JP2003281116A - Data processor, and method and program for data processing - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a data processor that is highly reliable compared with a conventional device, has a simple structure and capable of determining in a short time whether observation conditions affect given processes when an observer can freely determine the observation conditions. <P>SOLUTION: When events E<SB>1</SB>-ES occur f<SB>1</SB>-fS times, respectively, in the N processes carried out based on the first condition and occur g<SB>1</SB>-gS times, respectively, in the N processes carried out based on the second condition, a CPU 7 calculates data D by performing a given operation using data f<SB>1</SB>-fS and g<SB>1</SB>-gS, compares λS<SB>-1</SB>(ε) defined by χ<SP>2</SP>distribution using a specified level of significance (ε) and a degree of freedom (S-1) with the data D, and judges that the first and second conditions affect the events caused in the processes when the data D is greater than λS<SB>-1</SB>(ε). <P>COPYRIGHT: (C)2004,JPO

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a data processing device, a method thereof, and a program thereof for testing the goodness of fit of two probability distributions.

[0002]

2. Description of the Related Art S events (incidents) E ₁ , E
₂ ,. ． , E _S , when observing which one occurs, there are two conditions for observing that, the observation condition being A and the observation condition not being A (A). There is a case where it is desired to judge whether or not the difference in the observation conditions has some influence on the occurrence of the above S events. Conventionally, this determination is made as follows.
In the first method, whether or not the observation condition is A is considered as a probabilistic event, and the observation condition A and the events E ₁ , E
₂ ,. ． , E _S are independent, and a χ ² test is performed by observing the marginal distribution. In the second method, the χ ² test is performed for the variable X that follows the binomial distribution by utilizing that SIN ⁻¹ (X ^1/2 ) follows the normal distribution.

[0003]

However, in the first method described above, it is often the case that the observer can freely decide whether or not the observation condition A is not a probabilistic factor.
In this case, although the number of observations of A and A is constant as the observation conditions of both, they are treated as random variables, so that there is a problem that the reliability of the determination result is low. In addition, the above-mentioned second method involves a problem that the program becomes complicated and the processing time is long when it is executed by a computer with the operation processing of the function “SIN ⁻¹ (X ^1/2 )”. .

The present invention has been made in view of such circumstances, and in the case where the observer can freely determine the observation conditions,
To provide a data processing device, a method thereof, and a program thereof, which have higher reliability than conventional ones, and which have a simple structure and can determine whether or not an observation condition affects a predetermined process in a short time. With the goal.

[0005]

[Means for Solving the Problems]
Therefore, the data processor of the first invention is based on the first condition.
E in N steps that were performed₁ ~ E_S Is f₁ 
~ F_S Occurs N times, and the work is performed N times under the second condition.
The above E₁ ~ E_S Event of g₁ ~ G _S Reoccurs
Data f₁ ~ F_S And g₁ ~ G_S Enter
Inputting means and the input data f₁ ~ F_S and
g₁ ~ G_S By using the following equation (4)
An arithmetic means for performing the calculation of the data D and a designated significance
Χ of the level ε and the degree of freedom (S-1)² Distribution and defined by
λ_S-1 Comparing means for comparing (ε) with the data D,
As a result of the comparison, the data D is λ_S-1 Field larger than (ε)
In this case, the first condition and the second condition are
Judgment that determines that it affects the above-mentioned phenomenon
And means.

[0006]

[Equation 4]

The operation of the data processor of the first invention is as follows. Input means, data f _{1 to} f _S and g ₁
Enter ~ g _S. Next, the data D is calculated by performing the operation defined by the above equation (4) using the operation means and the input data f _{1 to} f _S and g _{1 to} g _S.
Next, the comparison means determines the designated significance level ε and the degree of freedom (S
−1) and χ ² distribution defined by λ _S-1 (ε) are compared with the data D. Next, when the data D is larger than λ _S-1 (ε) as a result of the comparison, the determining means determines that the first condition and the second condition affect the event that occurs in the step. Judge that it is giving.

