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Statistical properties of ion temperature gradient driven turbulence and anomalous flux are analysed in plasmas with low and improved energy confinement. The turbulence is simulated using the three dimensional fluid code, where the source is prescribed and the turbulence and temperature profile evolve self-consistently. The transition to the improved core confinement with an internal transport barrier is obtained by increasing the heating power. It is found that the momentums of the probability distribution function of flux fluctuations reduce to their Gaussian values when the transport barrier on the temperature profile forms. The formation of the oscillating structure with the properties of linear wave has been found at very high heating power.