b l y c o m p e t ew i t h s u b o r d i n a t e f e m a l e s f o r r e p r o d u c t i v e a c c e s s t o t h e m a l e s a n d h a v e s i g n i f i c a n t l y g r e a t e rr e p r o d u c t i v e su c c e s s ( D r i c k a m e r , 1 9 7 4 ; D u n b a r & D u n b a r , 1 9 7 7 ) . T h e r e f o r e , i f a ll f e m a l e sh a v e s y n c h r o n i z e d o v a r ia n c y c l e s , a d o m i n a n t f e m a l e c o u l d e n h a n c e h e r r e p r o d u c ! iv e p o te n t ia lb y m o n o p o l i z i n g t h e sp e r m , c o n s o r t s h i p a n d p r o t e c t i o n o f a d o m i n a n t m a l e . U s i n g a d i ff e r e n ta r g u m e n t , T u r k e ( 1 9 8 4 ) s u g g e s t s e a c h m a l e w o u l d b e o c c u p i e d w i t h a f e m a l e , i f t h e f e m a l e sh a v e s y n c h r o n o u s o v a r i a n c y c l e s a n d e x t e n d e d s e x u a l r e c e p t i v i t y . T h u s , a f e m a l e ' s r e p r o d u c -t i v e s u c c e s s i s in c r e a s e d b y h e r m a l e ' s e x c l u s i v e c o n s o r t s h i p a n d h i s i n c r e a s e d p a r e n t a l e f f o r t .

M c C l i n t o c k ' s s t u d y h a s b e e n r e p l i c a t e d t w i c e a n d h a s r e c e i v e d a d d i t i o n a l s u p p o r t f r o m t w oe x p e r i m e n t s . F o u r s t u d i e s f a i l e d t o r e p l i c a t e h e r s t u d y . T h i s r e v i e w e x a m i n e s t h e c a u s e s f o rt h e s e c o n f l i c t in g re s u lt s . F i r st , I r e v i e w t h e m e n s t r u a l s y n c h r o n y e x p e r i m e n t s a n d s t u d i e s a n dc o m p a r e t h e s e v e n f ie l d s t u d ie s , i .e . , r e s e a r c h i n w h i c h n o a t t e m p t w a s m a d e t o c o n t r o l e n v i r o n -m e n t a l f a c t o r s o r m a n i p u l a t e t h e b e h a v i o r o f t h e s u b j e c t s , o n t h e b a s i s o f s e v e n v a r i a b l e s .S e c o n d , I d e s c r i b e a n d e x p l a i n t h r e e e rr o r s t h a t b ia s t h e r e s u l ts o f m e n s t r u a l s y n c h r o n yresea rch . A nd , t h i rd , I u se t hese e r ro rs t o i nd i ca t e b i a ses i n t he t h ree s t ud i e s and tw o expe r i -m e n t s r e p o r t i n g m e n s t r u a l s y n c h r o n y . M y c o n c l u s i o n i s t h a t m e n s t r u a l s y n c h r o n y h a s n o t b e e nd e m o n s t r a t e d i n a n y o f t h e s e s tu d i e s o r e x p e r i m e n t s .

A RE VIEW O F ME N STRU A L SY N CH R O N Y STU D IESA l l th e s tu d i e s a n d e x p e r i m e n t s a r e b a s e d o n m e t h o d s i n t r o d u c e d b y M c C l i n t o c k ( 1 9 7 1 ) . I n

t h e s t u d i e s , s u b j e c t s w i t h n o p r e v i o u s s o c i a l c o n t a c t c o m e t o g e t h e r i n a s o c i a l s e t t i n g s u c h a sb e c o m i n g r o o m m a t e s . T h e a b s o l u t e d i f f e r e n c e b e t w e e n d a t e s o f t h e s u b j e c t s ' f i rs t p o s t - c o n t a c tm e n s e s o n s e t s i s d e t e r m i n e d . A f t e r a p e r i o d o f se v e r a l m o n t h s , t h e a b s o l u t e d i f f e r e n c e b e t w e e nt h e s u b j e c t s ' m e n s e s o n s e t s d a te s is d e t e r m i n e d o v e r t h e sa m e n u m b e r o f o n s e ts . A d e c r e a s ef r o m t h e i n i ti a l to t h e f i n al o n s e t a b s o l u t e d i f f e r e n c e i s d e f i n e d a s m e n s t r u a l s y n c h r o n y . I n t h ee x p e r i m e n t s , s u b j e c ts r e c e i v e d o n t h e ir u p p e r l ip s s c h e d u l e d a p p l i c a t i o n o f a x i l l a r y e x t r a c tt a k e n f r o m a d o n o r s u b j e c t . T h e a b s o l u t e d i f f e r e n c e b e t w e e n t h e f ir s t a p p l i c a t i o n a n d t h e i n it ia lm e n s e s o n s e t o f th e s u b j e c t is d e t e r m i n e d . T h e f i n al o n s e t a b s o l u t e d i f f e r e n c e i s d e t e r m i n e da f t e r a n e q u a l n u m b e r o f a p p l ic a t i o n s a n d s u b j e c t s ' o n s e t s . A s b e f o r e , a d e c r e a s e f r o m t h ein i t i a l t o t he f i na l ab so lu t e d i f fe rences i s de f ined a s synch rony .


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MENSTRUAL SYNCHRONYRESEARCH 567T h e f ir st p u b l i s h e d r e p l i c a ti o n o f M c C l i n t o c k ' s s t u d y w a s w h e n G r a h a m a n d M c G r e w(1980) r epor ted m ens t rual syn chrony in a sample o f 18 pai rs o f c loses t f r iends a t a co educat ionaluniver s i ty in Scot l and. The same year Russe l l e t a l . ( 1980) r epo r t ed an expe r i m en t i n w h i chf ive w om en s ynchr on i z ed t he i r m ens es ons e t s w i th an unknow n donor a f t e r be ing t rea ted ove rfour mens t rual cycles wi th the odor of a donor ' s ax i l l a ry secre t ions . The fo l lowing year , i n asecond repl i ca t ion of McCl in tock ' s s tudy, Quadagno e t a l . (1981) r epor ted mens t rual synchronyamo ng c lose f r iends and room ma tes a t a coeduc at ional s t a te univer s ity . F inal ly , i n 1986 Pre t i

e t a l . (1986) , in an exper im ent s imi lar to tha t of Ru sse l l e t a l . (1980) , fou nd tha t , a f ter two men-s t rual cycles , a s ample of 10 women exper i enced a s igni f i cant decrease in the absolu te d i f f er -ence betwe en the wo m en ' s m enses onset s and the appl i ca t ions of the dono r ' s ax i l l a ry secre t ions .Ho we ver , four o ther s tudies f a il ed to f ind m ens t rual syn chrony. P faf f (1980) d id no t findmens t rual syn chrony in samples o f room ma tes and c lose f r iends a t a coed ucat iona l s t a te univer -s it y ; J a r e tt ( 1 9 8 4 ) r e p o r t e d n o s i g n if ic a n t s y n c h r o n y i n a s a m p l e o f r o o m m a t e s f r o m t w ow om en ' s co l l eges ; and W i l s on e t a l . ( 1991) d i d no t f i nd m ens t r ua l s ynchr ony i n s am pl es o fpai r s and groups o f subjec t s in a soror ity and in a coopera t ive house on the cam pus o f a coedu -cat ional s tate univers i ty.The exper iment s in t roduced severa l cont ro l s , e .g . , s e l ec t ion of subjec t s wi th r egular cycleswho w ere not tak ing ora l cont racept ives , s chedul ing of the t rea tment cycles , double-bl ind t r ea t-men t procedu res , and cont ro l groups r eceiv ing p lace bo t rea tment s . The se ven s tudies , l ackingthe cont ro l s of the exper iment s , d i f f er in severa l ma jor var i ables tha t could ha ve inf luenced theou t com e o f the s t ud ie s . Seven o f t hese va r i ab le s w er e exam i ned t o de t e r m i ne w h i ch , i f any,migh t explain the conf l ict ing resul ts repor ted in the s tudies : (1) di f feren ces in the env ironm en-ta l s e t t ing , e .g . , coeducat ional univer s i ty or women ' s col l ege , (2) d i f f erences in the percentageof subjects us ing oral contracept ives , (3) di f ferences in the length of the s tudy per iod, (4) di f fer -ences in samp le s i ze , (5) d i f ferences in method of se l ec t ing the s tudy samp le , e .g ., volunteer s ors e l ec t ed by t he i nves t i ga t o r , ( 6 ) d i f f e r enc es i n age o f the s ub j ec t s , and ( 7 ) d i f f e r enc es i nrepor ted f r equency o f subjec t s wi th i r regular cy cles or amenor rhea . The f ir st s ix of these vari -ables show ed no s ignif i cant d i f ference betw een tho se s tudies r epor t ing s igni f icant l evel s of syn-chrony and those r epor t ing no s igni f i cant l evel s of synchrony, e .g . , subjec t s in a l l t he sampleswere in the same age r ange, and McCl in tock (1971) found synchrony but Jare t t (1984) d id notf i n d s y n c h r o n y , t h o u g h b o t h u s e d s u b j e c t s f r o m w o m e n ' s c o l l e g e s . T h e o n l y v a r i a b l e t h a tc l ea r l y d i f f e r en t i a t e s t he m ens t r ua l s ynchr ony s t ud i e s r epo r t i ng pos i t i ve r e s u l t s f r om t hos erepor ting nega t ive r esult s i s the r epor ted f r eque ncies o f me ns t rual cyc le i rr egular ity and am en-or rhea . M cCl in tock (1971) , Graham and McG rew (1980) , and Quadag no e t a l . (1981) founds i gn i fi can t l eve l s o f m e ns t r ua l s y nch r ony i n the i r s am p l es and r epo r t ed no p r o b l em s w i t hsubjec t s having i r r egular cycles or amenor rhea . P faf f (1980) , Jare tt (1984 ) , and W i l son e t a l .(1991) found no s ignif i cant level s of mens t rual syn chron y in the ir s amples , an d a l l of them hadto make changes in McCl in tock ' s methods to adjus t for h igh f r equencies of subjec t s wi th i r r eg-u l a r m e ns t r ua l cyc l e s o r am enor r hea . The p os s i b l e s ou r ce o f t h is d i f f e r ence i s cons i de r edbe low (Error II I) .