In the data processing apparatus of the first invention, preferably, the second condition is not the first condition. The data processor of the first invention preferably stores χ ² distribution table data for uniquely determining the λ _S-1 (ε) from the degree of freedom (S-1) and the significance level ε. The comparing means further includes a storage means for storing the distribution table data and specifies the λ _S-1 (ε) by using the significance level ε and the degree of freedom (S-1). The data processor of the first invention is preferably λ _S-1.
Further comprising λ _S-1 (ε) calculating means for calculating (ε),
The comparison means performs the comparison using the calculated λ _S-1 (ε).

Also, in the data processing method of the second invention, the events E _{1 to} E _S occur f _{1 to} f _S times in N steps performed under the first condition, and g event of the E ₁ to E _S, respectively in the step of N times performed under the conditions
_The data f _{1 to} f _S and g ₁ when they occur _{1 to} g _S times
~ G _S input step, and the input data f
_{Using 1 to} f _S and g _{1 to} g _S to calculate the data D by performing the operation defined by the following equation (5):
The step of comparing λ _S-1 (ε) defined by the specified significance level ε and the χ ² distribution of the degree of freedom (S-1) with the data D, and the result of the comparison, the data D is λ _S-1
If it is larger than (ε), it is determined that the first condition and the second condition influence the event occurring in the step.

[0010]

[Equation 5]

The program of the third invention is data
The processing contents performed by the processing device are described, and the data processing device is described.
The device is a machine-readable program,
E in N steps carried out under the conditions of₁ ~ E_S Event of
F respectively₁ ~ F_S Occurred twice and was performed under the second condition
In the above process N times, the E₁ ~ E_S Event of g ₁ 
~ G_S Data f₁ ~ F_S And g₁ ~
g_S And the input data f₁ ~ F
_S And g₁ ~ G_S Is defined by the following equation (6)
The procedure for calculating the data D by performing the calculation
Χ between the significance level ε and the degree of freedom (S-1)² Distribution and defined by
Λ_S-1 A procedure of comparing (ε) with the data D,
As a result of the comparison, the data D is λ_S-1 Field larger than (ε)
In this case, the first condition and the second condition are
Procedure to determine that it affects the above-mentioned phenomenon
Have and.

[0012]

[Equation 6]

[0013]

DETAILED DESCRIPTION OF THE INVENTION A computer according to an embodiment of the present invention will be described below. FIG. 1 is a configuration diagram of a computer 1 of this embodiment. As shown in FIG. 1, the computer 1 includes, for example, an interface 3, an operation unit 4, a display 5, a memory 6 and a CPU (Central P
rocessing unit) 7, which are connected via a bus 2. Here, the interface 3 corresponds to the input means of the present invention, and the memory 6 corresponds to the storage means of the present invention.

The interface 3 inputs and outputs data to and from an external device of the computer 1, for example. Operation part 4
Is an operation means such as a keyboard and a mouse, and outputs an operation signal according to an operation by a user to the CPU via the bus 2.
Output to 7. The display 5 displays a screen according to the display signal from the CPU 7.

The memory 6 stores a program 21 and χ ² distribution table data 22. The program 21 is a program that describes a procedure of processing performed by the CPU 7 described later. The χ ² distribution table data 22 is, for example, as shown in FIG. 2, a degree of freedom (S−1) and a significance level ε which is a probability of a reference (probability of judging that a certain hypothesis is correct but not correct). Table data specifying λ _S-1 (ε) from and. Further, S indicates the number of events that occur in a predetermined process.

The CPU 7 operates based on the program 21 and performs the processing described later. As shown in FIG. 3, the CPU 7
Is a random variable calculation unit 11, a comparison unit 12, and a determination unit 13.
Have and. It should be noted that the CPU 7 actually operates based on the program 21, and performs processing of functions corresponding to the random variable calculation unit 11, the comparison unit 12, and the determination unit 13.

The random variable calculation unit 11 is shown in FIG.
As shown in, the E _{1 to} E _S events occur f _{1 to} f _S times in the N times of steps performed under the first condition, and N times of the N times performed under the second condition. Data f ₁ when the events E _{1 to} E _S occur g _{1 to} g _S times respectively in the process
~ F _S and g _{1 to} g _S are used to perform the operation defined by the following equation (7) to calculate the data D which is a random variable.

