JP6828869B1 - Ability score conversion method, ability score conversion program, and ability score conversion device - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a technique for converting an ability score into a scale which is easy to understand intuitively. One of the typical ability score conversion methods of the present invention includes an acquisition step, an ability estimation step, and a scale conversion step. In the acquisition step, in the test performed on the analysis target, the result of the item of the test is acquired as a reaction pattern for the item of the analysis target. The ability estimation step estimates the ability score of the analysis target by reducing the influence of the item dependence of the test from the reaction pattern. In the scale conversion step, the ability score to be analyzed is ranked in the reference distribution (hereinafter referred to as "ability") based on the distribution determined for ranking the ability score (hereinafter referred to as "reference distribution"). Convert to an ordinal scale called "score conversion order"). [Selection diagram] Fig. 1

Description

The present invention relates to an ability score conversion method, an ability score conversion program, and an ability score conversion device.

Conventionally, as a classical test theory, a method of calculating an examinee's ability based on the "raw score (score)", "deviation value", and "raw score ranking" of an examination has been known. In this classical test theory, in a simple situation where all test takers take the same test only once, the abilities of each test taker can be compared and evaluated.

However, in regular qualification exams and mock exams, the exam questions are different each time, and the group of examinees is also different each time.

In this case, not only the difference in the ability of each examinee (specimen dependence) but also the difference in the examination questions taken at that time (item dependence) affects the raw score of the examinee.

In addition, the deviation value of the examinees is affected not only by the difference in the ability of each examinee (sample dependence) but also by the difference in the examinee group who took the examination at that time (group dependence).

Furthermore, the raw score ranking of examinees includes not only differences in the abilities of each examinee (sample dependence), but also differences due to examination questions (item dependence) and differences depending on the examinee group (group dependence). Affect.

Therefore, the ability of each examinee cannot always be accurately determined from the raw score, deviation value, and raw score ranking of the classical test theory.

In recent years, a capacity calculation method based on a new statistical model has been adopted as a test theory to solve such a problem.

For example, a new statistical model called item reaction theory estimates the parameters of item dependence (item difficulty, item discriminating power, guesswork, etc.) for each test item by pre- or simultaneous sample tests. The item reaction theory calculates the ability score of an examinee by reducing the effect of the estimated item dependence from the test result (reaction pattern) for each item of each examinee. According to the calculation of such ability, it is possible to accurately calculate the ability of each examinee without depending on the difference in the examination questions.

In addition, in Patent Document 1, "the overall correct answer rate (correct answer probability) of the examinees in the past examination is ranked and stored, and the overall correct answer rate (correct answer probability) of the individual examinees in this examination is stored in the past. The technology of "virtually calculating the ranking by applying it to the ranking of" is disclosed.

JP-A-2007-248773

By the way, in a new statistical model such as item reaction theory, there are many kinds of parameters to be handled, and complicated processing such as statistics and probability is performed. Furthermore, the numerical value of the ability score calculated is a numerical value dispersed in a positive / negative range.

Therefore, it is difficult for examinees and teachers who are accustomed to the conventional numerical values such as "raw score", "deviation value", and "raw score ranking" to intuitively understand whether the ability score is high or low. It was.

In addition, it was difficult to intuitively grasp how much learning and time was required from the "current ability score" to the "target ability score" from the abstract numerical value of the ability score.

In this way, the numerical value of the ability score is not a concrete measure, so its use is limited to some companies such as test takers and test question creators, and it is an obstacle to widespread use among examinees and teachers. It was.

In Patent Document 1, "ranking of correct answer probability" is dealt with. This "correct answer probability" is influenced by the difference (item dependence) depending on the examination question. In addition, the ranking within the group is also affected by the differences (group dependence) among the test taker groups. Therefore, the "ranking of correct answer probabilities" in Patent Document 1 does not calculate the ability of each examinee on an accurate scale.

Therefore, an object of the present invention is to provide a technique for converting an ability score into a scale that is intuitively easy to understand.