TH RE E E RRO RS I N TH E STU D Y O F M E N STRU A L SY N CH RO N YThe methods used in exper iment s and s tudies for de termining mens t rual synchrony in pa i r sof subjec t s have inc luded three types of errors : (1) fa i lure to r ecogn ize tha t a proba ble one -hal fof the pai rs in a sample sync hronize b y chance , (2) miscalcula t ion of the abso lu te d i f f erencebe t w e en i n it ia l m ens es ons e t s , and ( 3 ) exc l us i on f r om t he s am pl e o f t hos e s ub j ec t s o r s om e


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568 H.C . wtt.so.~o n s e t s o f s u b j e c t s i n o r d e r t o f it t h e n u m b e r o f o n s e t s t o th e s p e c i f i c a t i o n s o f t h e r e s e a r c hd e s i g n . A l l o f th e s e e r r o r s i n c r e a s e t h e p r o b a b i l i t y o f f i n d in g a s t a t i s t ic a l l y s i g n i f i c a n t l e v e l o fm e n s t r u a l s y n c h r o n y i n a s a m p l e . T h e s e t h re e e r r o rs a l s o o c c u r i n s a m p l e s o f g r o u p s o fs u b j e c ts . H o w e v e r , I w i l l p o s t p o n e d i s c u s s i o n o f t h e s p e c i a l c a s e o f g r o u p s a m p l e s u n t il m yr e v i e w o f M c C l i n t o c k ' s s a m p l e s o f g r o u p s . A r t if i ci a l d a t a a n d s a m p l e s f r o m s t u d i es c o n d u c t e db y W i l s o n e t a l . ( 1 9 9 1 ) a r e u s e d t o i l l u s tr a t e s o u r c e s o f t h e s e e r r o r s a n d h o w t h e y b i a s th er e s ul ts o f m e n s t r u a l s y n c h r o n y r e s e a r c h .E r r o r I

E r r o r I is t h e i m p l i c i t a s s u m p t i o n t h a t, a t t h e b e g i n n i n g o f t h e o b s e r v a t i o n p e r i o d , e i t h e r th ed i f fe r e n c e s b e t w e e n m e n s e s o n s e t s o f p a ir s o f s u b j e c t s a r e v a r y i n g r a n d o m l y o r t h e d i f f e re n c e sb e t w e e n m e n s e s o n s e t s o f su b j e c t s ar e i n cr e a s in g . N o n e o f th e s t u d ie s o r e x p e r i m e n t s m a k e s a ne x p l ic i t a s s u m p t i o n a b o u t t h e e x p e c t e d d i r e c ti o n o f c h a n g e b e t w e e n m e n s t r u a l o n s e t s , th o u g ht h e y a ll a s s u m e t h a t a d e c r e a s e i n o n s e t d i f f e r e n c e s b e t w e e n p a i r s o f s u b j e c t s o v e r th e s a m en u m b e r o f o n s e t s i s a n i n d i c a ti o n o f m e n s t r u a l s y n c h r o n y . H o w e v e r , a t th e b e g i n n i n g o f t h eo b s e r v a t i o n p e ri o d , a p p r o x i m a t e l y o n e - h a l f o f th e p a i r s o f a s a m p l e h a v e o n s e t d i f f e r e n c e s th a ta r e d e c r e a s i n g o v e r th e s a m e n u m b e r o f m e n s t r u a l c y c l e s . T h i s a p p a r e n t s y n c h r o n y i s d u e t oc h a n c e f a c t o r s a s s h o w n i n th e f o l l o w i n g s e t o f e q u a t i o n s .

F o r a n y r a n d o m l y p a i re d s u b j e c t s , th e r e l a ti o n s h i p b e t w e e n m e n s t r u a l o n s e t s o v e r t h e s a m en u m b e r o f c y c l e s i s e x p r e s s e d a s :

O~= IC~ (X , - Xb) + (T a o - Tbo)l (e qu at io n 1)W h e r e D~ i s t h e o n se t ab so lu t e d i f f e r en ce a t c y c le c~ ( i = 0 .1 ,2 ,3 .. .) , x a an d x b a r e th e m ea n

cy c le s l en g th s o f su b je c t s A a n d B , an d Tao an d Tbo a r e th e d a te s o f t h e in i t i a l o n s e t s f o r su b jec t sA a n d B a t c y c l e 0 .

T h r e e c a s e s a r e d e r i v e d f r o m e q u a t i o n 1:Ca se A. i f xa = xb , the n c~ (x , - x b) = 0 , an d o~ is the sa m e a t a l l o ns ets ;C a s e B . i f 2 , , x b a n d r a o = rbo, or if X~ > Xb an d T a o > Tbo, o r if Xb > X~ an d Xbo > T,o,

th en o~ in cr ea se s at the rate o f IC= (xa - Xb)l: an d,C a s e C . i f ~ . > x b an d T .o < Tbo, or if Xb > x . a n d T b o < V a o ,

th en c> de cr ea se s at th e rate o f I~ (x. - Xb)l un til o~ = 0,an d t>~ in cr ea se s at th e rat e o f IC~ (x. - Xb)l the rea fte r .

T h e s e t h r e e c o n d i t i o n s c a n b e r e s t a t e d a s f o l l o w s :C a s e A . i f r a n d o m l y p a i re d s u b j e c t s h a v e t h e s a m e m e a n c y c l e l e n g th s , t h e n o v e r a n

e q u a l n u m b e r o f c o n s e c u t i v e o n s e t s th e a b s o l u t e d i f f e r e n c e s b e t w e e n o n s e td a t e s r e m a i n s c o n s t a n t ; a n d

C a s e B . i f r a n d o m l y p a i r e d s u b j e c t s h a v e u n e q u a l m e a n c y c l e l e n g t h s a n d t h e i n it ia lo n s e t s o f b o t h s u b j e c t s o c c u r o n th e s a m e d a y , o r i f t h e s u b j e c t w i t h t h e g r e a t e rm e a n c y c l e l e n g t h h a s t h e s e c o n d r e c o r d e d o n s e t d a t e , t h e n o v e r an e q u a ln u m b e r o f c o n s e c u t i v e o n s e t s t h e o n s e t a b s o l u t e d i f f e re n c e s i n c r e a s e ( d iv e r g e )a t th e r a t e o f t h e d i ff e r e n c e b e t w e e n t h e m e a n c y c l e l e n g t h s o f t h e p a ir ; a n d

C a s e C . i f a p a i r o f s u b j e c ts h a s u n e q u a l m e a n c y c l e l e n g t h s a n d t h e s u b j e c t w i t h t h eg r e a t e r m e a n c y c l e l e n g th h a s t h e f i rs t r e c o r d e d o n s e t d a t e , t h e n o v e r a n e q u a ln u m b e r o f c o n s e c u t i v e o n s e t s t h e o n s e t a b s o l u t e d i f f e r e n c e s i n i t ia l ly d e c r e a s e( c o n v e r g e ) a t th e r a t e o f t h e d i f f e re n c e b e t w e e n m e a n c y c l e l e n g t h s o f th e p a i ru n t i l t h e o n s e t d i f f e r e n c e r e a c h e s 0 , a n d t h e r e a f t e r t h e y i n c r e a s e ( d i v e r g e ) a t t h es a m e r a t e t h e o n s e t d i f f er e n c e d e c r e a s e d .


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M~STRUAL SYNCHRONY RESEARCH 56 9T h u s , o v e r t h e f ir s t s e v e r a l o n s e t s , w h e t h e r t h e o n s e t d i f f e r e n c e o f r a n d o m l y p a i r e d s u b j e c t s

r e m a i n s c o n s t a n t ( c a s e A ) , i n c r e a s e s ( c a s e B ) o r d e c r e a s e s ( c a s e C ) i s d u e t o t h e c h a n c e f a c t o r so f t h e s u b j e c t s ' r e l a t i v e m e a n m e n s t r u a l c y c l e l e n g t h s a n d t h e o r d e r o f t h e i r i n i ti a l o n s e t d a te s .

F o r p u r p o s e s o f th i s d i s c u s s i o n , I a s s u m e c a s e s B a n d C e a c h h a v e a n e q u a l c h a n c e o fo c c u r r i n g , i . e. , p = q = 0 . 5 . J u s t i f ic a t i o n f o r t h i s d e c i s i o n i s t h a t c a s e A , w h e r e o n s e t d i f f e r e n c e sr e m a i n c o n s t a n t o v e r c o n s e c u t i v e o n s e t s , s e l d o m o c c u r s i n a c t u a l s a m p l e s . T h e d i s t ri b u t io n o fc a s es A , B a n d C a m o n g 5 9 p a i rs i n a s o r o r it y r o o m m a t e s s a m p l e ( W i l s o n e t a l . , 1991) i s onec a s e , 3 0 c a s e s , a n d 2 8 c a s e s , r e s p e c t i v e l y . F u r t h e r , c a s e s i n w h i c h t h e d i f f e r e n c e b e t w e e n t h ei n it ia l a n d f i n a l o n s e t s i s z e r o a r e d r o p p e d f r o m a n a l y s i s i n b o t h t h e W i l c o x o n a n d s i g n t e s ts a n dt h u s d o n o t a f f e c t t h e s t a t i s ti c a l t e st s c o m p a r i n g t h e i n i ti a l a n d f i n al m e a n o n s e t a b s o l u t e d i f f e r -e n c e s .

T h r e e c o n c l u s i o n s a r e d r a w n f r o m e q u a t i o n 1 a n d c a s e s A , B , a n d C . F i r st , f r o m c a s e C ,c h a n c e s y n c h r o n y i n a s a m p l e i s g r e a t e s t a t t h e b e g i n n i n g o f th e s t u d y p e r i o d a n d d e c l i n e st h r o u g h t im e a s s u c c e s s i v e o n s e t d i f f e r e n c e s a r e r e c o r d e d . F o r e x a m p l e , a s s u m e s u b j e c t A h a sa n i n it ia l o n s e t o n d a y 5 o f th e o b s e r v a t i o n p e r i o d a n d a m e a n c y c l e l e n g t h o f 3 0 d a y s , a n ds u b j e c t B h a s a n i n i t i a l o n s e t o n d a y 1 3 a n d a m e a n c y c l e o f 2 8 d a y s ; a n d l e t t h e o n s e t s a n dc y c l e l e n g t h s o f s u b j e c t B b e s u b t r a c t e d f r o m t h o s e o f s u b j e c t A ; t h e n t h e s u c c e s s i v e o n s e t r e a la n d a b s o l u t e d i f f e r e n c e s d e c r e a s e a n d t h e n i n c r e a s e a s s h o w n i n T a b l e I .

TABLE 1. MEAN CYCLE LENGTHS, ONSET DATES, AND ABSOLUTE AND REAL ONSET DIFFERENCESFOR TWO SUBJECTS ILLUSTRATING A CASE (C) (ARTIFICIAL DATA)

OnsetsMeanSubject Cycle Le ng th 01 02 03 04 05 06 07 08 09 10A 30 5 35 65 95 125 155 185 215 245 275B 28 13 41 69 97 125 153 181 209 237 265

A bso lu t e d i f fe ren ce (day s ) 8 6 4 2 0 2 4 6 8 10R e al d i f f e r e n c e ( d a y s ) - 8 - 6 - 4 - 2 0 + 2 + 4 + 6 + 8 + 1 0I n th i s e x a m p l e , t h e o n s e t r e a l a n d a b s o l u t e d i f f e r e n c e s r e a c h e d 0 ( p e r f e c t s y n c h r o n y ) a t t h e

f i ft h o n s e t , t h o u g h t h e c y c l e l e n g t h s o f t h e t w o s u b j e c t s r e m a i n e d c o n s t a n t . T h e r e a f t e r , th e o n -s e t d i f f e r e n c e s c o n t i n u e d t o i n c r e a s e ; h o w e v e r , i t i s n o t u n t i l t h e t e n t h o n s e t t h a t t h e o n s e t a b -s o l u t e d i f f e r e n c e ( 1 0 d a y s ) i s g r e a t e r t h a n t h e i n i t ia l o n s e t a b s o l u t e d i f f e r e n c e , a t w h i c h p o i n t n os y n c h r o n y i s in d i c at e d . T h u s , t h e p o ss i b il it y o f c h a n c e s y n c h r o n y i n a s a m p l e d e c r e a s e s o v e rs u c c e s s i v e o n s e t s . A c o r o l l a r y t o th i s c o n c l u s i o n i s t h a t E r r o r I is s e l f - c o r r e c t i n g o v e r ti m e .

