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Unbiased Estimation of Mean Squared Deviation in Data Matrix Analysis

Learn how to calculate the mean squared deviation of each observation in a data matrix relative to the grand mean of all observations. This unbiased estimation method is crucial for analyzing large datasets and understanding population distributions.

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Unbiased Estimation of Mean Squared Deviation in Data Matrix Analysis

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  1. is an unbiased estimate of . • Consider the following data matrix. • Note that • To obtain the mean squared deviation of each observation in the data matrix • about the grand mean of all observations, we may proceed as follows: • As N approaches infinity the distribution of all N observations in the data • matrix approaches the distribution of the population from which each • was sampled. Observation 1 2 ….. i …… n ……….M 1 X11 X21 Xi1 Xn1 M.1 2 X12 X22 Xi2 Xn2 M.2 . . . . . . . . j X1j X2j Xij Xnj M.j . . . . . . . . N X1N X2N XiN XnN M.N Sample

  2. continued

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