In order to solve the above problems, one of the typical ability score conversion methods of the present invention includes an acquisition step, an ability estimation step, and a scale conversion step.
In the acquisition step, in the test performed on the analysis target, the result of the item of the test is acquired as a reaction pattern for the item of the analysis target.
The ability estimation step estimates the ability score of the analysis target by reducing the influence of the item dependence of the test from the reaction pattern.
In the scale conversion step, the ability score to be analyzed is ranked in the reference distribution (hereinafter referred to as "ability") based on the distribution determined for ranking the ability score (hereinafter referred to as "reference distribution"). Convert to an ordinal scale called "score conversion order").

According to the present invention, it is possible to convert the ability score into an intuitively easy-to-understand measure called the ability score conversion order that does not depend on the difference between tests.

Issues, configurations, and effects other than those described above will be described in more detail in the description of the embodiments.

FIG. 1 is a diagram showing a configuration of an ability score conversion device. FIG. 2 is a diagram illustrating an acquisition step and an ability estimation step. FIG. 3 is a diagram illustrating an item characteristic curve. FIG. 4 is a diagram showing the likelihood Lx (θ) of the ability score θ. FIG. 5 is a diagram illustrating a scale conversion step. FIG. 6 is a diagram illustrating a probability density function and a reference distribution. FIG. 7 is a diagram illustrating the correspondence between the ability score and the ability score conversion order. FIG. 8 is a diagram illustrating the correspondence between the ability score conversion order and the sufficiency rate. FIG. 9 is a diagram illustrating the processing operation of the cost calculation step. FIG. 10 is a diagram showing a step change in the ability score conversion order when the target sufficiency rate is achieved in the order of priority. FIG. 11 is a diagram showing stepwise changes in the overall sufficiency rate when the target sufficiency rate is achieved in the order of priority. FIG. 12 is a diagram illustrating the processing operation of the simulation step. FIG. 13 is a diagram for explaining the expected result of the ability score conversion order. FIG. 14 is a diagram illustrating a supplement to the cost calculation step.

Hereinafter, examples of the present invention will be described with reference to the drawings.

It is assumed that the present invention is not limited to the academic ability test, but is widely applied to all fields in which ability is evaluated and calculated. Therefore, in the following description, terms such as "analysis target", "ability score", and "sufficiency rate" will be used instead of "examinee", "scholastic ability", and "correct answer rate", respectively.

<Structure of Example 1>
FIG. 1 is a diagram showing the configuration of the ability score conversion device 100.
In the figure, the ability score conversion device 100 includes an acquisition unit 110, an ability estimation unit 120, a scale conversion unit 130, a cost calculation unit 140, and a simulation unit 150.

The acquisition unit 110 acquires the scoring results of each item of the test for each analysis target as a reaction pattern (a group of correct / incorrect information for each question item, etc.) indicated by the analysis target for each item.

The ability estimation unit 120 estimates the ability score indicating the ability value to be analyzed by performing a process of reducing the influence of the item dependence of the test from the reaction pattern.

A distribution for ranking ability scores (hereinafter referred to as "reference distribution") is defined in the scale conversion unit 130. The scale conversion unit 130 uses, for example, as this reference distribution.
(1) Unified distribution: Distribution defined for unified ranking of ability scores (2) Partial distribution: Select and use the distribution defined for ranking within a predetermined subgroup to which the analysis target belongs. be able to.

The scale conversion unit 130 converts the ability score of the analysis target into an ordinal scale called "ability score conversion order" which is the order in the reference distribution by obtaining the position of the ability score of the analysis target in the distribution range of the reference distribution. To do.

In addition, the scale conversion unit 130 outputs processing data (for example, formula parameters, data table, graph display data, etc.) indicating the correspondence between the ability score conversion order and the sufficiency rate at which the analysis target satisfies the test items. create.

The " sufficiency rate " here corresponds to the "probability of correctly answering the test items" in the case of an academic ability test. In the case of a test such as an experiment, the sufficiency rate corresponds to "the probability that the data of the experimental items of the experimental sample (analysis target) satisfy a predetermined passing condition". In tests such as purchase inspection, the sufficiency rate corresponds to the "probability that the purchased product passes the inspection item of the purchase". In the case of a test such as a product yield inspection, the sufficiency rate corresponds to the "probability that the product yields in the inspection items".

The cost calculation unit 140 divides the rank difference between the "target rank set as a target in the reference distribution" and the "ability score conversion rank" by the "magnitude of the ability score conversion rank" based on the arithmetic processing. , Find the target achievement cost to be analyzed.