N o t e t h a t th e s i g n c h a n g e a t o n s e t d i f f e r e n c e 0 o c c u r s b e c a u s e t h e c y c l e l e n g t h d i f f e r e n c eb e t w e e n o n s e t s is a d d e d t o t he i m m e d i a t e l y p r e c e d i n g o n s e t d i f f e re n c e . B e t w e e n o n s e t s 0 3 a n d0 4 , t h e s e v a l u e s h a v e d i f f e r e n t s i g n s: t h e o n s e t d i f f e r e n c e at o n s e t 0 3 i s - 4 a n d t h e d i f f e r e n c eb e t w e e n c y c l e l e n g t h s is + 2 ; t h u s , t h e o n s e t d i f f e r e n c e at o n s e t 0 4 i s - 4 + 2 = - 2 . A f t e r th eo n s e t d i f f e r e n c e r e a c h e s 0 , t h e o n s e t d i f f e r e n c e s b e g i n t o i n c r e a s e a t t h e s a m e r a t e a t w h i c h t h e yd e c r e a s e d , b u t w i t h a s i g n c h a n g e , a n d t h e o n s e t s c o n v e r t f r o m c a s e C t o c a s e B . T h i s i sb e c a u s e b e g i n n i n g w i th o n s e t 0 6 , s u b j e c t A n o w h a s b o t h t h e g r e a t e r c y c l e l e n g t h s a n d o n s e t sl a t e r t h a n t h o s e o f s u b j e c t B . I n g e n e r a l , ( 1 ) a n o n s e t d i f f e r e n c e i n c r e a s e s w h e n t h e o n s e t d i f fe r -e n c e a n d t h e c y c l e l e n g th d i f f e r e n c e b o t h h a v e t h e s a m e s i g n [ c a s e B ] a n d d e c r e a s e s w h e n t h eo n s e t d if f e r e n c e a n d t he c y c l e l e n g t h d i f f e r e n c e h a v e o p p o s i t e s i g n s [ c a s e C ] . A n i m p o r t a n te x c e p t i o n to t h e s e c o n d s t a t e m e n t o c c u r s w h e n t h e m a g n i t u d e o f t h e c y c l e l e n g t h d i f f e r e n c e is


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570 H.C. W~t~, 'm o r e t h a n t w i c e t h e m a g n i t u d e o f t h e o n s e t d i f fe r e n c e . Fo r e x a m p l e , i f t h e o n s e t d i f fe r e n c e i s-2 and the cyc le l eng th d i f fe rence to the nex t onse t i s +5 , then the onse t d i f fe rence inc reases to+ 3 . In th i s ca se , the 0 d i f fe rence i s r eached an d exce eded in a s ing le cyc le , a s ind ica ted by thechange in the s ign o f the onse t d i f fe rence . I unde rs co re th i s po in t because i t i s c ruc ia l to unde r -s t a n d i n g t he l a t er d i s c u s s i o n o f s y n c h r o n y i n g r o u p s o f s u b j e c t s.T h e s e c o n d c o n c l u s i o n t o b e d r a w n f r o m e q u a t i o n 1 is t h a t th e m a g n i t u d e o f c h a n g e i n t hed i f fe rence be twe en in i t i a l and f ina l onse t s o f sub jec t s i s i r r e levan t , s ince i t is a p roduc t o f thed i f f e re n c e b e t w e e n t h e m e a n c y c l e l e n g t h s o f t h e s u b j ec t s a n d t h e n u m b e r o f c y c l e s o v e r w h i c ho n s e t d i f fe r e n c e s a re m e a s u r e d , n e i t h e r o f w h i c h a r e n e c e s s a r i l y r e l a t ed t o m e n s t r u a l s y n c h r o n y .Fu r t he r , in c a s e s o f d e c r e a s i n g o n s e t d i f f e r e n c e s , t h e m a g n i t u d e o f c h a n g e b e t w e e n t h e i n it i aland f ina l onse t abso lu te d i f fe rences i s l imi ted by the m agn i tude o f the in i t ia l onse t abso lu te d i f -fe rence . The re fo re , the in i t i a l and f ina l onse t abso lu te d i f fe renc es a re co r re la ted ; the l a rge r thei n i t ia l o n s e t d i f f e r e n c e , t h e g r e a t e r t h e p o s s i b l e d e c r e a s e i n t h e m a g n i t u d e o f t h e d i f f e r e n c ebe tw een the in i t i a l and f ina l onse t d i f fe rences . I t fo l low s , then , tha t the ca lcu la t ion o f dec reas -ing and inc reas ing d i f fe rences i s a symmetr ica l ; dec reas ing onse t d i f fe rences have a l imi t s e t byt h e m a g n i t u d e o f t h e i n i t i a l o n s e t d i f f e r e n c e , w h i l e i n c r e a s i n g o n s e t d i f f e r e n c e s h a v e n o s u c hl i m i t. T h i s a s y m m e t r y is c r it i c al i n t es t s t h at m e a s u r e b o t h t h e d i r e c t i o n a n d t h e m a g n i t u d e o fthe d i f fe rences be tw een the in i t i a l and f ina l onse t d i f fe rences , s ince the g rea te r w e igh t g iven theinc reas ing (d ive rgen t ) d i f fe rences can lead to the re ten t ion o f the nu l l hypo the s i s wh en i t shou ldbe re jec ted . 1 F ina l ly , the rea l mag n i tud e o f chan ge i s no t r eco rded fo r those pa i r s in ca se C .No te , fo r the exam ple in Tab le I , tha t the rea l mag n i tud e o f change i s 18 days ; how ever , theabso lu te d i f fe rence a t onse t 10 ind ica te s a d i f fe rence o f on ly two day s . I sugges t tha t a s ign te stind ica t ing on ly the d i rec t ion o f change i s a su f f ic ien t s ta t i s t i ca l t e s t a t th i s s tage in mens t rua ls y n c h r o n y i n v e s ti g a t io n , g iv e n t h e p ro b l e m s o f m e a s u r i n g t h e m a g n i t u d e o f c h a n g e . O v e r t h ef irs t few onse ts , the nu l l hyp oth esis is p = q --- 0 .5 , w here p and q are the pro babi l i t ies of syn-c h r o n y ( o n s e t c o n v e r g e n c e ) a n d a s y n c h r o n y ( o n s e t d i v e r g e n c e ) , r e s p e c t i v e l y . H o w e v e r , s i n c ec a s e C c a u s e s t h e n u m b e r o f a s y n c h r o n o u s p a i rs t o i n c r ea s e o v e r t i m e , t h e g e n e r a l n u l l h y p o t h e -s i s is p < q . The te s t hyp o thes i s i s p> q . The s ign te s t is the nonp a ram e t r ic equ iv a len t o f theb inomia l t e s t ; the re fo re , l eve l s o f s ign i f icance fo r pa i r s 2 5 , t h e n o r m a l a p p r o x i m a t i o n t o t h e b i n o m i a ld i s t r ibu t ion is u sed (S iege l , 1956 ) .T h e t h i r d c o n c l u s i o n t o b e d r a w n f r o m e q u a t i o n 1 i s t h a t t h e p r o b a b i l i t y o f a s t a t i s t i c a l l ys i g n i fi c a n t l e v e l o f s y n c h r o n o u s c a s e s o c c u r r i n g b y c h a n c e i s r e la t e d d i r e c t l y t o t h e l e n g t h o ft h e s t u d y p e r i o d a n d t h e s a m p l e s i ze . A n o b s e r v a t i o n p e r i o d o f t h r e e o r f o u r c y c l e s d o es n o ta l l o w s u f f i c ie n t t i m e f o r t h e c o n v e r g i n g o n s e t s o f c a s e C t o c o n v e r t t o t h e d i v e r g i n g o n s e t s o fcase B . And , the sma l le r the samp le s ize , the g rea te r the p rob ab i l i ty o f f ind ing synch ron y byc h a n c e . M c C l i n t o c k ( 1 9 8 3 b , p . 1 31 ) s ta t e d t h a t s y n c h r o n y o c c u r s i n 6 9 - 8 3 % o f th e p a i rs o fs u b j ec t s in s t u d i e s o f m e n s t r u a l s y n c h r o n y . T h e r e f o r e , a c h a n c e o c c u r r e n c e o f a t le a s t 8 0% s y n -c h r o n o u s c a s e s i n s a m p l e s o f 5 p a ir s i s p - - 0 . 1 9 a n d o f 1 0 p ai r s i s p =0 . 0 5 5 , a b o v e t h e u s u a l l yaccep ted 0 .05 leve l o f s ta t i s ti ca l s ign i f icance .T h e p r o b a b i l i t y o f c o m m i t t i n g E r r o r I is r e d u c e d b y u s i n g l a rg e s a m p l e s o f p a ir s a n d b yreco rd ing the onse t d i f fe rences ove r a long enou gh pe r iod so the pa ir s tha t a re in i t i a l ly conve rg -i n g b y c h a n c e h a v e t i m e t o c o n v e r t t o d i v e r g i n g o n s e t s. I s u g g e s t a s a r u le o f t h u m b , i f t hes a m p l e s i ze i s 2 0 p a ir s o r l e s s , t h e n t h e o b s e r v a t i o n p e r i o d s h o u l d c o v e r a m i n i m u m o f n i n ecyc le s (10 onse t s ). F ina l ly , the s ign te st , wh ich cons id e rs on ly the d i rec t ion o f change be tw eenI See Ja re tt (1984) for a possibl e soluUon to this problem.


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MENSTRUAL SYNCHRONY RESEARCH 571i n i t i a l a n d f i n a l m e a n o n s e t d i f f e r e n c e s , i s a m o r e a p p r o p r i a t e t e s t t h a n t h o s e t h a t c o n s i d e r t h em a g n i t u d e o f th e c h a n g e . T h e m a g n i t u d e o f c h a n g e b e t w e e n i n i ti a l a n d f i n a l o n s e t d i f f e r e n c e si s i r r e l e v a n t , s i n c e i t is d e t e r m i n e d b y t h e i n i ti a l o n s e t d i f f e r e n c e , t h e d i f f e r e n c e b e t w e e n m e a nc y c l e l e n g th s o f p a i r s o f s u b je c t s , a n d t h e n u m b e r o f c y c l e s o v e r w h i c h o n s e t s a r e r e c o r d e d .E r r o r H

E r r o r I I o c c u r s w h e n t h e a b s o l u t e d i f f e r e n c e b e t w e e n t h e i n it i al m e n s e s o n s e t d a t e s o f a p a i ro f s u b j ec t s is i n c o r r e c t l y d e t e r m i n e d . T h i s e r r o r in t r o d u c e s a b i a s i n t w o w a y s . F i r s t, th e i n c o r -r e c t o n s e t d i f f e r e n c e a l w a y s i s g r e a t e r th a n t h e c o r r e c t o n s e t d i f f e r e n c e , t h u s i n c r e a s i n g t h ei n it ia l m e a n o n s e t a b s o l u t e d i f f e r e n c e . S e c o n d , a n i n c o r r e c t i n it i al o n s e t d i f f e r e n c e r e v e r s e s th ed i r e c ti o n o f c h a n g e b e t w e e n t h e c o n s e c u t i v e o n s e t d i f f e r e n c e s o f a p a ir , a s d e f i n e d b y e q u a -t io n 1 , c a s e s B a n d C . T h i s o c c u r s b e c a u s e c o r r e c t i n g a n o n s e t d i f f e r e n c e c h a n g e s t h e o r d e r o fi n it ia l o n s e ts ; t h e s u b j e c t w i t h t h e f i rs t ( e a rl i e s t) r e c o r d e d o n s e t h a s t h e s e c o n d ( l a te s t ) r e c o r d e do n s e t a f t e r t h e c o r r e c t i o n .

