# 统计代写|抽样理论作业代写sampling theory代考|PSY279

## 统计代写|抽样理论作业代写sampling theory代考|Order or Disorder of the Units Making Up a Lot

Let us consider a set of units. Experience shows that we can look at it in two different ways:

• The whole population of these units in which, because of the definition of a population, the order of the various units is irrelevant.
• The chronological series made by these units when they are arranged following a certain pattern in which the order of the various units is highly relevant.

Many misconceptions in sampling have their origin in the confusion between a population and a chronological series. Conventional statistics ignore chronological series, and considers a lot of material essentially as a random population. The trouble is that most of the time, a lot of material is not strictly a random population, which means that neighboring fragments are not totally independent from one another. Thus, it is essential to find out if we are dealing with a population or a chronological series.
Exactly the same as homogeneity is the zero of heterogeneity, a random population is the zero of a chronological series. Furthermore, there is no risk in applying results which are valid to a chronological series to a population, while the reverse is most certainly not true.
Experience shows that perfect disorder is the exception, and order or partial order is the rule. This originates in the fact that our industrial activities are well framed in time and space, generating a correlation over time and space, and also in the fact that gravity is omnipresent, generating segregation along a vertical axis during transportation or handling of particulate materials. It is essential to remember that there is often no legitimate way to assume the absence of correlation between the characteristics of one unit and its position within the lot. This is probably a very important concept to take into account in modern astronomy.

## 统计代写|抽样理论作业代写sampling theory代考|Constitution and Distribution Heterogeneities

The two types of heterogeneity investigated in this chapter are those encountered in a zero-dimensional lot. By definition, the various units of a zero-dimensional lot form a population in which their order is nonexistent or at least considered irrelevant.

The notion of heterogeneity is somewhat confusing in the minds of many people, and there are several reasons for this:

• There are several types of heterogeneity:
• The heterogeneity consisting of a difference between the composition of the different units of a lot, such as between fragments, if we are talking about a lot of particulate material as an example. This heterogeneity is defined as the Constitution Heterogeneity $\mathrm{CH}$.
• There is another form of heterogeneity which is defined as the Distribution Heterogeneity $D H$, consisting of a difference between the spatial distribution of the different units within the lot, such as different fragments of a lot of particulate material. Their physical characteristics explain somewhat the reasons for their position. Everyone knows that this kind of spatial heterogeneity is generated because fragments have different shapes, densities, and weight, to mention only a few of their intrinsic properties.
• Most authors speaking of heterogeneity never specify the type of heterogeneity they refer to, thus creating confusion for those trying hard to understand the complex concept of heterogeneity. Not only is it essential to differentiate Constitution Heterogeneity from Distribution Heterogeneity but, furthermore, it is necessary to specify the characteristic of the unit taken into consideration:
• Example 1: A lot of pure silica is finely ground. This material is homogeneous as far as its mineral constitution is concerned, and heterogenous as far as its particle size distribution is concerned.
• Example 2: A material feeding a flotation plant and containing molybdenite, galena, chalcopyrite, and so on, is screened to obtain a well-calibrated size fraction. The material of this size fraction is homogeneous as far as its particle size distribution is concerned, but still very heterogeneous as far as its mineral composition is concerned.
• Our objective in this chapter is to clearly define and study these two important forms of heterogeneity associated with a given constituent of interest, and to link them to one another.

# 抽样理论代考

## 统计代写|抽样理论作业代写采样理论代考|组成大量的单位的顺序或无序

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• 总体:这些单元的整体，由于种群的定义，其中各个单元的顺序是不相关的。
• 由这些单元按一定的模式排列而成的时间序列，其中各个单元的顺序高度相关

## 统计代写|抽样理论作业代写采样理论代考|构成与分布异质性

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