The accurate experimental determination of nuclear reactor core physics parameters is of great importance for its safe operation. In particular, the accurate determination and prediction of criticality during the initial fuel loading of a nuclear reactor are essential for a safe nuclear reactor startup. Also, the degree of subcriticality or shutdown margin of a nuclear core with its control rods inserted is an important parameter for the operation of a nuclear reactor throughout the core operating lifetime. There are several methods utilized to determine both the criticality and the shutdown margins. All of these methods depend on measuring the response of neutron detectors and the calibration of the control rods. However, neutron detectors respond only to the neutron flux in the cor e in the vicinity of the nuclear detectors. During initial reactor core fuel loading, the reactivity of the core is determined from the multiplication of the neutrons of the startup source by the addition of nuclear fuel. Reactivity is determined from the multiplication factor by a constant which is related to the source-detector geometry in the core. In this research a method was studied which allowed the determination of reactivity independent of the source-detector geometry. Reactivity measurements of the 10 kw University of Maryland pool training reactor (UMR) were made by conventional methods and by a statistical process, the variance-to-mean ration method, and the results were compared with calculational methods. The theoretical method selected to determine the UMR core reactivity was based on the multigroup, multiregion, diffusion theory. The accuracy of the theoretical model was determined for the just critical UMR core. Agreement to within 0.2% ΔK/K was obtained between the control rod measured and the calculated reactivity for the UMR full core, and smaller UMR supercritical cores. The statistical technique of the variance-to-mean ratio of the number of counts for various counting gate openings, as a means to determine the degree of subcriticality, or shutdown margin, has been proven to be an effective method. A BF3, thermal neutron proportional detector, with a sensitivity of 12.1 counts/sec per n/cm2/sec, was placed inside of an eleven feet long aluminum tubing. The end of the tubing containing the detector was inserted in the center Glory Hole of the UMR core. The current pulses from the proportional detector was amplified and fed to a TMC 1024-channel pulse analyzer. The pulses were counted for different Δt gate openings from 10-4 seconds to 10 seconds. For each Δt gate opening, 1023 samples were taken. The printed output from the TMC-1024 was collected, giving the number of counts received per Δt, as well as the integral of all the counts received during a period of time, equal to 1023 x Δt seconds. From the integrated value for the number of counts the average count c for the gate opening Δt was obtained. The printed output was transferred to IBM cards acceptable to a "Reactor Noise" code written for the IBM-7090. This code calculated the average value, c, for each Δt (which gave a check on the validity of the data transferred to the IBM cards by comparing it with the value obtained during the measurement), the standard deviation o, and the variance-to-mean ratio for all the data taken for each Δt seconds gate opening. Plots of the values of the variance-to-mean ratio versus gate openings were obtained for several UMR full core with the rods banked at various degrees of insertion (shutdown margins), and also for various UMR subcritical cores. Measurements of the shutdown margins by the variance-to-mean technique were in agreement with the values obtained from the rod calibration for negative reactivities of less than -1. 00% ΔK/K, and within ten percent for negative reactivities of approximately -2. 0% ΔK/K. Measurements of the reactivity of small UMR cores indicated that for UMR core conditions of 0. 5% ΔK/K subcritical, experiment and theory for 1-Keff were found to be only 6 parts in 100 apart, and for 2. 0% ΔK/K subcritical, experiment and theory were found to be only 8 parts in 100 apart. The variance-to-mean technique was compared to the inverse multiplication method for determination of criticality during the UMR fuel loading, and was found to be a more accurate method, primarily, because of its independence of the source-detector geometry effects. The system utilized for the statistical data processing is exact, however cumbersome, due to the amount of data to process and the amount of peripheral hardware utilized in the reduction of the data. It appears from this study that greater overall counting efficiency for the same amount of statistical data would permit more accurate measurements at larger degrees of subcriticality, perhaps, in the region of -4. 0% ΔK / K to -5. 0% ΔK / K . A system is proposed in this study to measure negative reactivity continuously, and directly, by means of a small computer capable of accepting the output of a multichannel scaler. The computer would have a fixed internal logic capable of calculating reactivity from the variance-to-mean analysis of the neutron detector counts.