Sains Ma1aysiana 26(1): 53-60 (1997)                                                                           Sains Fizis dan Gunaan/

                                                                                                                                         Physical and Applied Sciences

Spektrometri Nuklear: Perbandingan Dua Kaedah

Pengiraan Ujian χ²

(Nuclear Spectrometry: Comparing two methods of

calculating the c² test)

Supian bin Samat

Jabatan Fizik

Universiti Kebangsaan Malaysia

43600 UKM Bangi Selangor D.E. Malaysia

ABSTRAK

Dari penyesuaian kedua-dua terkecil berpemberat, dua kaedah pengiraan ujian χ² diterbitkan dan dikaji. Kaedah pertama yang menggunakan pemberat purata memberikan kaedah standard yang terkenal, iaitu χ²_cal1 = (x)^-1 Σ(x-x_i)² dan kaedah kedua yang menggunnakan pemberat statistik memberikan χ²_cal2 = Σ(x)^-1 (x-x_i)² . Ditunjukkan secara teori setiap kaedah mempunyai  tersendiri, iaitu purata aritmatik untuk χ²_cal1 dan purata harmonik untuk χ²_cal2. Penggunaan teori ini kepada data nuklear ujikaji, walau bagaimanapun, menunjukkan yang kedua-dua kaedah memberikan nilai χ²_cal yang hampir sama, bebas dari jenis x yang digunakan. Pendekatan untuk menentusahkan pemberat malar bersamaan dengan (x)^-1 dalam kaedah piawai juga dibincangkan.

ABSTRACT

From the weighted least-squares fit, two methods of calculation of χ² test were derived and investigated. The first method which uses a mean weight yields the well known standard method. ie. χ²_cal1 = (x)^-1 Σ(x-x_i)² and the second method which uses the statistical weight yields χ²_cal2 = Σ(x)^-1 (x-x_i)². It is theoretically shown that each method has its own type of . ie. arithmetic mean for χ²_cal1 and harmonic mean for χ²_cal2. Application to the experimentally determined nuclear data, however showed that the two methods gave almost the same χ²_cal values, I irrespective of x used. An approach to verify that the mean weight equals to (x)^-1  in the standard method is also discussed..

RUJUKAN/REFERENCES

IAEA.. 1984. IAEA-TECDOC-311. Vienna.

Supian bin Samat & C. J. Evans. 1991. Private Communication.

Supian bin Samat & C. J. Evans. 1992. Statistics and Nuclear Counting: Theory, Prob1em and Solutions: Serdang. Universiti Pertanian Malaysia Publisher.