The cost calculation unit 140 obtains the target achievement cost of the analysis target for each field, and obtains the priority order of the field to be achieved based on the target achievement cost for each field.

Further, the cost calculation unit 140 converts the target achievement cost into a scale indicating actual labor such as real time required as consideration for the target achievement cost.

The simulation unit 150 obtains the time change of the ability score conversion order in a plurality of tests performed in time series. The simulation unit 150 simulates a future change in the ability score conversion order based on the obtained time change, and outputs the result.

The ability score conversion device 100 may be configured as a computer system equipped with a CPU (Central Processing Unit), a memory, or the like as hardware. By executing the ability score conversion program stored in the computer-readable medium by this hardware, the functions of each part of the above-mentioned ability score conversion device 100 are realized, and the ability score conversion method is executed by the computer system.

For some or all of this hardware, dedicated equipment, machine learning machines, DSP (Digital Signal Processor), FPGA (Field-Programmable Gate Array), GPU (Graphics Processing Unit), PLC (programmable logic), etc. It may be substituted.

In addition, even if a part or all of hardware and programs are centralized or distributed to servers on the network to configure a cloud system, a service of ability score conversion method can be provided to multiple client terminals (users). Good.

Subsequently, the step operation of each part of the ability score conversion device 100 will be described in order with reference to mathematical formula examples.

The calculation process is repeated for each n items # i (1 ≦ i ≦ n) of the test for each analysis target X (X = A, B, C ...). In order to avoid complicated explanations due to such repetition, if it is not necessary to distinguish the analysis target or the item, the distinction by the subscripts x and i may be omitted as appropriate.

<About acquisition steps>
FIG. 2 is a diagram illustrating an acquisition step and an ability estimation step.
In the figure, the acquisition unit 110 collects test results Tx (x = a, b, c ...) For each test for analysis target X (X = A, B, C ...) From a data server or the like that stores the test results. Then, it is stored in the database 210 in the acquisition unit 110. As a result of this accumulation, the results of a plurality of tests performed in time series are accumulated in the database 210.

The acquisition unit 110 extracts the scoring results (binary value of correctness, etc.) for each test item #i from the database 210 for each analysis target, and estimates the ability as the reaction pattern TFi (1 ≦ i ≦ n) for the item #i. Output to unit 120.

Further, the acquisition unit 110 applies an maximum likelihood estimation method or the like to the results of the sample test in the database 210 to estimate the item-dependent parameter par # i (1 ≦ i ≦ n) for each test item # i. .. Further, the acquisition unit 110 may acquire these parameters par # i (1 ≦ i ≦ n) from the data server for the test question pool.

The parameter par # i for each of these items includes, for example, the item discriminating power ai for each item and the item difficulty level bi. The acquisition unit 110 outputs the obtained parameter par # i to the capacity estimation unit 120.

<About the ability estimation step>
The ability estimation unit 120 creates an item characteristic function θtoPi (θ) for the i-th item # i based on the item discriminating power ai and the item difficulty bi included in the i-th parameter par # i.

FIG. 3 is a diagram illustrating an item characteristic curve of this item characteristic function θtoPi (θ).
In the figure, the horizontal axis shows the ability score θ (−∞ ≦ θ ≦ ∞), and the vertical axis shows the sufficiency rate P (0 ≦ P ≦ 1) such as the probability of correct answer.

The item characteristic function θtoPi (θ) here is a function representing the correspondence between the ability score θ as shown in the equation [Equation 1] and the satisfaction rate Pi (1 ≦ i ≦ n) of the item #i. ..

The capacity estimation unit 120 processes the maximum likelihood estimation method based on the equations [Equation 2] and [Equation 3] to obtain the reaction pattern TFi (1 ≦ i ≦ n) of the analysis target X (X = A, B, C ...). ) To reduce the influence of item dependence and estimate the ability score θx of the analysis target X.

式中のａｒｇｍａｘ｛｝は、括弧内の尤度Ｌｘ（θ）が最大となるθｘの値を求める最大点作用素である。

Argmax {} in the equation is the maximum point operator for finding the value of θx at which the likelihood Lx (θ) in parentheses is maximized.

