This study aimed at constructing a criterion-reference test to measure the research and statistical competencies of graduate students at the Jordanian governmental universities, the test has to be in its first form of (50) multiple choice items, then the test was introduced to (5) arbitrators with competence in measurement and evaluation to determine the cut-off score using Angoff method amounted to (0.69), the test was applied to an experimental sample of (80) students ( males and females from the International Islamic University to check out the difficulty and discrimination coefficients of the items, based on these coefficients, (5) items have been deleted, then the test which consists of (45) items in its final form, was applied to the total sample consisting of (275) students (males and females) from the Jordanian governmental universities (University of Jordan, Al-Yarmouk, Mu'tah), the stability coefficient was estimated using Kuder-Richardson-20 coefficient (0.83) to be used in the verification of Livingston stability at the cut-off score, its value reached (0.87). The results showed that there is statistically significant differences in the degree of possession of competencies attributed to gender, also showed a statistically significant differences in the possessing of competencies attributed to scientific degree in favor of the doctorate, and there was no effect of the interaction between the two variables (sex and scientific degree) to acquire skills, and the results showed that there is a clear decline in the mastery of graduate students at Jordanian universities for research and statistical competencies, the proportion of the expert students who are over the cutoff score was (0.57).