[0018]

[Equation 7]

In the present embodiment, for example, in a factory that manufactures a certain product, the product is classified into grades 1, 2, 3 and 4 according to its quality, and a specific chemical is used for a certain material in the manufacturing process. Check the number of product grades in two cases when they are not used, and consider whether or not the use of the chemical affects the product grade distribution. Then, when the presence or absence of the use of the chemical and the number of each grade are as shown in FIG. 4 (B), the data D is as in the following formula (8). In this case, S = 4.

[0020]

[Equation 8]

The comparison unit 12 is shown in FIG. 2 with the significance level ε input by the user via the operation unit 4 or a predetermined significance level ε and the degree of freedom (S-1) as keys. λ _S-1 (ε) is obtained by referring to the χ ² distribution table data 22. The comparing unit 12 then obtains the obtained λ _S-1 (ε).
And the data D calculated by the random variable calculation unit 11 are compared. Based on the comparison result of the comparison unit 12, the determination unit 13 determines that the first and second conditions affect the event occurring in the process when the data D is larger than λ _S-1 (ε). If not, it is determined that the first and second conditions do not affect the events that occur in the process. Specifically, the determination unit 13 uses the comparison unit 1 in the example shown in FIG.
Based on the result of the comparison of 2, it is determined that the use of the chemical influences the grade of the product when the data D is larger than λ _S-1 (ε), and if not, the use of the chemical is judged. Judge that it does not affect the grade of the product. In the example shown in FIG. 4B, the data D is "about 8.3" as shown in the above equation (8).
9235 ”, and λ _4-1 (0.05) becomes“ 7.814 ”.
73 ”, and D> λ _4-1 (0.05), so it is determined that the use of the chemical affects the grade of the product.

An operation example of the computer 1 shown in FIG. 1 will be described below. FIG. 5 is a flowchart for explaining the operation example. Step ST1: The user performs the process N times under the first condition, performs the process N times under the second condition, and the events E _{1 to} E _S occur in the process under the first condition, respectively. And how many times each of the events E _{1 to} E _S occurred in the step of the first condition, and the above-mentioned data f _{1 to} f
Collect _S and g _{1 to} g _S.

[0023] Step ST2: data f ₁ is collected in step ST1 ~f _S and g ₁ to g _S is inputted to the computer 1 through the interface 3 or the operation unit 4, for example, is stored in the memory 6.

[0024] Step ST3: random variable calculation unit 11 of the CPU7, using the data stored in the memory 6 f ₁ ~f _S and g ₁ to g _S at step ST2, the above formula (7)
The calculation shown in (1) is performed to calculate the data D.

Step ST4: Comparison unit 12 of CPU 7
Is a significant level ε input by the user through the operation unit 4, or a predetermined significant level ε and the degree of freedom (S-1) as keys, and the χ ² distribution table data 22 shown in FIG. To obtain λ _S-1 (ε).

Step ST5: The comparing section 12 obtains the obtained λ _S-1 (ε) and the random variable calculating section 11 in step ST3.
The data D calculated by is compared.

Step ST6: If the data D is larger than λ _S-1 (ε) based on the comparison result of step ST5, the decision section 13 proceeds to the process of step ST7, and if not, it returns to step ST8. Go to processing.

Step ST7: The judging section 13 judges that the first and second conditions influence the phenomenon occurring in the process, and displays a screen showing the judgment result on the display 5, for example. Step ST8: The determination unit 13 determines that the first and second conditions do not affect the phenomenon that occurs in the process, and, for example, displays a screen showing the determination result on the display 5.

As described above, according to the computer 1, the number of observations N under the first condition and the second condition is N.
When is a constant, it is treated as a constant instead of a random variable as in the conventional first method, and therefore highly reliable determination can be performed. Further, according to the computer 1, the function “SIN ⁻¹ (X
^Since it is not necessary to perform complicated calculation such as " ^1/2 )", the program 21 can be simplified and the processing time can be shortened.

The present invention is not limited to the above embodiments. For example, in the above-described embodiment, λ _S-1 is used by using the χ ² distribution table data 22 stored in the memory 6 shown in FIG.
Although the case of obtaining (ε) is illustrated, in the present invention, for example, without using the χ ² distribution table data 22, the CPU 7 may perform a predetermined calculation to calculate λ _S-1 (ε). . For example, when the degree of freedom n (= S-1) is 3, the CPU 7
Λ that satisfies the following formula (9) is calculated.