A l l m e n s t r u a l s y n c h r o n y r e s e a r c h h a s a s t a r t i n g d a t e ( d a y 1 ) t h a t e s t a b l i s h e s a c a l e n d a r o fc o n s e c u t i v e d a y s f o r r e c o r d i n g m e n s e s o n s e t s o f th e s u b j e c ts . T h i s s t a r t i n g d a te s o m e t i m e s s e p -a r a te s t h e o n s e t s o f a p a ir o f s u b j e c ts i n s u c h a m a n n e r t h a t t h e a b s o l u t e d i f f e r e n c e b e t w e e n t h ef ir s t r e c o r d e d o n s e t s i s g r e a t e r th a n t h e a b s o l u t e d i f f e r e n c e b e t w e e n t h e f ir s t r e c o r d e d o n s e t o fo n e s u b j e c t a n d t h e u n r e c o r d e d o n s e t o f th e s e c o n d s u b j e c t t h a t o c c u r r e d b e f o r e d a y 1 . F o re x a m p l e , l e t s u b j e c t A h a v e a m e a n c y c l e l e n g th o f 3 0 d a y s a n d a n o n s e t 2 6 d a y s b e f o r e d a y 1 ,l e t s u b j e c t B h a v e a m e a n c y c l e l e n g t h o f 2 8 d a y s a n d a n o n s e t 4 d a y s b e f o r e d a y 1 , a n di n d i c a te t h e o n s e t a n d th e o n s e t d a t e s i m m e d i a t e l y p r e c e d i n g d a y 1 b y m i n u s s i g n s . T h e s e t w oo n s e t s w o u l d n o t b e r e c o r d e d i n a n a c t u a l st u d y . T a b l e I I s h o w s s u b j e c t s A a n d B ' s u n r e c o r d e do n s e t s b e f o r e d a y 1 a n d t h e f i rs t f o u r r e c o r d e d o n s e t s a f t e r d a y 1 :

T A B L E II. O N S E T S F O R S U B J EC T S A A N D B

OnsetsM e a nS u b j e c t C yd e L eng th - 01 01 02 03 04A 30 -26 4 34 64 94B 28 - 4 24 52 80 108

I n c o ~ e ~ o n s e t a b s o l u ~ d i f f e r e n c e ( d a y s ) 2 2 2 0 1 8 1 6 1 4C o r r e ~ o n s e t a b s o l u ~ d i f f e r e n c e ( d a y s ) 8 1 0 1 2 1 4T h e a b s o l u t e d i f f e r e n c e b e t w e e n t h e f i r s t r e c o r d e d o n s e t s o f s u b j e c t s A a n d B a f t e r d a y 1 is

2 0 d a y s . H o w e v e r , th e a b s o l u te d i f f e r e n c e b e t w e e n s u b j e c t B ' s o n s e t b e f o r e d a y 1 a n d s u b -j e c t A ' s f ir s t o n s e t a f t e r d a y 1 i s o n l y 8 d a y s . T h u s , t h e 2 0 d a y s d i f f e r e n c e b e t w e e n t h e f i r str e c o r d e d o n s e t s is n o t th e l e a s t a b s o l u t e d i f f e r e n c e b e t w e e n t h e o n s e t s o f t h e t w o s u b j e c t s . T h em e t h o d f o r c a l c u l a t in g t h e l e a s t i n it ia l o n s e t a b s o l u t e d i f f e r e n c e f o r a p a i r o f s u b j e c ts is t oc o m p a r e t h e f i rs t r e c o r d e d o n s e t d a t e o f s u b j e c t A t o t h e f i rs t a n d s e c o n d r e c o r d e d o n s e t d a t e s o fs u b j e c t B , t h e n t o c o m p a r e t h e f ir s t r e c o r d e d o n s e t d a t e o f s u b j e c t B t o th e s e c o n d r e c o r d e do n s e t d a te o f s u b j e c t A . T h e l e a s t o f t h e s e t h r e e v a l u e s i s t h e c o r r e c t o n s e t a b s o l u t e d i f f e r e n c eb e t w e e n t h e s u b j e c t s ' i n i t ia l o n s e t d a t e s . F o r t h e a b o v e e x a m p l e , 1 4- 241 = 2 0, 1 6 -5 21 = 46 a n d124 - 341 =10 , and t he c o r r ec t i n i t i a l o nse t ab so lu t e d i f fe renc e i s 10 day s a t t he f i r s t onse t . Th i sc o r r e c t i o n c h a n g e s t h e i n i ti a l o n s e t o f s u b j e c t A f r o m d a y 4 t o d a y 3 4 . H e r e a f t e r , t h e o n s e t d i f-f e r e n c e is d e t e r m i n e d b e t w e e n r e c o r d e d o n s e t n fo r s u b je c t B a n d r e c o r d e d o n s e t n + l f o r


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572 H . C . W z t. 5oh 's u b j e c t A . T h i s c h a n g e a l s o r e v e r s e s t h e o r d e r o f o n s e t d i f f e r e n c e s , a c c o r d i n g t o e q u a t i o n 1,f r o m c a s e C t o c a s e B ; t h e i n c o r r e c t d i f f e r e n c e s a r e d e c r e a s i n g a t t h e r a t e o f t w o d a y s p e r c y c l e ,w h i l e t h e c o r r e c t o n s e t d i f f e r e n c e s a re i n c r e a s i n g a t t h e r a t e o f t w o d a y s p e r c y c l e .

T h e m a x i m u m a b s o lu t e d i f f e r e n c e b e t w e e n i n it ia l o n s e t s i s o n e - h a l f t he c y c l e l e n g th o f th es u b j e c t w i t h t h e e a r l i e s t o n s e t , s i n c e t h e o n s e t o f t h e s u b j e c t w i t h t h e l a t e s t o n s e t s m u s t f a l lb e t w e e n e i t h e r th e f i r st a n d s e c o n d o n s e t s o r s e c o n d a n d t h i r d o n s e t s o f t h e o t h e r s u b j e c t. I n th ee x a m p l e a b o v e , s u b j e c t A h a s t h e e a r l i e s t r e c o r d e d o n s e t a t d a y 4 a n d a c y c l e l e n g t h o f 3 0 d a y sb e t w e e n b o t h o n s e t s 0 1 a n d 0 2 a n d o n s e t s 0 2 a n d 0 3 ; t h e r e f o r e , t h e f i rs t o n s e t o f s u b j e c t B m u s tb e w i t h i n 1 5 d a y s o f t h e fi rs t o r s e c o n d o n s e t o f s u b j e c t A . T h e 2 0 - d a y d i f f e r e n c e b e t w e e n t h ef ir st t w o r e c o r d e d o n s e t s i s g r e a t e r t h a n 1 5 d a y s a n d i n d i c a te s a n e r r o r i n t h e c a l c u l a t i o n o f t hec l o s e s t i n i t i a l o n s e t a b s o l u t e d i f f e r e n c e . A n e x c e p t i o n t o t h i s r u l e i s w h e n t h e d i f f e r e n c eb e t w e e n t h e i n i ti a l o n s e ts o f th e t w o s u b j e c t s i s g r e a t e r t h a n o n e a n d o n e - h a l f t i m e s t h e c y c l el e n g th o f t h e s u b j e c t w i t h t h e f i r st (e a r l i e st ) r e c o r d e d o n s e t . I n t h e e x a m p l e a b o v e , s u b j e c t B ' so n s e t w o u l d h a v e t o o c c u r a t d a y 5 4 , i . e ., 5 0 d a y s a f t e r t h e f i r s t o n s e t o f s u b j e c t A , i n o r d e r t oh a v e a c o r r e c t e d o n s e t d i f f e r e n c e o f 2 0 d a y s . T h i s o c c u r s i n sa m p l e s w i t h s u b j e c t s h a v i n gi r r e g u la r c y c l e s o r a m e n o r r h e a . T h e m i n i m u m i n it ia l o n s e t d i f f e r e n c e b e t w e e n a p a i r o fsub j ec t s i s ze ro , s i nce bo th sub j ec t s can have t he i r f i r s t onse t s on t he same day .

A n e s t i m a t e o f t h e r a n g e o f v a r i a ti o n f o r t h e i n i ti a l o n s e t a b s o l u t e d i f f e r e n c e i n a s a m p l e o fp a i r e d s u b je c t s i s z e r o t o o n e - h a l f t h e m e a n c y c l e l e n g th o f s u b j e c ts i n t h e s a m p l e . E r r o r s i n t h ec a l c u l a t i o n o f t h e c l o s e s t i n i t i a l o n s e t a b s o l u t e d i f f e r e n c e o c c u r i n a b o u t 2 2 % o f t h e p a i r s i n as a m p l e , i f th e i n i t ia l o n s e t d i f f e r e n c e i s c a l c u l a te d f r o m o n l y t h e f i rs t r e c o r d e d o n s e t s o f b o t hs u b je c ts . T h e n u m b e r o f p o s si b le o n s e t d i f f e re n c e s g r e a te r t h an o n e - h a l f t h e m e a n c y c l e l e ng t his c a l c u l a t e d b y f ir s t d e t e r m i n i n g t h e n u m b e r o f p o s s i b l e o n s e t d i f f e r e n c e s f o r a sa m p l e . F o r as a m p l e w i t h a m e a n c y c l e o f l e n g t h X s , t h e n u m b e r o f p o s s i b l e o n s e t d i f f e r e n c e s i s ~s 2. T h en u m b e r o f p o s s i b l e o n s e t d i f f e r e n c e s g r e a t e r t h a n o n e - h a l f t h e m e a n c y c l e l e n g th is[ (x s /2 - 11 (x s /2 ) ] .2 Fo r exam ple , i f t he sam p le m ean cyc l e l eng th i s 28 days , t he t o t a l poss ib l en u m b e r o f o n s e t d i f f e r e n c e s i s 282 = 78 4; th e n u m b e r o f o n s e t d i f f e r e n c e s g r e a t e r t h a n 1 4 d a y s i s13 x 14 =182 ; and t he pe r cen t age o f onse t d i f fe r ence s t ha t exce ed 14 days i s (182 /784) x 100 =23.2"/,.T h e e x p e c t e d f r e q u e n c i e s o f o n s e t d i f f e r e n c e s g r e a te r t h a n Y s/2 f o r m e a n c y c l e l e n g th s f r o m2 6 - 3 2 cla ys r a ng e f r o m 2 1 . 4 0 - 2 3 . 4 4 % .

M c C l i n t o c k p e r c e i v e d a p r o b l e m i n c a lc u l a t i n g th e i n i ti a l o n s e t d i f f e r e n c e . H e r c o r r e c t i o n ist o c a l c u l a te " t h e d i f f e r e n c e b e t w e e n t h e d a te o f o n s e t i n O c t o b e r f o r o n e a r b i t r a r i l y c h o s e nm e m b e r o f t he p a i r a n d t h e c l o s e s t d a te o f o n s e t f o r t h e o t h e r . . . " ( M c C l i n to c k , 1 9 7 1, p . 2 4 4 )H e r m e t h o d c o r r e c t s 5 0 % o f t h e e r r o r s , s i n c e s h e d o e s n o t c o m p a r e t h e f ir s t o n s e t o f t h e o t h e rs u b j e c t t o th e s e c o n d o n s e t o f th e a r b i t r a r il y c h o s e n s u b j e c t . I n th e a b o v e e x a m p l e , h e r m e t h o dw o u l d n o t h a v e c o m p a r e d s u b j e c t B ' s f i rs t o n s e t t o s u b j e c t A ' s s e c o n d o n s e t . T h u s , e r r o r s o c c u ri n a b o u t 1 1 % o f t h e p a i r s i n a s a m p l e i f o n l y M c C l i n t o c k ' s c o r r e c t i o n i s a p p li e d .

