CN1547114A - Method for deciding significance factor using Daniel plot - Google Patents

Abstract

The invention belongs to computer application field, whose main function is for data analysis and for proposing the correspondent computer software. By using the invention, a linear and its confidence belt at two sides of the linear on the Daniel diagram, thus the prominent factor can be judged scientifically. The invention has a high accuracy. At the same time, the invention proposes the correspondent computer software.

Description

A kind of drawing with the Daniel point judged the method for significant factors

Technical field

The invention belongs to computer application field, its major function is to be used for data analysis and to propose correspondent computer software.

Background technology

It is a kind of normal probability paper figure (shown in Figure of description 1) that Daniel (Denier) point is drawn, and the horizontal ordinate on the figure is an effect value, and ordinate is the normal probability paper inverse function value of effect.The concrete steps of drawing are as follows:

1. calculate the main effect and the interaction thereof of factor.No matter whether these interaction reality exist, must all calculate;

2. effect is pressed series arrangement from small to large;

3. calculate the corresponding normal probability paper of each factorial effect, obtain the contrafunctional value of respective standard normal distribution by the standardized normal distribution table;

4. horizontal ordinate is an effect value on Daniel figure, and ordinate is the normal probability paper inverse function value of effect, and point is drawn and the corresponding point of effect.

After finishing Daniel figure, can come decision factor or its interactive conspicuousness according to the distribution situation of point.Generally, most points are gathered into straight line, and the effect corresponding with these points is considered to not remarkable, then is considered to significant with those away from the point of straight line corresponding factor or reciprocation.How on Daniel figure, to make above-mentioned straight line, just simulated straight line approx in the past, have very strong subjectivity according to each factor corresponding point on Daniel point is drawn, the shortage scientific basis, sometimes even can get the wrong sow by the ear.Up to the present, there is not judgement Daniel point to paint the report of the scientific approach of middle significant factors in the world as yet.

Summary of the invention

We develop a kind of the drawing with the Daniel point and judge the method for significant factors by research.Utilize this method, can on Daniel figure, draw the confidence belt of straight line and both sides thereof, thereby scientifically judge significant factors.Through checking repeatedly, prove that this method has very high accuracy.

The present invention is achieved in that

Asking for of 1 straight-line equation

The present invention rearranges (1 (i), i=1,2 with n factor according to the ascending order of its effect value earlier ... n), utilize following formula to calculate the probability of n factor again:

p(i)＝(i-0.5)/n，i＝1，2……n，

By looking into gaussian distribution table, obtain the standardized normal distribution inverse function value v (i) of p (i).The effect value l of factor (i) be horizontal ordinate with and corresponding v (i) be ordinate, in the drawing of Daniel point, draw out n point.Then choosing n*50%-n*100% effect value from n effect value is k effect value.K effect value is l (1), l (2) ... l (k), k≤n wherein, the contrafunctional value of Dui Ying normal probability paper is respectively u (1) with it, u (2) ... u (k) obtains following straight-line equation after the recurrence:

u＝a*l+b，

In the formula, $a=\frac{\underset{i=1}{\overset{k}{\mathrm{\Σ}}}u\left(i\right)*l\left(i\right)-\stackrel{\‾}{u}*\underset{i=1}{\overset{k}{\mathrm{\Σ}}}u\left(i\right)}{\underset{i=1}{\overset{k}{\mathrm{\Σ}}}l{\left(i\right)}^2-\stackrel{\‾}{l}*\underset{i=1}{\overset{k}{\mathrm{\Σ}}}l\left(i\right)},$

b＝ u-a* l，

$\stackrel{\‾}{u}=\underset{i=1}{\overset{k}{\mathrm{\Σ}}}u\left(i\right)/k,$

$\stackrel{\‾}{l}=\underset{i=1}{\overset{k}{\mathrm{\Σ}}}l\left(i\right)/k,$

Asking for of 2 confidence belt equations

If x is an any point, its fiducial interval is [y ₁, y ₂], then the confidence belt equation of regression straight line is:

y ₁＝a*x+t _α*ss*[(x- l) ²/xx] ^1/2+y ₁₁，

y ₂＝a*x-t _α*ss*[(x-l) ²/xx] ^1/2+y ₂₂，

T in the formula _a---level of significance α=0.025 time, the t critical value when degree of freedom is n;

