Cross-correlation analysis of the productivity of sugar beets and factors, that it is formed

f

а=93,5

      і=1,4

by a yield

f

у

by a yield

f

у

а=38,23

і=1,98

(і=1,98)

X_і

T=|x_{i –} x_сер|_/σ

n_т=F(t)*n*i/σ

n_т

ν=L-3=5-3=2

a=0,05; 0,01; 0,001 

χ²_р=5,489

χ²_т(0,05; 2)=6,0     χ²_т(0,01; 2)=9,2        χ²_т(0,001; 2)=13,8 

     As, χ²_т> χ²_р;    6,0>5,489 a hypothesis about normality of distributing of general aggregate is not cast aside, that empiric and theoretical frequencies differ between itself insignificant.

       2.7   Selective method 

     The selective is name such supervision which gives description of all aggregate of units on the basis of research of some its part. The aggregate of mathematical facilities and grounds which use for application of selective supervision got the name of selective method.

     In statistical practice a selective supervision is applied at the study of budgets by populations, for the account of prices. Lately a selective method is widely used for the different questioning of public opinion on political, economic and commercial questions, in the advanced study at statistical treatment of results of researches.

     Distinguish general and selective aggregates. A general aggregate is a general aggregate of units, from which selected part of units. A selective aggregate is part of general aggregate which will inspect electorally.

     The task of selective supervision can be a study of the medium-sized probed sign or specific gravity of the probed sign.

     The important condition of scientific organization of selective supervision is the correct forming of selective aggregate. On the method of selection of units for a supervision distinguish such types of forming of selective aggregate:

     - repeated - if each is selected unit again goes back into a general aggregate and in future can be selected repeatedly;

     - безповторна - at which every selected unit does not go back into a general aggregate, that meets in виборці only one time.

      A безповторний selection is mainly used in statistics, as he allows to get more exact results by comparison to repeated and engulfs more units of aggregate. Separately examine such basic types of selective supervision: actually casual selection, mechanical, serial and typical selections,  combined but other

     In an order to give description of all aggregate of units, it is needed to define the possible limits of rejections of selective middle and particle from middle in a general aggregate. These rejections are named select an error.

     Middle select an error is calculated after such formulas: 

                                                              At the repeated selection 

            

 for middle -; - for a particle; 

                                     At without the repeated selection

      where δ² – dispersion of sign which varies; w – a particle of units is aggregates which has certain signs; N – number of units of general aggregate; n – number of units of selective aggregate.

      Maximum select an error: , where t – coefficient of multipleness of error (coefficient of trust). Value of t at probability 0,863 evened 1, and at probability 0,954 evened 2.

      Will apply theoretical material in practice. Will consider that given in relation to the level of the productivity - it 10% random without repeated sample. That 30 economies is a selective aggregate, then  a general aggregate makes 300 economies.  Utillizing information  of previous calculations (d² =4.8), will show it in calculations.

      Will define middle select an error for middle:  

       = =0.144c

      Will define middle select an error for a particle:

      w=3/30=0.1

       = =0.0027c 
 

      Will define maximum select an error :

      =2*0,144=0,288 c

      =2*0.0027=0.0054 c

     Middle and maximum select an error - sizes are named, they are expressed in those  units, that and mean arithmetic and middle quadratic deviation. Limits middling descriptions make in a general aggregate:

• for middle Х=  х ±∆
• for a particle Р= w ±∆

Conducting these calculations, we can with probability 0,954 (3 1000 cases 954) to assert that a level of the productivity of cereals in a general aggregate can’t be less than after 36.62c, but he will not be greater after 37.198 c (36.91±0.288).  P= 0,1±0,0054

      Organizing a selective supervision it is needed to define the quantity of selective aggregate, at what limit of possible error does not exceed some set size.

      Formulas are for the calculation of necessary quantity of selection: 

1. for middle:

• -repeated -
• without repeated -

2. for a particle:

• - repeated

• without repeated -

Will expect the quantity of selection for middle: 

Will expect the quantity of selection for a particle: 
 

 Section ІІІ. Correlation analysis of the productivity of sugar beets and factors, that it is formed 

      3.1. Grade correlation 

      Intercommunication between signs which it is possible to range, foremost on the basis of ball estimations, measured the methods of grade correlation. Name the numbers of natural row, which in obedience to the values of sign get  the elements of aggregate and definitely put in an order it, grades. Range is conducted on every sign separately: the first grade gets the least value of sign, last - to most.

      The amount of grades equals the volume of aggregate. Obviously, with the increase of volume of aggregate the degree of «recognizableness» of elements diminishes. As grade correlation does not need inhibition of any mathematical pre-conditions in relation to distributing of signs, in particular requirements of distributing normality, it is expedient to utillize the grade estimations of closeness of connection for the aggregates of small volume. 

Grades, given the elements of aggregate after signs і , mark accordingly and . Depending on the degree of connection between signs grades are definitely correlated. At direct functional connection = , that a rejection is between grades consequently, and sum of squares of rejections At a functional feed-back where — number of grades. If connection absents between signs shows by itself middle arithmetic these extreme values: . This is the maximal sum of squares of rejections of grades. Consequently, in default of connection  

     Leaning against the noted mathematical identity, K. Spirmen offered a formula for the coefficient of grade correlation:

     A coefficient of grade correlation  is the same characteristics, as well as linear coefficient of correlation: changes in limits from -1 to +1, at the same time estimates the closeness of connection and specifies on his direction.

     Will expect grade correlation and will define the crowd conditions of connection between the productivity of sugar beets, quality of soil and bringing of mineral fertilizers. 

Таблица 26. Information and calculation данні for the calculation of grade correlation

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