T h e e s t i m a t e d i n it ia l m e a n o n s e t d i f f e r e n c e f o r a s a m p l e , a f t e r a l l in i ti a l o n s e t d i f f e r e n c e sh a v e b e e n c o r r e c t e d , is o n e - f o u r t h t h e s a m p l e m e a n c y c l e l e n g t h . 3 A n i n i ti a l m e a n o n s e t d i f fe r -e n c e g r e a t e r t h a n t h e e s t i m a t e d i n i t ia l m e a n o n s e t d i f f e r e n c e i n d ic a t e s p r o b a b l e e r r o r s i n c a l c u -

2 T h e t o t a l n u m b e r o f p o s s i b le o n s e t s f o r sa m p l e m e a n c y cl e le n g t h o f X s i s t h e n u m b e r o f p e r m u t a U o n s o f X st a k e n t w o a t a t i m e , ( X s" 1)(X s). p l u s a n a d d i t i o n a l s e r i e s o f o n s e t d i f f e r e n c e s X s f o r o n s e t d i f f e r e n c e s o f 0 ,{(I, I), (2.2), (3.3)... (Xs , X s)} , s i n c e b o t h o n s e t s a l s o c a n o c c u r o n t h e s a m e d a y . T h e r e f o r e . ( X s " 1)(X s) + X s +X sL T h e n u m b e r o f p e r m u t a t i o n s g r e a t e r t h a n o n e - h a l f t h e s a m p l e m e a n c y cl e l e n g t h i s X s / 2 t ak e n t w o a t at im e . T h e m e a n c y c le le n g t h i s r o u n d e d t o t h e n e a r e s t w h o l e n u m b e r f o r e a s e o f c a l c u l a t i o n , a n d i f X s i s a no d d n u m b e r , X s / 2 i s r o u n d e d t o th e n e x t h i g h e s t w h o l e n u m b e r , s i n c e o n s e t d i f f er e n c e s a r e r e c o r d e d o n l y i nw h o le n u m b e r s .


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ME'~$TRUAL SYNCHRONY RESEARCH 573l a t io n s o f s o m e i n i t i a l o n s e t d i f f e r e n c e s , o r a s a m p l e w i t h s u b j e c ts w h o h a v e i r r e g u la r c y c l e s o ra m e n o r r h e a , o r b o th .

I a g a i n u s e t h e r o o m m a t e s s a m p l e ( s u b j e c t s, 9 2 , p a i rs , 5 9 , s i n c e s o m e o f t h e s u b j e c ts h a dm o r e t h a n o n e r o o m m a t e ) f r o m t h e s o r o r i t y s t u d y t o i l l u s t r a t e E r r o r I I ( W i l s o n e t a l . , 1991).T h e s u b j e c t s in t h i s s a m p l e h a d 3 5 6 c y c l e s o v e r th e 1 5 0 - d a y s t u d y p e r i o d . T h e m e a n c y c l el e n g t h w a s 3 0 . 6 2 + 9 . 4 8 d a y s , o r a p p r o x i m a t e l y 3 1 d a y s . T h e r e s u l t s ar e a s f o l l o w s :

(a ) The expec ted mean in i t i a l onse t d i f fe rence i s 7 .75 days (31 /4 ) ; the obse rved mean in i t i a lonse t d i f fe rence i s 7 .03 d ays .

( b ) T h e e x p e c t e d n u m b e r o f c a s e s i n w h i c h t h e f i rs t re c o r d e d o n s e t d a t e s y i e l d e d i n c o r r e c tin i t ia l onse t d i f fe rences is 12 .9 (21 .86% ) . The ob se rved nu m ber o f inco r rec t in i t ia l onse t d i ffe r -ences i s 14 (23 .73% ) .

( c ) T h e e x p e c t e d n u m b e r o f i n i t i a l o n s e t d i f f e r e n c e s c o r r e c t e d b y t h e m e t h o d d e s c r i b e d b yM c C l i n t o c k i s 6 . 4 (1 0 . 9 3 % ) . T h e o b s e r v e d n u m b e r o f c a s e s c o r r e c t e d b y Mc C l i n t o c k ' s m e t h o dis 6 (10 .17%).

( d ) T h e e x p e c t e d n u m b e r o f a d d i t i o n a l i n i t i a l o n s e t d i f f e r e n c e s c o r r e c t e d b y t h e m e t h o dd e s c r ib e d a b o v e a l s o i s 6. 4 ( 1 0 .9 3 % ) . T h e o b s e r v e d n u m b e r i s 8 ( 1 3 .5 6 % ) .T h e s o r o r i t y r o o m m a t e s s a m p l e f it s t h e e x p e c t e d v a l u e s v e r y c l o s e ly . H o w e v e r , a f t e r a l l t h eco r rec t ions fo r in i t i a l onse t d i f fe rences a re made , th ree onse t d i f fe rences in the sample s t i l l ex -c e e d e d t h e e x p e c t e d m a x i m u m v a l u e o f 1 5 .5 d a y s . T h e s e i n i ti a l o n s e t d i f f e r e n c e s w e r e 1 7 , 2 0 ,a n d 3 2 d a y s . T h e s e c a s e s a l l o c c u r r e d b e c a u s e o n e o r b o t h s u b j e c ts h a d c y c l e le n g t h s t h a t e x -c e e d e d t h e s a m p l e m e a n c y c l e l e n g t h , e. g . , th e i n i t ia l o n s e t o f o n e s u b j e c t o c c u r r e d o n d a y 4 9 i none pa i r and on day 66 in a second pai r . I unde rsco re tha t these cases occu r on ly in samples wi ths u b je c ts w h o h a v e u n u s u a l l y l o n g c y c l e l e n g t h s o r a m e n o r r h e a , l i k e t h o s e i n t h e s o r o r i ty s a m p l e .

T h e e r r o r s f r o m E r r o r I I , l i k e th e o c c u r r e n c e s o f c a se s B a n d C o f e q u a t i o n 1 , a r e c h a n c ee v e n t s w i t h o u t p r e d i c t a b le d i r e c t i o n a n d m a y i n c r e a s e o r d e c r e a s e t h e n u m b e r o f s y n c h r o n o u sc a s e s i n a s a m p l e . E r r o r I I c a n b e a v o i d e d b y t h e m e t h o d f o r c a l c u l a t i n g t h e i n i ti a l o n s e ta b s o l u t e d i f f e re n c e d e s c r i b e d a b o v e . A n o t h e r p r o c e d u r e f o r c o r r e c t i n g i n i t i a l o n s e t d i f f e r e n c esi n e x p e r i m e n t a l s a m p l e s i s d e s c r i b e d b e l o w i n th e r e v i e w o f P r e ti e t a l . (1986) .E r r o r I I I

E r r o r I II o c c u r s w h e n s u b j e c t s a re e x c l u d e d f r o m s a m p l e s o r w h e n t h e o n s e t s o f s o m es u b j e ct s a re e x c l u d e d i n t h e c a l c u l a t i o n s o f fi n a l o n s e t a b s o l u t e d i f f e r e n c e s . B o t h e x c l u s i o n sb i as s a m p l e s t o w a r d s h o w i n g m e n s t r u a l s y n c h r o n y b y r e d u c i n g d i s p e r s i o n i n f in a l o n s e tabso lu te d i f fe rences .Su b j e c t s a r e e x c l u d e d f r o m s a m p l e s b e c a u s e t h e y ( 1 ) l e a v e t h e s a m p l e a s i t w a s i n i t i a l l yd e f in e d , (2 ) v o l u n t a r i l y w i t h d r a w f r o m t h e s a m p l e , o r ( 3) f a i l to h a v e t h e n u m b e r o f o n s et ss p e c i fi e d b y t h e r e s e a rc h d e s i g n . Su b j e c t s w h o l e a v e s a m p l e s , e . g . , w h o w i t h d r a w f r o m c o l l e g eo r m o v e t o a n o t h e r d o r m i t o r y , a re s e l e c t e d r a n d o m l y a n d h a v e n o c o n s i s t e n t e f fe c t o n t e s t s f o rm e n s t r u a l s y n c h r o n y . S u b j e c t s w h o v o l u n t a r i l y w i t h d r a w f r o m s a m p l e s c r e a te a b i as t o w a r ds y n c h r o n y i f t h e y a r e e x p e r i e n c i n g i r re g u l a r c y c l e s o r a m e n o r r h e a . A n e c d o t a l i n f o r m a t i o n f r o mt h e s o r o r i ty a n d c o o p e r a t i v e h o u s e s t u d i es s u g g e s t t h i s p o s s i b i li t y ( W i l s o n e t a l . , 1991). A fe ws u b j ec t s e x p r e s s e d t h e i r c o n c e r n s t h a t t h e i r i r re g u l a r c y c l e s m i g h t a d v e r s e l y i n f l u e n c e o u r s t u d y .N o n e o f o u r p a r ti c i p a n t s v o l u n t a r i l y w i t h d r e w . V o l u n t a r y w i t h d r a w a l s w e r e r e p o r t e d b y R u s s e l l3Th|s method of estlmating the correct initial m ean onset absolute differenceappears in a letter fromDr. Richard W halen to Dr. David Quadagno in 1982 (see note 4). It first appeared in print, to m y knowledge,in a n a rticle by PreU et al . (1986).


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574 H .C . W~LSO~e t a l . ( 1 9 8 0 ) , P f a f f ( 1 9 8 0 ), a n d J a r e t t (1 9 8 4 ) , b u t n o f o l l o w - u p s t u d y w a s m a d e t o d e t e r m i n ew h y t h e s u b j e c t s w i t h d r e w .

T h e m o s t f r e q u e n t r e a s o n s u b j e c t s o r o n s e t s o f s u b j e c t s a r e e x c l u d e d f r o m s a m p l e s i s t h a tthe sub jec t s f a i l to have the number o f onse t s spec i f ied by the re sea rch des ign ; thus , the in i t i a la n d f i n a l o n s e t a b s o l u t e d i f fe r e n c e s c a n n o t b e c o m p a r e d o v e r t h e s a m e n u m b e r o f c o n s e c ut i v ec y c l e s f o r b o t h s u b j e c ts . T h i s u s u a l l y o c c u r s b e c a u s e s o m e s u b j e c t s h a v e i r r e g u l a r c y c le s o ra m e n o r r h e a . H o w e v e r , c y c l e ir r e g u l a ri t y a n d a m e n o r r h e a m a y n o t b e e v i d e n t i f t h e i n v e s ti g a t o rreco rds on ly a se t number o f onse t s , o r i f a l l o f the reco rded onse t s a re no t u sed in ca lcu la t ingf inal onse t a bso lu te d i f fe rences .Th is b ia s i s i l lu s t ra ted by the so ro r i ty roommates sample (Wi lson e t a l . , 1991). Th e obser-v a t io n p e r io d w a s 1 50 d a y s f r o m S e p t e m b e r 1 t o J a n u a r y 2 8 . W e e x p e c t e d t h a t th e 9 2 s u b j ec t swou ld have f ive onse t s , w i th an in i t i a l onse t in Sep tember and a f ina l onse t in Janua ry . Morethan one -ha l f (n = 50 ) d id have f ive onse t s . Ho wev er , the o the r 42 sub jec t s h ad e i the r l e ss thanf iv e o n s e t s ( n =3 0 ) o r m o r e t h a n f i v e o n s e t s ( n = 1 2) . T h e r a n g e o f o n s e t f r e q u e n c i e s i n t h es a m p l e w a s f r o m t w o t o s e v e n . I n o u r s t u d y w e d e m o n s t r a t e d t he e f f e c t s o f e x c l u d i n g s u b j ec t sw i t h i r r e g u la r c y c l e s b y e l i m i n a t i n g t h o s e p a i r s o f s u b j e ct s h a v i n g t h e m o s t e x t r e m e v a r i at i o n inme an cyc le l eng ths . W hen a l l 59 pa i r s a re in the samp le , the f ina l m ean onse t abso lu te d i ffe r -ence i s 14 .95 days g rea te r than the in i t i a l mean onse t abso lu te d i f fe rence . In the man ipu la teds a m p l e , w h e n t h e r e r e m a i n o n l y t h o s e 2 6 p a i rs i n w h i c h b o t h s u b j e ct s h a v e m e a n c y c l e l e n g th sin th e r a n g e 2 4 . 6 - 3 2 . 5 d a y s , t h e f in a l m e a n o n s e t a b s o l u t e d i f f e r e n c e is o n l y 0 . 7 2 d a y s g r e a t e rt h a n t h e i n i ti a l m e a n o n s e t a b s o l u t e d i f f e r e n c e , a r e d u c t i o n o f 1 4 .2 3 d a y s i n t h e f i n a l o n s e tabso lu te d i f fe rence .