$\mathrm{ss}={\left\{\right[\underset{i=1}{\overset{k}{\mathrm{\Σ}}}{(u\left(i\right)-\stackrel{\‾}{u})}^2-{\mathrm{\α}}^2*\underset{i=1}{\overset{k}{\mathrm{\Σ}}}{(l\left(i\right)-\stackrel{\‾}{l})}^2]/(n-2)\}}^{1/2},$

$\mathrm{xx}=\underset{i=1}{\overset{k}{\mathrm{\Σ}}}{(l\left(i\right)-\stackrel{\‾}{l})}^2,$

N＜100 o'clock

y ₁₁＝ u-a*l+t _α*ss*(1+1/n)，

y ₂₂＝ u-a*l-t _α*ss*(1+1/n)，

N 〉=100 o'clock

y ₁₁＝ u-a*l+t _α*ss/n，

y ₂₂＝ u-a*l-t _α*ss/n，

We draw out above-mentioned straight line and confidence belt (shown in Figure of description 2) automatically by computing machine by the software of development on Daniel figure.

3 decision methods

On new Daniel figure (shown in Figure 2 in as Figure of description), except that putting, also has the confidence belt of straight line and its both sides with effect is corresponding.The pairing effect of point in the confidence belt is considered to not remarkable.Otherwise, all points on the confidence belt boundary curve or outside the confidence belt, it is significant that pairing effect all is considered to.

The development of 4 computer softwares

We have developed correspondent computer software according to said method, and the structured flowchart of this software sees shown in the Figure of description 3 that the use process flow diagram of this software is seen shown in the Figure of description 4.

Description of drawings

Accompanying drawing 1 is that old Daniel point is drawn

The new Daniel point that accompanying drawing 2 is drawn for the inventive method is drawn

Accompanying drawing 3 is the structured flowchart according to the software that the inventive method proposed.

Accompanying drawing 4 is the use process flow diagram according to the software that the inventive method proposed

Embodiment

Below in conjunction with drawings and Examples the present invention is described in detail:

Be to use the example that old Daniel point is drawn in the accompanying drawing 1, total n=30 factorial effect value.Utilize following formula to calculate the probability of 30 factors:

p(i)＝(i-0.5)/30，i＝1，2……30，

By looking into gaussian distribution table, obtain the standardized normal distribution inverse function value v (i) of p (i), the horizontal ordinate on the figure is an effect value, ordinate is the normal probability paper inverse function value of effect.Being difficult for determining which factor by the old as can be known Daniel point drawing of accompanying drawing 1 is significant factors.

Accompanying drawing 2 is that the present invention is applied to same example in the accompanying drawing 1, and can easily determine factor X28 by the new as can be known Daniel point drawing of accompanying drawing 2 is significant factors.

Claims (2)

1, a kind of drawing with the Daniel point judged the method for significant factors, it is characterized in that will be at certain index ascending series arrangement of effect value of each factor in test, calculate the probability of n factor again, obtain the contrafunctional value of respective standard normal distribution by the standardized normal distribution table, effect value with each factor is a horizontal ordinate, the corresponding contrafunctional value of probability is an ordinate, point is painted corresponding point on the Daniel point is drawn, choose the some match straight line of factor sum 50-100%, draw confidence belt according to this straight line, be on the confidence belt boundary curve and confidence belt beyond its corresponding factor of point be exactly significant factors at this index.

2, method that draw to judge significant factors with the Daniel point according to claim 1 is characterized in that differentiating automatically the computer software of the Daniel point drawing of significant factors.

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