FIG. 4 is a diagram depicting the likelihood Lx (θ) of the ability score θ in the reaction pattern {0,0,1,1} for the item characteristic curves of items # 1 to # 4 shown in FIG.

In the case of FIG. 4, the likelihood Lx (θ) becomes maximum when “θx = 0.1”. Therefore, the ability score θx of the analysis target X showing the reaction pattern {0,0,1,1} is estimated to be "0.1".

<About scale conversion steps>
FIG. 5 is a diagram illustrating a scale conversion step.
Since the ability score θx obtained by the ability estimation unit 120 is an abstract numerical value, it is difficult to understand intuitively. Therefore, the scale conversion unit 130 converts the ability score θx of the analysis target X into a specific scale called the ability score conversion order Rankx using the equation [Equation 4].

式中の能力スコア変換順位Ｒａｎｋｘは、０〜Ｎの範囲の実数値をとるが、必要に応じて整数に丸めてもよい。

The ability score conversion order Rankx in the formula takes a real value in the range of 0 to N, but may be rounded to an integer if necessary.

The total number N in the equation is a constant assumed as the total number of the analysis target X. In addition, when the ability score conversion rank is displayed as a percentage such as "top percentage", N = 100% may be set.

PDF (θ) in the equation is a probability density function of the ability score θ. A normal distribution is used as a general PDF (θ). Of course, if the probability density function of the ability score θ is known in the past statistics, the probability density function may be used.

Here, “N × PDF (θ)” corresponds to a reference distribution determined for use in ranking the ability score θ. As this reference distribution, one of the following (1) and (2) is selectively used.
(1) Unified distribution: Distribution defined for unified ranking of ability scores (2) Partial distribution: A predetermined subgroup to which the analysis target belongs (for example, a group of examinees who take an examination at XX University) ) The distribution defined for ranking

When a unified distribution is used as the reference distribution, for example, N = 10000 may be used as a large number having the required number of effective digits for the total number N and a well-cut number.

Further, when selecting a partial distribution as the reference distribution, a number of a scale assumed as a subgroup to be analyzed may be used as the total number N.

When selecting a partial distribution as the reference distribution, the probability density function PDF (θ) predicted from the past statistics on the subpopulation may be used as the probability density function PDF (θ).

FIG. 6 is a diagram illustrating the probability density function PDF (θ) and the reference distribution.
The probability density function PDF (θ) shown in FIG. 6 [A] shows a normal distribution with a mean μ = 0 and a standard deviation σ = 1 as an example.
The reference distribution shown in FIG. 6 [B] is obtained by multiplying this probability density function PDF (θ) by the total number N = 10000 as a coefficient.

The rank of the ability score θx in the reference distribution is the value obtained by accumulating the reference distribution in the integration range from the position of the ability score θx on the horizontal axis of the reference distribution to the ability score ∞ (diagonal area shown in FIG. 6 [B]). Area value of). This value corresponds to the ability score conversion order Rankx obtained by converting the ability score θx.

FIG. 7 is a diagram illustrating a correspondence relationship between the ability score θ and the ability score conversion rank Rank.
In the figure, the horizontal axis shows the ability score θ, and the vertical axis shows the ability score conversion order Rank in descending order. Here, as the probability density of the reference distribution, the normal distribution with mean μ = 0 and standard deviation σ = 1 is used (solid line curve in the figure), and the normal distribution with mean μ = 0 and standard deviation σ = 2 is used. Two examples are shown when used (dotted curve in the figure).

As shown in FIG. 7, in the scale conversion based on the reference distribution, the ability score θ and the ability score conversion rank Rank have a one-to-one correspondence. Therefore, the scale conversion unit 130 can uniquely convert the ability score conversion order Rankx of the analysis target X into the ability score θx by Rtoθ (Rank), which is an inverse function of θtoR (θ).

Further, once the ability score θx of the analysis target X is determined, the scale conversion unit 130 uses the item characteristic function θtoPi (θ) to set the ability score θx to the sufficiency rate Pi for each item #i (1 ≦ i ≦ n). Can be uniquely converted to.

Therefore, the scale conversion unit 130 uses RtoPi (Rank), which is a composite function of Rtoθ (Rank) and the item characteristic function θtoPi (θ), to change the ability score conversion order Rankx of the analysis target X to item #i (1 ≦ i ≦). It can be uniquely converted into a sufficiency rate Pi for each n).