E r r o r I I I is a n i m p o r t a n t s o u r c e o f b i a s i n m e n s t r u a l s y n c h r o n y r e s e a r c h o n l y t o t h e e x t e n ttha t cyc le i r r eg u la r i ty and onse t va r iab i l i ty occu r in samples . I no ted in the in t roduc t ion tha tcyc le i r r egu la r i ty i s the on ly kno wn fac to r tha t d i f fe ren t ia te s those s tud ie s tha t f a i l to f ind men-s t ru a l s y n c h r o n y f r o m t h o s e t h a t r e p o rt e d m e n s t r u a l s y n c h r o n y . M y a r g u m e n t i s th a t c y c lei r r e g u la r i t y a n d a m e n o r r h e a a r e c h a r a c t e r i s ti c o f c o l l e g e - a g e w o m e n . T h i s a r g u m e n t is s u p-p o r t e d b y c r o s s - s e c t io n a l , l o n g i t u d i n a l , a n d c l in i c a l s tu d i e s o f m e n s t r u a l c y c l e s a m o n g w o m e na g e s 1 7 - 2 2 y r . C o l l e t t e t a l . (1954) repo r ted tha t the wides t r ange in mens t rua l cyc le l eng th i si n a g e s 1 7 - 2 4 a n d 4 0 - 5 0 i n a c r o s s -s e c t io n a l s a m p l e o f 1 4 6 w o m e n . T w o o f t h e m o s t c om p r e -hens ive repo r t s o f long i tud ina l s tud ie s o f mens t rua l cyc le h i s to r ie s a re Tre loa r e t a l . (1967) andVol lman (1977) . Tre loa r e t a l . ( 1 9 6 7 , p . 1 2 4 ) , re p o r t in g a s t u d y o f 2 ,7 0 2 w o m e n w i t h a l m o s t276 ,000 reco rded cyc le s , no te the g rea te s t va r iab i l i ty in mens t rua l cyc le in te rva l s i s be fo re age21 and a f te r age 39 : "T he f i r s t f ew y ea rs o f m ens t rua l l i f e , like the la s t few, a re ma rked usua l lyby a va r ia t ion pa t te rn o f mix ed sho r t and long in te rva l s wi th a cha rac te r i s t i c t r ans i t ion in to ando u t o f t h e r e l a ti v e l y m o r e r e g u l a r p a t t e m s o f m i d d l e l i f e . " A n d V o l l m a n ( 1 9 7 7 , p . 5 5 ), b a s e d o nh is s t u d y o f o v e r 3 1 , 0 0 0 c y c l e s r e c o r d e d b y 6 5 6 w o m e n , s t a t ed : " Sh o r t ( _ 4 1 d a y s ) m e n s t r u a l c y c l e s a r e m o r e p r e v a l e n t i n a d o l e s c e n t a n d c l i m a c t e r i c w o m e n . "A d o l e s c e n t s a r e in th e c h r o n o l o g i c a l a g e g r o u p 1 1 - 2 2 y r . V o l l m a n ( 1 97 7 , p p . 5 5 - 6 8 ) f o u n dh i s o b s e r v a ti o n s t o b e i n a g r e e m e n t w i t h t h o s e o f T r e lo a r e t a l . (1967) and o the r long i tud ina la n d c r o s s - s e c t i o n a l s t u d i e s o f v a r i a t i o n s i n m e n s t r u a l c y c l e l e n g t h b y c h r o n o l o g i c a l a ge .Fu r t he r , i rr e g u l a r c y c l e s a re a s s o c i a t e d w i t h s u p p r e s s e d o v a r i a n f u n c t i o n ; u n d e r g r a d u a t e w o m e nh a v e h i g h e r f r e q u e n c i e s o f a n o v u l a t o r y c y c l e s ( C o l l e t t e t a l . , 1954 ; D or ing , 1969) and low ers a l i v ar y p r o g e s t e r o n e p r o f i le s c o m p a r e d t o m o r e m a t u r e w o m e n ( E l l i s o n e t a l . , 1987) . Thesec o m b i n e d d a t a c l e a r l y i n d i c a t e t h a t h i g h f r e q u e n c i e s o f i r r e g u l a r c y c l e s a n d a m e n o r r h e a a r ee x p e c t e d in s a m p l e s d r a w n f r o m c o l l e g e - a g e w o m e n .F r e q u e n c i e s o f ir r e g u l a r c y c l e s i n c o l l e g e - a g e w o m e n a r e m o r e p r o b l e m a t i c , s i n c e f r e-


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MENSTRUAL SYNCHRONY RESEARCH 575quenc i e s va r y w i t h r e s ea r ch ob j ec t i ves , s am pl e s e l ec t i on , pe r cen t age o f s ub j ec t s t ak i ng o r a lcont racept ives , methods for da ta col l ec t ion , and l ength of observat ion per iod . Frequencies ofcom b i ned o li gom enor r hea and am enor r hea va r y f r om 10 .6% o f 900 w om en v i s it ing a s t uden theal th center (Singh, 1981) to 13 .9% of 991 col l ege w om en (1 7- 23 yr ) r esponding to a ques -t ionnai re (Bachm ann & Kem ma nn, 1982) . Frequ encies of cycle ir r egulari ty var i ed f rom 28.2%i n a s am p l e o f 211 s t uden t nu r s es w ho had m ens t r ua l c e s s a t i on pe r i ods o f 6 w k t o 12 m o(McC ormick , 1975) to 31 .4% in a samp le of 2 ,349 w om en regi s ter ing a t Edinburgh Univer s i tywh o repor ted they had " fa i r ly ir r egular cycles" (21 .0%) o r "ext rem ely i r r egular cycles" (10 .4%)(Sheldrake & Cormack , 1976) .

The observat ion per iods in the s tudies r epor t ing mens t rual synchrony in pa i r s of subjec t sr anged f r om 4 - 6 m o . A com par ab l e obs e r va ti on pe r iod i s the 150 days f o r t he 92 s ub j ec ts inthe soror i ty roommates sample (Wi l son e t a l . , 1991) . Usin g Sing h's (1 981, p. 300 ) def ini tions,24 s ub j ec t s ( 26 . 1% ) expe r i enced a t l ea s t one pe r i od o f o l i gom enor r hea ( m ens t r ua l i n t e r va l sbe t w een 38 days and 3 t oo ) o r s econda r y am enor r hea ( ces s a t i on o f m ens t r ua t i on f o r a t l ea s t3 mo ) . The m ean cy cle length of these 24 sub jec t s was 51 .7 d ays . In addi t ion , there were 11subjec t s in the room ma tes sam ple wi th cycle l engths _


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57 6 H .C . W~t.SONRE VIEW S O F ME N STRU A L SY N CH RO N Y E XPE RIME N TS A N D STU D IE S

I n t h i s s e c t i o n I w i l l r e v i e w t h e e x p e r i m e n t s o f R u s s e l l e t a l . ( 1 9 8 0 ) a n d P r e t i e t a l . ( 1 9 8 6 )a n d t he s t u d ie s o f Q u a d a g n o e t a l . ( 1 9 8 1 ) , G r a h a m a n d M c G r e w ( 1 9 8 0 ) , a n d M c C l i n t o c k(1969 , 1971 ) . A l l repo r t ed f i nd ing s t a t i s t ica l l y s i gn i f i can t m ens t rua l sync h ron y . I w i l l desc r ibet h e e x p e r i m e n t s a n d s t u d i e s , d i s c u s s w h e r e e r r o r s m i g h t h a v e o c c u r r e d , a n d s h o w h o w t h e s ee r r o r s m i g h t h a v e i n f l u e n c e d t h e i r r e s u lt s .R u s s e l l e t a l . ( 1 9 8 0 )

T h e s e i n v e s t i g a t o r s r e p o r t e d m e n s t r u a l s y n c h r o n y i n a s a m p l e o f f i v e s u b j e c t s t r e a t e d o nt h e i r u p p e r l ip t h r e e ti m e s a w e e k w i t h a s o l u t io n c o n t a i n i n g a l c o h o l a n d t h e u n d e r a r m o d o ro b t a in e d f r o m a d o n o r s u b j e c t. T h e d o n o r " h a d a h i s to r y o f a v e r y r e g u la r m e n s t r u a l c y c l e o f2 8 d a y s " a n d o f " d r i v i n g " t h e m e n s t r u a l c y c l e s o f w o m e n w i th w h o m s h e a s s o ci a te d ( R u s s e ll e ta l . , 1 9 8 0 , p. 7 3 7 ) . F o u r o f t h e s u b j e c ts s y n c h r o n i z e d w i t h t h e d o n o r ' s o n s e t s o v e r a p e r i o d o ff i ve o n s e t s ( f o u r c y c l e s ) . T h e i n i ti a l m e a n o n s e t a b s o l u t e d i f f e r e n c e b e t w e e n t h e f i v e s u b j e c tsa n d th e d o n o r w a s 9 . 3 d a y s , a n d t h e f i n a l m e a n o n s e t a b s o l u t e d i f f e r e n c e w a s 3 .4 d a y s .A n a l y s i s o f v a r i a n c e f o r r e p e a t e d m e a s u r e s s h o w e d t h e p r o b a b i l i t y o f th i s d i f f e r e n c e b e i n g d u et o c h a n c e i s p < 0 . 0 1 . A c o n t r o l s a m p l e o f s i x s u b je c t s t r e a te d o n l y w i t h a n a l c o h o l s o l u t io n d i dn o t s y n c h r o n i z e ; t h e i n it ia l a n d f i n a l m e a n o n s e t a b s o l u t e d i f f e r e n c e s w e r e 8 . 0 a n d 9 . 2 d a y s .

E r r o r I : A c c o r d i n g t o e q u a t i o n 1 , t h e p r o b a b i l i t y is t h a t c a s e s B w i t h i n c r e a s i n g o n s e t d if f e r -e n c e s a r e e q u a l t o c a s e s C w i t h d e c r e a s i n g o n s e t d i f f e r e n c e s o v e r th e f i rs t f e w o n s e t s . T h e r e a ref o u r s y n c h r o n o u s c a s e s i n t h is s a m p l e o f f iv e c a s e s o b s e r v e d o v e r f o u r c y c l e s . A s i g n t e sts h o w s f o u r o r f iv e p o s i t i v e r e s u l t s a r e e x p e c t e d t o o c c u r b y c h a n c e a b o u t 1 9 t i m e s o u t o f 1 0 0( p = 0 . 1 8 8 ) . M e n s t r u a l s y n c h r o n y is n o t d e m o n s t r a te d i n th is s a m p l e , s i n ce t h e c h a n c e p ro b a -b i l it y o f s y n c h r o n y i s g r e a t e r t h a n t h e u s u a l l y a c c e p t e d s i g n i f ic a n c e l e v e l o f 0 . 0 5 .

