European Journal of Mathematics and Computer Science Vol. 5 No. 2, 2018 ISSN

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1 Europea Joural of Mathematc ad Computer Scece Vol. 5 o., 018 ISS APPLICATIO OF ASYMPTOTIC DISTRIBUTIO OF MA-HITEY STATISTIC TO DETERMIE THE DIFFERECE BETEE THE SYSTOLIC BLOOD PRESSURE OF ME AD OME OVER 45 YEARS OF AGE Oyedkach O. Joh johkady@yahoo.com Departmet of Phycal Scece Rhema Uverty, IGERIA & Joeph O. Ou Joephou35@yahoo.com Departmet of Stattc Aba State Polytechc, IGERIA ABSTRACT e have appled the derved aymptotc dtrbuto of the Ma-htey tattc to the ytolc blood preure of dfferet group; me ad wome, to determe f there a dfferece ther blood preure. The aaly howed there o dfferece betwee the blood preure of me ad wome at 0.05 ad 0.01 gfcace level. The ame reult wa obtaed whe Ma-htey tattc wa appled to a maller ample of the ytolc blood preure of me ad wome. Keyword: Sytolc blood preure, Ma-htey Stattc, Aymptotc dtrbuto. I. ITRODUCTIO Uder the aumpto that two group X ad Y are depedetly ad detcally dtrbuted wth dtrbuto fucto F ad G ot ecearly kow, Gurevch (009), the Ma-htey tattc broadly ued to terpret whether there are dfferece the dtrbuto of the two group or dfferece ther meda. The Ma-htey tet wa developed a a tet of tochatc equalty, Ma (1947). The aymptotc dtrbuto of Ma-htey rema of teret, ad Ferge (1994) uggeted a umber of tet ad evaluate the aymptotc gfcace level, ad compared the aymptotc power for ome of thee tet. he ormalty hold, Ma-htey tet ha a aymptotc effcecy of about 3 whe compared to t-tet, Leham (1999). The geeral cocepto that blood preure creae wth age, ad that me are more at rk for cardovacular ad real deae tha ther premeopaual wome couterpart utl after meopaue Reckelholff (001). However, accordg to Brea (1986), true ato blood preure related to may factor cludg phycal Progreve Academc Publhg, UK Page 9

2 Europea Joural of Mathematc ad Computer Scece Vol. 5 o., 018 ISS actvte, emotoal tate etc. Th paper amed at examg the ytolc blood preure of me ad wome over 45 year of age ad ue the aymptotc dtrbuto of Ma-htey tattc to determe whether there a gfcat dfferece the ytolc blood preure of the two group. II. Ma htey Stattc Let x,..., 1 x m ad y,..., 1 y be two depedet radom ample of ze m ad repectvely from two populato F ad G. The Ma htey tattc gve by 1 1 here the um of the rak of y. The ull hypothe H 0 rejected f m. III. Dervg the Aymptotc Dtrbuto of Ma htey Stattc Let the rak of y be R y. Thu R y 1 E E R y E R y But E R y Thu E Therefore R y E E m Progreve Academc Publhg, UK Page 10

3 Europea Joural of Mathematc ad Computer Scece Vol. 5 o., 018 ISS But R y R y cov R y, R y j 1 1 R y E R y E R y cov R y, R y k E R y f E R y P R y k, R y f j j j 1 1 Coder k f k1... k k k f R y k f R y k f 1 Thu 1 1 cov R y, R y R y j Uder the ull hypothe the tattc Progreve Academc Publhg, UK Page m 1 4 1

4 Europea Joural of Mathematc ad Computer Scece Vol. 5 o., 018 ISS m d m 1 0,1 1 5 The ull hypothe rejected f m m 1 C z 1 IV Applcato ad dcuo e have obtaed the ytolc blood preure of 8 wome ad 9 me aged over 45 year, ad appled Ma-htey tet o the pooled data. The tattc, 34.5 ad the crtcal value 56. The ull hypothe could ot be rejected at a gfcace level of 0.05, whch ugget that there o dfferece betwee the ytolc blood preure of me ad wome. At a gfcace level of 0.01, the crtcal value 46, gvg the ame reult. e the creaed the ample ze to 5 wome ad 6 me, ad appled the aymptotc dtrbuto of Ma-htey tattc a derved above. The aaly gve 75.5 ad C At a gfcace level of 0.05, the ull hypothe could ot be rejected, alo uggetg there o dfferece the blood preure of me ad wome. The ame reult hold at a gfcace level of 0.01 whch gve a crtcal value of Th agree wth the Ma-htey tet. Table I gve a ummary of the aaly. Table I: value of calculated tattc ad crtcal value Crtcal value Ma-htey tattc , m 8 Aymptotc dtrbuto , m 5 COCLUSIO Aymptotc dtrbuto of Ma-htey tattc a oparametrc method whch ha bee appled to the ytolc blood preure of me ad wome over the age of 45 to determe f th a dfferece ther blood preure. Baed o the data ued th work, there o gfcat dfferece betwee the ytolc blood preure of me ad Progreve Academc Publhg, UK Page 1

5 Europea Joural of Mathematc ad Computer Scece Vol. 5 o., 018 ISS that of wome at gfcace level of 0.05 ad REFERECES [1] Brea, M., E. O Bre ad K. O Malley (1986): The Effect of Age o Blood Preure ad Heart Rate Varablty Hyperteo, Joural of Hyperteo, 4(uppl 6): S6-S7 [] Ferger,D. A. (1994): O the Power of oparametrc Chage Pot-Tet, Metrka, vol. 41, pp 7-9 [3] Gurevch, G. (009): Aymptotc Dtrbuto of Ma-htey Type Stattc for oparametrc Chage Pot Problem, Computer Modellg ad ew Techologe, vol. 13, o. 3, pp 18-6 [4] Leham, E. L. (1999): Elemet of Large Sample Theory, Sprger, pp [5] Ma, H. B. ad D. R. htey (1947): O a Tet of hether Oe of Two Radom Varable Stochatcally Larger tha the Other, A. Math. Stattc, 18,pp [6] Reckelhoff, J. F. (001): Geder Dfferece the regulato of Blood Preure, PubMed, 37(5) Progreve Academc Publhg, UK Page 13