Further, the scale conversion unit 130 can uniquely convert the satisfaction rate Pi of the item #i (1 ≦ i ≦ n) into the ability score conversion order Rankx by PitoR (Pi), which is an inverse function of RtoPi (Rank). it can.

FIG. 8 is a diagram exemplifying a comparison between the (old) item characteristic curve in the conventional item reaction theory and the (new) item characteristic curve newly introduced by the present invention.
In the figure, the left side is the (old) item characteristic curve, which shows the correspondence between the sufficiency rate and the ability score. In addition, the right side is the (new) item characteristic curve, which shows the correspondence between the ability score conversion order and the sufficiency rate.

By using the above-mentioned function RtoPi (Rank), the scale conversion unit 130 can create a "correspondence between the ability score conversion order and the sufficiency rate" which is the basis of the (new) item characteristic curve.

In the conventional (old) item characteristic curve, both the ability score (horizontal axis) and the sufficiency rate (vertical axis) are abstract numerical values that have undergone complicated processing such as statistics and probabilities. Therefore, the relationship with the test scores was complicated and difficult for students and teachers to understand.

However, with the (new) item characteristic curve, the relationship between the ability score conversion order (horizontal axis) and the sufficiency rate (vertical axis) can be intuitively understood.

<Cost calculation step>
FIG. 9 is a diagram illustrating the processing operation of the cost calculation step.
In the figure, the cost calculation unit 140 is given a target sufficiency rate Ptarget. The target sufficiency rate Ptarget may be a uniform value based on, for example, the passing score of the test. Further, the target sufficiency rate Ptarget may be set to a different value for each field by allocating passing points for each field.

By substituting this target sufficiency rate Ptarget into the above function PitoR (Pi), the cost calculation unit 140 sets the target rank Rank for each item #i (1 ≦ i ≦ n) as shown in the equation [Equation 5]. Convert to _{target (i)} .

The cost calculation unit 140 extracts a set S satisfying the condition of the equation [Equation 6] from the item #i (1 ≦ i ≦ n).

This set S is a set in which the ability score conversion rank Rankx of the analysis target X extracts the item #i lower than the target rank Rank _{target (i)} , that is, a set of unachieved items #s.

Next, the cost calculation unit 140 obtains the target achievement cost Cost (s) required by the analysis target X in order to achieve the target rank Ranktarget (s) for the unachieved item #s by the equation [Equation 7]. ..

式中の分子は、目標順位と能力コスト変換順位との順位差であって、この順位差が大きいほど目標達成コストは大きくなると想定できる。

The numerator in the formula is the rank difference between the target rank and the ability cost conversion rank, and it can be assumed that the larger the rank difference, the larger the target achievement cost.

In addition, the denominator in the formula is the current ability cost conversion order, and it can be assumed that the smaller the value of this ability cost conversion order, the higher the analysis target of the higher group must be overtaken, and the higher the target achievement cost. ..
Therefore, as shown in the equation [Equation 7], the target achievement cost can be estimated by the arithmetic process of dividing the "rank difference" by the "magnitude of the ability score conversion rank".

The cost calculation unit 140 sorts the target achievement cost Cost (s) for each field (here, by item # s that has not been achieved) according to a predetermined sorting rule (for example, in ascending order of the target achievement cost). Determine the priority of areas to be achieved (here, unachieved items #s).

When the target rank Ranktarget (s) is achieved stepwise in this priority order, the ability score conversion rank Rankx of the analysis target X changes stepwise by following the target rank Ranktarget (s) in descending order.

FIG. 10 is a diagram showing a step change in the ability score conversion order when the target satisfaction rate of the items is achieved in the order of priority.
In the figure, the horizontal axis is the “number of items (number of problems) that achieved the target sufficiency rate”, and the vertical axis is the “ability score conversion order”.
The “ideal effort cost order” in FIG. 10 is a case where the review was carried out firmly with the target sufficiency rate Ptarget = 90%. "Sufficient effort cost order" is a case where a standard review is performed with a target sufficiency rate of Ptarget = 75%. "In order of required effort cost" is a case where a simple review is performed with a target sufficiency rate of Ptarget = 50%.

