Currently inorganic scintillator detectors are used in all commercial Time of Flight Positron Emission Tomograph (TOF-PET) devices. The J-PET collaboration investigates a possibility of construction of a PET scanner from plastic scintillators which would allow for single bed imaging of the whole human body. This paper describes a novel method of hit-position reconstruction based on sampled signals and an example of an application of the method for a single module with a 30 cm long plastic strip, read out on both ends by Hamamatsu R4998 photomultipliers. The sampling scheme to generate a vector with samples of a PET event waveform with respect to four user-defined amplitudes is introduced. The experimental setup provides irradiation of a chosen position in the plastic scintillator strip with an annihilation gamma quanta of energy 511~keV. The statistical test for a multivariate normal (MVN) distribution of measured vectors at a given position is developed, and it is shown that signals sampled at four thresholds in a voltage domain are approximately normally distributed variables. With the presented method of a vector analysis made out of waveform samples acquired with four thresholds, we obtain a spatial resolution of about 1 cm and a timing resolution of about 80 ps
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