[0031]

[Equation 9]

[0032]

According to the present invention, when the observer can freely determine the observation condition, the observation condition is more reliable than the conventional one, and the observation condition is a predetermined process in a short time in a simple structure. It is possible to provide a data processing device, a method thereof, and a program thereof, which can determine whether or not the data is affected.

[Brief description of drawings]

FIG. 1 is an overall configuration diagram of a computer according to an embodiment of the present invention.

FIG. 2 is a diagram for explaining the χ ² distribution table data shown in FIG. 1.

FIG. 3 is a diagram for explaining a function of a CPU shown in FIG.

FIG. 4 is a diagram for explaining data used by the computer shown in FIG. 1 for a target process.

FIG. 5 is a diagram for explaining an operation example of the computer shown in FIG.

[Explanation of symbols]

1 ... Computer, 2 ... Bus, 3 ... Interface, 4
... Operating section, 5 ... Display, 6 ... Memory, 7 ... CP
U, 11 ... Random variable calculation part, 12 ... Comparison part, 13 ... Judgment part, 21 ... Program, 22 ... χ ² distribution table data

Claims (6)

[Claims] 1. An E process performed N times under the first condition.
₁ ~ E_S Is f₁ ~ F _S Occurrence of the second article
In the above N times of the above steps, the E₁ ~ E_S Thing
Each elephant is g₁ ~ G_S If it occurs once, Data f₁ ~ F_S And g₁ ~ G_S Input means to input
When, The input data f₁ ~ F_S And g₁ ~ G_S For
Then, the data D is calculated by performing the operation defined by the following equation (1).
Computing means for calculating Χ of the specified significance level ε and the degree of freedom (S-1)² distribution
Λ defined by_S-1(Ε) is compared with the data D
Comparison means, As a result of the comparison, the data D is λ_S-1 Field larger than (ε)
In this case, the first condition and the second condition are
Judgment that determines that it affects the above-mentioned phenomenon
A data processing device having means. [Equation 1] 2. The data processing apparatus according to claim 1, wherein the second condition is a condition that the second condition is not the first condition. 3. Further comprising a storage means for storing χ ² distribution table data for uniquely determining the λ _S-1 (ε) from the degree of freedom (S-1) and the significance level ε, the comparison The data processing device according to claim 1, wherein the means uses the significance level ε and the degree of freedom (S-1) to search the distribution table data to identify the λ _S-1 (ε). A wherein λ _S-1 (ε) further λ _S-1 (ε) calculating means for calculating, the comparing means, the comparison with the calculated λ _S-1 (ε) The data processing device according to claim 1, wherein 5. E in N steps performed under the first condition
₁ ~ E_S Is f₁ ~ F _S Occurrence of the second article
In the above N times of the above steps, the E₁ ~ E_S Thing
Each elephant is g₁ ~ G_S If it occurs once, Data f₁ ~ F_S And g₁ ~ G_S Step to enter
When, The input data f₁ ~ F_S And g₁ ~ G_S For
Then, the data D is calculated by performing the operation defined by the following equation (2).
And a step of calculating Χ between the specified significance level ε and the degree of freedom (S-1)² distribution
Λ defined by_S-1(Ε) is compared with the data D
Step, As a result of the comparison, the data D is λ_S-1 Field larger than (ε)
In this case, the first condition and the second condition are
Step that determines that it is affecting the event that occurs
And a data processing method. [Equation 2] 6. The content of processing performed by the data processing device is described.
The data processing device can be read by a machine-readable
Gram, E in N steps carried out under the first condition₁ ~ E_S Thing
Elephants are f₁ ~ F _S Occurs under the second condition
In the above N times, the above E₁ ~ E_S Of each event
g₁ ~ G_S If it occurs once, Data f₁ ~ F_S And g₁ ~ G_S And the steps to enter The input data f₁ ~ F_S And g₁ ~ G_S For
Then, the calculation defined by the following equation (3) is performed to obtain the data D
And the procedure to calculate Χ of the specified significance level ε and the degree of freedom (S-1)² distribution
Λ defined by_S-1(Ε) is compared with the data D
Procedure, As a result of the comparison, the data D is λ_S-1 Field larger than (ε)
In this case, the first condition and the second condition are
Procedure to determine that it affects the above-mentioned phenomenon
A program having and. [Equation 3]