Further, the cost calculation unit 140 may obtain the step change of the overall sufficiency rate of the test according to the step change of the ability score conversion order Rankx. Further, the cost calculation unit 140 may obtain the step change of the raw score of the test according to the step change of the total sufficiency rate of the test.

FIG. 11 is a diagram showing stepwise changes in the overall sufficiency rate when the target sufficiency rates of the items are achieved in order of priority.
In the figure, the horizontal axis is the “number of items (number of problems) that achieved the target sufficiency rate”, and the vertical axis is the sufficiency rate of all items. The value obtained by multiplying this overall sufficiency rate by the full score of the test corresponds to the "raw score of the test". The upper and lower dotted lines shown in FIG. 11 indicate a range that is statistically within a 95% probability.

As a real problem, the actual exam questions are evaluated based on the height of the raw score, so displaying the transition of the raw score is effective in encouraging the analysis target (in this case, the examinee) to make learning efforts in order of priority. is there.

Further, as the ability score conversion rank Rankx rises stepwise, the magnitude of the target achievement cost Cost (s) in the equation [Equation 7] also changes stepwise. Therefore, the cost calculation unit 140 may obtain the step change of the target achievement cost Cost (s) by recalculating the equation [Equation 7] according to the step change of the ability score conversion order Rankx.

<About the processing operation of the simulation step>
FIG. 12 is a diagram illustrating the processing operation of the simulation step.
In the figure, the simulation unit 150 acquires the ability score conversion ranks Rankxi and Rankxj of the analysis target X from the scale conversion unit 130 for each of the tests conducted in time series at different times ti and tj.

The simulation unit 150 calculates the rank change cost Cost _(tj-ti) spent by the analysis target X for improving the rank of (Rankxi-Rankxj) during the period (tj-ti) by the equation [Equation 8].

This rank change cost Cost _(tj-ti) is a cost value spent between tests (the period from ti to tj ₎ in the analysis target. Further, the ranking change cost Cost _(tj-ti) takes a positive value when the ranking improves with the passage of time, and takes a negative value when the ranking decreases.

Since the ranking change cost Cost _(tj-ti) was spent throughout the period (tj-ti), the cost per unit time is "Cost _(tj-ti) / (tj-ti)".

Assuming that the analysis target X will continue to spend the cost per unit time thereafter, the simulation unit 150 sets the rank change cost that can be spent in the remaining period (t _target −tj) until the target deadline t _target [Equation 9]. ] Formula.

Assuming that the analysis target X improves the ranking while allocating the ranking change cost obtained by the above equation to the target deadline t _target , the simulation unit 150 determines future changes such as the ability score conversion ranking (for example, the target deadline). The ability score conversion order Rankx _estimate ) expected for t _target is predicted as a simulation.

FIG. 13 is a diagram for explaining the expected result of the ability score conversion order.
In the figure, the horizontal axis is the date and the vertical axis is the ability score conversion order. The solid line plot is the past transition of the ability score conversion order. The dotted line is the transition forecast of the ability score displacement ranking, assuming that the latest ranking change cost Cost will continue to some extent. In the figure, as a target ranking, a boundary line indicating, for example, the 8000th place is also shown.

The analysis target (in this case, the examinee) changes the transition of the actual ability score conversion ranking up and down with respect to this transition forecast (dotted line) depending on whether the latest ranking change cost Cost is maintained or increased or decreased. Will be possible.

The cost here is also on an abstract scale, so it is difficult to understand intuitively. Therefore, the simulation unit 150 may convert this cost into a measure of actual labor. By adopting a specific measure such as the learning time spent for the cost as this actual effort, it becomes easier to intuitively understand how much actual effort is required.

The simulation unit 150 creates a correspondence table between the cost Cost and the actual labor effect based on the past statistical processing, and uses it as a conversion function of the following equation.
Effect = CtoE (Cost)
Cost = EtoC (Effort)

The simulation unit 150 uses this conversion function to convert the above-mentioned rank change cost Cost into the actual labor effect. This practical effort effect makes it possible to specifically know how much learning time is required for the analysis target X. Further, by dividing this actual labor effect by the number of days until the target deadline t _target , it becomes possible to specifically know how much learning time per day is required for the analysis target X.

