Quality & Quantity (2007) 41:905–911 © Springer 2007
Validity of the Statistical Estimation
International Society of a Statistical Science, 536 OasisDrive, Santa Rosa, CA 95407, U.S.A.
Abstract. Conventional statistical methods of the estimation of population parameters are
abstract and unreliable because these statistical methods are based on unwarranted assump-
Key words: statistical estimation, unwarranted assumptions, axiomatic statistical methods.
The analysis of relationships between statistical phenomena is one of the
primary objectives of statistical science. Validity of inferences, achieved on
the basis of such statistical relationships, depends on the quality of the
statistical information. This statistical axiom can be paraphrased as fol-
lows: statistical inferences are only as good as the data on which they are
based. Good statistical data are such data, which can authentically charac-
terize homogeneous statistical phenomena. Hence, good statistical data are
homogeneous statistical data.
The statistical estimation of population parameters is broadly used in
the analysis of relationships between statistical phenomena. This estimation
is carried out with the help of the sampling distribution method and the
Central Limit Theorem.
According to this method, the sampling distribution of generalized
statistical measures, or simply statistics (mean, proportion, standard devia-
tion, regression and correlation coefﬁcients), is normal under certain condi-
tions. The normal distribution of statistics is a condition that must be met
when standard deviations of generalized statistical measures, i.e., standard
errors of generalized statistical measures are computed. Standard errors
are employed in estimating population parameters with a certain degree of
The estimation of population parameters depends on the type of the
population. The ﬁrst type is a population that has a normal distribution.
The second type is a population that has a distribution, which is not
normal. This distribution can be homogeneous or heterogeneous.
The ﬁrst type (normal population). Random samples, selected from a nor-
mal population, can be large or small. They are used for computing