E r r g r II : T h e e x p e c t e d m a x i m u m r a n g e o f v a r ia t io n b e t w e e n t h e o n s e t s o f th e s u b j ec t s a n dt h o s e o f t h e d o n o r i s 0 - 1 4 d a y s , a n d t h e e x p e c t e d i n i ti a l m e a n o n s e t a b s o l u t e d i f f e r e n c e i s7 . 0 d a y s . T h i s i s s o b e c a u s e t h e d o n o r h a d a c o n s t a n t c y c l e o f 2 8 d a y s , a n d i n a ll c a s e s t h e f ir s to n s e t o f t h e d o n o r p r e c e d e d t h e f i r st o n s e t o f t h e s u b j e c t s ( R u s s e l l, p e r s o n a l c o m m u n i c a t i o n ) .T h e a c t u a l i n i t ia l m e a n o n s e t a b s o l u t e d i f f e r e n c e o f 9. 3 d a y s i s 2 .3 d a y s g r e a t e r t h a n t h e e x -p e c t e d m e a n . I n s p e c t i o n o f F ig . 1 in R u s s e l l e t a l . ( 1 9 8 0 , p . 7 3 8 ) s h o w s t h e i n i t i a l m e a n o n s e ta b s o l u t e d i f f e r e n c e is n o t a f f e c t e d b y a n y s u b j e c t ' s h a v i n g a n i n i ti a l o n s e t g r e a t e r t h a n o n e a n do n e - h a l f t h e le n g t h o f t he d o n o r ' s c y c l e ( > 4 2 d a y s ). F u r t h e r m o r e , n o c o r r e c t i o n w a s m a d e f o rin i t i a l onse t d i f fe rences ; t he i n i t i a l onse t ab so lu t e d i f fe rence w as ca l cu l a t ed a s t he d i f fe rence i nd a y s f r o m t h e t i m e o f th e d o n o r ' s f i r s t o n s e t ( t h e b e g i n n i n g o f t h e a p p l i c a ti o n s ) t o t h e f i r st o n s e to f t h e s u b j e c t s f o l l o w i n g t h e f ir s t a p p l i c a t i o n ( R u s s e l l , p e r s o n a l c o m m u n i c a t i o n ) . I t f o l l o w s ,

T A B L E I I I . ONSETSF O R T H E D O N O R A N D A S EL EC T ED S U B JE C T

SubjectOnsets

01 02 03 04 05 06A (Dono r) 1 29 57B (Subject) 17 42 63

Incorre c t d i fferenc e I6 13 6Co rrect d i fference 12 15 22

85 113 [141 ]86 113I 027 28


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MENSTRUALSYNCHRONYRESEARCH 577t h e r e f o r e , t h a t a t l e a s t o n e o f t h e f i v e i n i t i a l o n s e t d i f f e r e n c e s ( 2 2 % ) i s p r o b a b l y i n c o r r e c t .F i g u r e 1 o f R u s s e l l e t a l . ( 1 9 8 0 ) s h o w s a n i n i t ia l o n s e t d i f f e r e n c e b e t w e e n t h e d o n o r a n d a s u b -j e c t o f 1 6 d a y s . T h i s o n l y c o u l d o c c u r i f t h a t i n it i a l o n s e t a b s o l u t e d i f f e re n c e w a s i n c o r r e c tl yc a l c u la t e d . I c o n s t r u c t e d a c a l e n d a r f o r th e o n s e t d a te s f o r t h e d o n o r a n d s u b j e c ts b a s e d o n t h ei n f o r m a t i o n t h a t th e d o n o r h a d a 2 8 - d a y c y c l e l e n g t h , h e r o n s e t a l w a y s o c c u r r e d f ir s t, a n d t h ed i f f e re n c e s b e t w e e n t h e d o n o r ' s a n d s u b j e c t s ' c o n s e c u t i v e o n s e t s s h o w n i n F i g u r e 1 o f R u s s e l le t a l . ( 1 9 8 0 ) . T h e f i rs t o n s e t o f t h e d o n o r i s r e c o r d e d a s d a y 1 o f t h e e x p e r i m e n t . T a b l e I I Is h o w s t h e c a l e n d a r f o r t h e s u b j e c t w h o s e i n i t i a l o n s e t a b s o l u t e d i f f e r e n c e w i t h t h e d o n o r w a s1 6 d a y s . B o t h t h e i n c o r r e c t a n d c o r r e c t e d o n s e t d i f fe r e n c e s o v e r c o n s e c u t i v e o n s e t s ar e s h o w n .

T h e c o r r e c t i n i t ia l o n s e t a b s o l u t e d i f f e r e n c e is 1 2 d a y s , t h e d i f f e r e n c e b e t w e e n d o n o r ' ssecond onse t and the su b jec t ' s f i r st onse t (29 - 17~ 12 ). A s ix th onse t fo r the don or i s add ed inb racke t s so tha t the onse t s can be ca lcu la ted fo r fou r cyc le s . Cor rec t ing the in i t i a l onse t d i f fe r -e n c e r e v e r se s t h e d i r e c t i o n f r o m d e c r e a s i n g o n s e t s t o i n c re a s i n g o n s e t s o v e r ti m e . R a t h e r t h a n af ina l onse t d i f fe renc e o f 0 days a t ons e t 05 fo r do nor and sub jec t , the f ina l onse t d i f fe rence is 28days (141 - 11a -28 ) . W i th the co r rec ted in i t i a l onse t d i f fe rence o f 12 days an d the co r rec ted f ina lo n s e t d i f f e r en c e o f 2 8 d a y s , t h e i n i t i a l m e a n o n s e t a b s o l u t e d i f f e r e n c e f o r t h e s a m p l e i s 8 .5 d a y sa n d t h e f i n a l m e a n o n s e t a b s o l u t e d i f f e r e n c e is 9 . 0 d a y s . T h u s , t h e e x p e r i m e n t a l s a m p l e i n d i-c a t es s y n c h r o n y d i d n o t o c c u r.

E r r o r I I I: T h e 1 6 s u b j e c t s w h o v o l u n t e e r e d f o r th e e x p e r i m e n t w e r e d i v i d e d e q u a l l yb e t w e e n t h e e x p e r i m e n t a l g r o u p w h o r e c e i v e d t h e d o n o r ' s o d o r a n d t h e c o n t r o l g r o u p .H o w e v e r , " [ b ] e c a u s e o f s u b j e c t a t t ri t io n t h e f i n a l n u m b e r o f s u b j e c ts w a s e l e v e n , w i t h f i v e int h e e x p e r i m e n t a l g r o u p a n d s i x i n t h e c o n t r o l g r o u p . " ( R u s s e l l e t a l . , 1 9 8 0 , p. 7 3 7 ) T h er e a so n s f o r t h r ee s u b j e c t s w i t h d r a w i n g f r o m t h e e x p e r i m e n t a r e u n k n o w n ( R u s s e ll p e r s o n a lc o m m u n i c a t i o n ) . D o t y ( 1 9 8 1 ) p o i n t e d o u t t h a t t h e e x p e r i m e n t d i d n o t u s e a d o u b l e - b li n d p r o -c e d u r e : T h e i n v e s t i g a t o r w h o a p p l i e d t h e a p p l i c a t i o n s w a s t h e d o n o r o f t h e a x i l l a r y e x t r a c t .S h e k n e w w h i c h o f t h e s u b j e c ts w e r e e x p e c t e d t o s y n c h r o n i z e w i t h t h e a p p l ic a t i o n s o f th ee x t r a ct , a n d , n o m a t t e r h o w s u b t l y a n d u n i n t e n d e d , c o u l d h a v e s i g n a l e d h e r e x p e c t a ti o n t o th es u b j ec t s d u r i n g th e t h r e e w e e k l y t r e a t m e n t s . Su b j e c t s w h o p e r c e i v e t h e y f a i l to m e e t t h e e x p e c -t a t io n s o f t h e r e s e a rc h g o a l s m a y b e m o r e l i k e l y t o v o l u n t a r i l y w i t h d r a w f r o m a p ro j e c t. I f so ,w i t h d r a w a l f r o m t h is s m a l l s a m p l e o f o n e o r m o r e s u b j e c t s w h o f a i l e d t o s y n c h r o n i z e w i t h th ed o n o r ' s a p p l i c a ti o n s c o u l d h a v e b i a s e d t h e e x p e r i m e n t t o w a r d f i n d i n g s y n c h r o n y b y r e d u c i n gd ispe rs ion a t the f ina l ons e t d i f fe rence .

I n s u m m a r y , t he e x p e r i m e n t o f R u s s e l l e t a l . ( 1 9 8 0 ) s h o w s e v i d e n c e o f a l l t h r e e er ro r s : T h en u m b e r o f s y n c h r o n o u s c a s e s i s t o o f e w t o b e s t a t i s ti c a l ly s i g n i f ic a n t (E r r o r I ) , o n e o f t h e f o u rs y n c h r o n o u s c a s e s h a s a n i n c o r r e c t i n i t i a l o n s e t d i f f e r e n c e w h i c h , w h e n c o r r e c t e d , c a u s e s t h ei n i ti a l m e a n o n s e t d i f f e r e n c e t o b e g r e a t e r t h a n t h e f i n a l m e a n o n s e t d i f f e r e n c e ( E r r o r I I) , a n do n e o r m o r e s u b je c ts m a y h a v e w i t h d r a w n f r o m t h e e x p e r i m e n t b e ca u s e t h e i r c y cl e b e h a v io rwas no t m ee t in g the expec ta t io ns o f the inves t iga to r s (Er ro r 11 I). I conc lu de tha t Russe l l e t a l .( 1 9 80 ) d i d n o t d e m o n s t r a t e m e n s t r u a l s y n c h r o n y i n s u b j e c ts t r e a t e d w i t h a x i l l a r y e x t ra c t f r o m af e m a l e d o n o r .P r e t i e t a l. ( 1 9 8 6 )T h e e x p e r i m e n t o f P r e t i e t a l . ( 1 9 8 6 ) i s p a t t e r n e d a f t e r t h a t o f R u s s e l l e t a l . (1980) . I hav ew r i t t e n a c r i t ic a l r e v i e w o f th i s e x p e r i m e n t e l s e w h e r e ( W i l s o n , 1 9 8 7 ) . I r e v i e w t h e e x p e r i m e n th e r e t o s h o w t h e i m p r o v e m e n t s i n r e s e ar c h d e s i g n o v e r t h a t o f R u s s e l l e t a l . , a d i f f e r e n t m e t h o df o r c o r r e c ti n g f o r t h e i n i ti a l o n s e t d i f f e r e n c e s, a m e t h o d o f r e d u c i n g t h e c a s e s o f m e n s t r u a li r regu la r i ty , and how a p rocedu ra l e r ro r can be the sou rce o f E r ro r I I . The 19 sub jec t s in th i s


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57 8 H .C . WIL.-C~Ne x p e r i m e n t w e r e s e l e c t e d f r o m a l a r g e r s a m p l e o n t h e b a s i s o f r e p o r t i n g t h e y h a d r e g u l a r m e n -s t r ua l c y c l e s i n th e r a n g e o f 2 9 . 5 + 3 d a y s . T h e 1 0 s u b j e c t s i n t h e e x p e r i m e n t s a m p l e h a d as o l u t io n o f a l c o h o l a n d a x i l l a r y e x t r a c t a p p l i e d t o th e u p p e r l ip t h r e e t i m e s a w e e k . T h e a x i l la r ye x t ra c t c a m e f r o m p a d s w o r n b y f o u r w o m e n d u r i n g t h r e e c o m p l e t e m e n s t r u a l c y c le s . E x t ra c tf r o m 5 o f t h e s e 1 2 c y c l e s w a s c o m b i n e d i n t o 1 0 e x t r a c t c o m p o s i t e s c o o r d i n a t e d t o c o n f o r m t od a y s 2, 5, 8, 1 1 , 14 , 1 7 , 2 0 , 2 3 , 2 6 , a n d 2 9 o f a 2 9 + 2 - d a y m e n s t r u a l c y c l e . T h e r e s e a r c h d e s ig ns p e c i f i e d t h e e x t r a c t b e a p p l i e d i n 2 2 - t o 2 5 - d a y c y c l e s . E i g h t o f t h e s u b j e c t s s y n c h r o n i z e dw i t h t h e a p p l i c a t io n c y c l e s a f t e r th r e e o n s e t s ( t w o m e n s t r u a l c y c l e s ) , a n d t h e i n it i al m e a n o n s e ta b s o l u t e d i f f e r e n c e o f 8 .3 d a y s d e c r e a s e d t o a f i na l m e a n o n s e t a b s o l u t e d i f f e r e n c e o f 3 .9 d a y s .A n a n a l y s i s o f v a r ia n c e w i t h r e p e a t e d m e a s u r e s s h o w e d t h e p r o b a b i l i ty o f a 4 . 4 - d a y r e d u c t i o no c c u r r in g b y c h a n c e w a s p < 0 . 0 5 . O n l y t h r ee o f th e n i n e s u b je c ts i n t h e c o n t r o l s a m p l e s y n -c h r o n i z e d w i t h t h e a p p l i c a t i o n c y c l e s , a n d t h e in i t ia l m e a n o n s e t a b s o l u t e d i f f e r e n c e o f 6 . 2 2d a y s a t o n s e t 01 i n c r e a s e d t o a f i n a l m e a n a b s o l u t e d i f f e r e n c e o f 7 . 5 6 d a y s a t o n s e t 0 3 .