The simulation unit 150 may use this actual labor effect instead of the rank change cost Cost to simulate and predict future changes such as the ability score conversion rank.

<Supplementary information on cost calculation steps>
In the cost calculation step described above, the case where the target achievement cost is obtained for each item has been described. Here, we supplement another case in which the cost of achieving the target is calculated for each test.

FIG. 14 is a diagram illustrating a supplement to the cost calculation step.
In the figure, the cost calculation unit 140 acquires the ability score conversion order Rankx0 of the analysis target X from the scale conversion unit 130 for the test at the latest time point t0.

The cost calculation unit 140 is given a target ranking Rank _target to be achieved in the target deadline t _target . This target ranking Rank _target is, for example, a ranking that ensures passing the test.

Based on the equation [Equation 10], the cost calculation unit 140 obtains the target achievement cost Cost _(target-t0) for the analysis target X to raise the rank of the ability score conversion rank Rankx0 to the target rank Rank _target .

Cost calculation unit 140, by dividing the period of this goal cost _{Cost (ttarget-t0)} Future _{(t target} -t0), goals cost per unit time _{"Cost (ttarget-t0) / (} t target -T0) "is calculated.

Further, as shown in FIG. 14, the cost calculation unit 140 spends the cost for improving the ranking of the analysis target X in the past period (t0-ti) based on the ability score conversion ranks Rankxi and Rankx0 at the time points ti and t0. Estimate Cost _(t0-ti) .

The cost calculation unit 140 divides this target achievement cost Cost _(t0-ti) by the past period (t0-ti) to obtain "Cost ₍ t0-ti)" as the cost per unit time spent by the analysis target X in the past. _"ti) / (t0-ti)" is calculated.

Here, if the target achievement cost per unit time is α times the cost per unit time of the period (t0-ti), the analysis target X takes α times the cost of the past in order to achieve the target ranking. It is possible to provide advice (display on the screen, etc.) that you should spend.

Further, the cost of the abstract numerical value may be converted into the actual labor Effort such as learning time by using the conversion function CtoE (Cost) between the cost Cost and the actual labor Effort described above. Furthermore, by dividing this actual labor effect by the number of days remaining until the target deadline t _target, it becomes possible to provide specific advice on how much learning time is required per day for the analysis target X.

Note that FIG. 14 illustrates that, on the premise that the conversion function CtoE (Cost) has linearity, it is necessary to have α times the actual labor as well as the cost.

<Effect of Example 1>
(1) In Example 1, the ability score to be analyzed is converted into a rank (ability score conversion rank) in the reference distribution of the ability score. This ability score conversion ranking is different from an abstract numerical value such as an ability score, and is a concrete evaluation scale of ranking, that is, "ranking in what position among how many people", so it is easy to understand intuitively. Therefore, in the first embodiment, the ability score can be converted into an intuitively easy-to-understand evaluation scale called the ability score conversion order.

(2) Conventional Patent Document 1 deals with "ranking of correct answer probability". This "correct answer probability" is affected by the difference in exam questions (item dependence), so it did not accurately calculate the ability of each examinee.

On the other hand, in the first embodiment, the "rank of ability score" is treated as the rank of ability score conversion. This ability score is less affected by differences in exam questions (item dependence). Therefore, in the first embodiment, the ability of each examinee can be accurately calculated by handling the ability score conversion order.

(3) In the first embodiment, "a unified distribution predetermined for the unified ranking of the ability scores" can be selected as the reference distribution as the population when obtaining the ability score conversion order. Further, in the first embodiment, “total number N × normal distribution” is specifically used as this unified distribution. Since these reference distributions are not real distributions but virtual distributions and can always be constant, there is no difference in the population to be analyzed (group dependence). Therefore, in Example 1, by selectively using the unified distribution, it becomes possible to calculate the ability of each examinee more accurately without the influence of group dependence.

(4) Further, in the first embodiment, "a partial distribution predetermined for ranking a predetermined subgroup to be analyzed" can be selected as the reference distribution as the population when obtaining the ability score conversion ranking. .. Since such a reference distribution is not a real distribution but a virtual distribution and can always be constant, there is no difference in the group to be analyzed (group dependence). Therefore, in Example 1, by selectively using the partial distribution, it is possible to more accurately calculate the ability of each examinee within a predetermined subgroup without the influence of group dependence. Become.