E r r o r I : A p p l i c a t i o n o f t h e s i g n t e s t s h o w s t h e p r o b a b i l i t y i s p = 0 . 0 5 5 t h a t b y c h a n c e e i g h to r m o r e c a s e s o u t o f te n w i l l h a v e r e d u c e d ( s y n c h r o n o u s ) o n s e t s , s l i g h t l y g r e a t e r t h a n t h eu s u a l l y a c c e p t e d l e v e l o f s i g n if i c a n c e . A l s o , t w o c y c l e s d o n o t a l l o w e n o u g h t i m e f o r c o r r e c t -i n g c h a n c e c o n v e r g e n c e a s d e f in e d b y c a s e C , e q u a t i o n 1 .

E r r o r H : P r e t i e t a l . ( 1 9 8 6 , p . 4 7 9 ) e s t i m a t e d f o r t h e i r s a m p l e s t h e r a n g e o f i n i ti a l o n s e t d if -f e r e n c e s t o b e t w e e n 0 a n d 1 4 .7 5 d a y s a n d t h e i n it ia l m e a n o n s e t a b s o l u t e d i f f e r e n c e t o b e 7 .3 8d a y s . T h e o n s e t a b s o l u t e d i f f e r e n c e s s h o w n i n t h e i r T a b l e 1 r a n g e f r o m 1 - 1 2 d a y s , an d t h ei n it ia l m e a n o n s e t d i f f e r e n c e e x c e e d e d t h e e x p e c t e d m e a n b y l e ss t h a n 1 da y . T h e i n it ia l o n s e td i f f e r e n c e s w e r e c a l c u l a t e d a s f o l l o w s : A s u b j e c t c o u l d b e g i n t h e a p p l i c a ti o n s a t a n y p h a s e o fh e r m e n s t r u a l c y c l e . I f s h e r e c e i v e d t he f i r st tr e a t m e n t d u r i n g t h e p r e o v u l a t o r y p h a s e o f h e rc y c l e , t h e i n i ti a l o n s e t d i f f e r e n c e w a s t h e n u m b e r o f d a y s b e t w e e n t h e t i m e o f t h e f i rs t t r e a t m e n ta n d t h e m e n s e s p r e c e d i n g t h e t r e a t m e n t . I f a s u b j e c t r e c e i v e d h e r f i rs t t r e a t m e n t d u r i n g t h e p o s -t o v u l a t o r y p h a s e o f h e r c y c l e , th e i n i ti a l o n s e t d i f f e r e n c e w a s t h e n u m b e r o f d a y s b e t w e e n t h et i m e o f th e f i rs t t r e a t m e n t a n d h e r m e n s e s o n s e t f o l l o w i n g t h e t r e a t m e n t . T h e p r e o v u l a t o r y a n dp o s t o v u l a t o r y c a s e s w e r e e q u a l l y d i v i d e d i n th e s a m p l e o f 1 0 s u b je c t s . T h i s p r o c e d u r e e s t a b -l is h e s a ll o f th e p r e o v u l a t o r y s u b j e c t s a s c a s e s C , a c c o r d i n g t o e q u a t i o n I . T h e o n s e t d i f f e r -e n c e s a r e i n i t ia l l y e x p e c t e d t o d e c r e a s e o v e r c o n s e c u t i v e o n s e t s , b e c a u s e t h e s u b j e c t s h a d t h ee a r l i e r o n s e t d a t e s a n d l o n g e r c y c l e s ( e x p e c t e d 2 9 . 5 + 3 d a y s ) , w h i l e t h e t r e a t m e n t d a t e s w e r el a te r a n d t h e c y c l e s ( 2 2 - 2 5 d a y s ) w e r e l e ss th a n t h o s e o f t h e s u b j e c t s . T h e p o s t o v u l a t o r ys u b j e c ts a r e a l l c a s e s B , a n d t h e o n s e t d i f f e r e n c e s a r e i n i ti a l ly e x p e c t e d t o i n c r e a s e o v e r c o n s e c -u t i v e o n s e t s b e c a u s e t h e t r e a t m e n t s , w h i c h h a d t h e s h o r t e r c y c l e , o c c u r r e d e a r l i e r t h a n t h esub j ec t s ' f i r s t onse t s .

I n s p e c t i o n o f t h e i r T a b l e 1 (P r e t i e t a l . , 1 9 8 6 , p . 4 8 0 ) s h o w s f o u r o f t h e p r e o v u l a t o r y c a s e s ,a s e x p e c t e d , h a d d e c r e a s i n g o n s e t d i f f e r e n c e s w i t h t h e t r e a tm e n t s o v e r th e t h r e e o n s e t s , a n d o n ec a s e h a d a d e c r e a s i n g o n s e t b e t w e e n o n s e t s 0 1 a n d 0 2 a n d a n i n c r e a s e b e t w e e n o n s e t s 0 2 a n d0 3 a c c o m p a n i e d b y a s i g n c h a n g e , a g a i n as e x p e c t e d . H o w e v e r , n o n e o f t h e p o s t o v u l a t o r yc a s e s s h o w e d i n c r e a s i n g c o n s e c u t i v e o n s e t s , a s e x p e c t e d f o r c a s e s B . F o u r o f t h e s e c a se ss h o w e d a d e c r e a s e i n o n s e t d i f f e r e n c e s b e t w e e n o n s e t s 0 1 a n d 0 3 , a n d t h e f i f th c a s e h a d t h es a m e v a l u e a t o n s e t s 0 1 a n d 0 3 . U s i n g t h e i n f o r m a t i o n i n t h e a u t h o r s ' T a b l e 1 , I c a l c u la t e d t hea c t u a l c y c l e l e n g t h s f o r t h e a p p l i c a t io n s ( W i l s o n , 1 9 8 7 , p p . 5 4 2 - 5 4 3 ) . T h e a p p l ic a t i o n c y c l el e n g th s b e t w e e n o n s e t s 01 a n d 0 2 r a n g e d f r o m 3 3 - 3 6 d a y s f o r t h e p o s t o v u l a t o r y c a s e s , i n s te a do f th e 2 2 - t o 2 5 - d a y c y c l e s s p e c if i e d b y t h e r e s e a r c h d e s ig n . P r e t i ( 1 9 8 7 ) c o n f i r m s m y c a l c u l a -t io n s . T h e e f f e c t o f t h e s e l o n g f i r s t a p p l i c a t io n c y c l e s i s t o c o n v e r t t h e p o s t o v u l a t o r y c a s e s f r o mc a s e s B t o c a s e s C , s i n c e n o w t h e f i rs t t r e a tm e n t s o c c u r r e d e a r l i e r t h a n t h e s u b j e c t s ' o n s e t d a t e s,


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MENSTRUAL SYNCHRONYRESEARCH 579and the mean treatment cycles were greater than the mean cycle lengths of the subjects. Whenthe treatment cycles of the postovulatory cases are corrected to a 22- to 25-day cycle length,the sample has the characteristics of a sample of randomly paired subjects (Wilson, 1987).Also, three of the subjects, who were reported to have had their cycle lengths "modulated" bythe treatments, had constant cycle lengths over the two recorded cycles.Error HI: There are no indications that subjects were excluded or withdrew from this exper-iment. A double-blind procedure ensured that the technician who applied the treatments did notknow the purpose of the study, nor which of the solutions contained the axillary extract (Preti e ta l . , 1986, pp. 477-478). Also, the subjects were selected because they reported having regularcycles, and it is probable they all had at least two cycles in the 13 week duration of the experi-ment.In summary, the number of synchronous pairs in the experimental sample of Preti e t a l .(1986) is too few, and the duration of the experiment is too short to be statistically significant(Error I). More importantly, errors in some of the applications of the axillary extract show foursubjects with decreasing onset differences over consecutive onsets. These four subjects haveincreasing onset differences when the lengths of the applications are corrected and do not syn-chronize with the treatment applications (Error II). Finally, three of the subjects said to havehad their cycles changed by the treatment applications had constant cycle lengths. This experi-ment fails to demonstrate that menstrual cycles can be altered by applications of female axiUaryextract or that the subjects ' onsets synchronized with the treatment applications.Q u a d a g n o e t a l. ( 1 9 8 1 )These investigators found menstrual synchrony in a sample of women at a coeducationalstate university. The observation period was from October-March. Tests for menstrual syn-chrony were conducted for 62 pairs of close friends, 70 pairs of roommates, and a controlsample of 70 pairs of randomly matched subjects (Quadagno, personal communication). Initialmean onset absolute differences were 21.76 days for roommates, 18.71 days for close friends,and 19.79 days for the control group. Final mean onset absolute differences are 12.34, 8.91,and 17.75 days, respectively. Student's t-test showed statistically significant levels of menstrualsynchrony for the close friends (p < 0.01) and roommates (p < 0.01), but not for the controlsample. Based on the information in Table II of Quadagno e t a l . (1981, p. 241), the estimatedmean cycle length of the subjects was 30.6 days.Error I: The number of pairs in the roommates and close friends samples was too great toexpect that synchrony might occur by chance, as defined by equation 1.Error II: The expected initial mean onset difference for the samples was 7.6 days, based onan estimated mean cycle length of 30.6 days. The initial mean onset absolute differences of18.71 days for close friends and 21.76 days for roommates are two to three times that theexpected value. Quadagno (personal communication) acknowledges these initial mean onsetabsolute differences are incorrect. 4Errgr III: Quadagno e t a l . (1981, p. 240) stated the "menstrual onsets for March werechosen to follow the initial October onset by an equal number of cycles." However, only fouronset dates were recorded for this 6-mo period: "Questionnaires were distributed twice during4 This error was first pointed o ut by Dr. Richard Whalen in a letter to Dr. David Quadag no. Dr. Qua dagno re-calculated t he initial and final mea n on set differences for his sa mpl es and found a significant level of men-strual s ynchrony (p


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580 H.C. Wlt~.,,'the academic year (October and March)... The questiormaires provided the researchers withthe following information about each woman.., day of last and second-to-last menstrualflow.. ." (Quadagno et a l . , 1981, p. 240)

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Wilson - Critical Review of Menstrual Synchrony Research