(5) In Example 1, the correspondence relationship between the "ability score conversion order" obtained by converting the ability score and the " sufficiency rate " in which the analysis target corresponding to the ability score satisfies the test items is generated and output. To do. (See the graph on the right side of Fig. 8)

Through this correspondence, examinees, teachers, etc. can know specifically what percentage of the correct answers (satisfaction) can be achieved in the examination if the current ability score conversion ranking is used.

In addition, this correspondence allows the examinee, the teacher, and the like to know specifically what percentage of the correct answer (satisfaction) should be in the ability score conversion order.

Furthermore, this correspondence allows students, teachers, etc. to know how many people should pass in the ability score conversion order in order to achieve the target sufficiency rate in the examination. In this case, the examinee can set an intuitive and concrete goal of excluding how many people.

(6) In the first embodiment, the rank difference between the "target rank set as a target in the reference distribution" and the "ability score conversion rank" is divided by the "magnitude of the ability score conversion rank" by an arithmetic process. , Find the cost of achieving the goal to be analyzed

In this arithmetic processing, the larger the number of overtakes (rank difference), the larger the target achievement cost. In addition, the smaller the value of the ability cost conversion order, the more it is necessary to overtake the analysis target of the higher group, and the higher the target achievement cost.
Therefore, the above-mentioned arithmetic processing of the first embodiment makes it possible to estimate a reasonable target achievement cost.

(7) In the first embodiment, the target achievement cost is converted into a value indicating actual labor such as real time required for the target achievement cost. Since the goal achievement cost is an abstract value, it is difficult to intuitively understand how much it is. Therefore, in the first embodiment, it is converted into a value indicating the actual labor such as the actual time (for example, learning time) required for the consideration of the target achievement cost. Therefore, it is possible to provide specific advice on how much actual effort is required to achieve the target achievement cost.

(8) In the first embodiment, the priority order of the fields to be achieved is obtained based on the target achievement cost obtained for each field such as items. Therefore, it is possible to provide advice to allocate the actual labor to be analyzed at an appropriate timing according to the target achievement cost for each field. In addition, when deciding the priority order in ascending order of cost, it is possible to maximize the number of fields to achieve the goal immediately after the start of the priority order. , Achievement-oriented and rational learning advice becomes possible.

(9) In Example 1, in a plurality of tests conducted in a time series, the time change of the ability score conversion order is obtained, and the future change of the ability score conversion order is obtained as a simulation based on the time change. As a result, it becomes possible to estimate how far the analysis target can raise the ability score conversion ranking by the target deadline.

<Other supplementary items>
In the above-described embodiment, the description has been made on the premise of the statistical model of the item reaction theory. However, the present invention is not limited to this. The present invention can be applied to any data set consisting of "individual ability and items for evaluating it".

Further, in the above-described embodiment, the priority order for achieving the goal is determined for each test item. However, the present invention is not limited to this. Goal achievement priorities may be determined for each desired field, such as a department or subject.

Further, as a field where the present invention is expected to be applied, there is an application to an evaluation technique in the medical field. In the medical field, it is common to evaluate various item data such as evaluation of disease risk and prognosis. Since such evaluations also undergo complicated processing of statistics and probabilities, the ability score that finally indicates the results of treatments and clinical trials becomes an abstract numerical value. Therefore, it was difficult to explain to patients and their families. However, the application of the present invention makes it possible to provide easy-to-understand explanations to patients and their families by introducing a specific measure called ability score conversion order.

The present invention is not limited to the above-described examples, and includes various modifications. For example, the above-described embodiment has been described in detail in order to explain the present invention in an easy-to-understand manner, and the present invention is not necessarily limited to the one including all the configurations and steps described. It is also possible to add / delete / replace other configurations with respect to a part of the embodiment.

100 ... Ability score conversion device, 110 ... Acquisition unit, 120 ... Ability estimation unit, 130 ... Scale conversion unit, 140 ... Cost calculation unit, 150 ... Simulation unit

Claims (9)

Ability score conversion method performed by a computer system
In the test performed on the analysis target, an acquisition step of acquiring the result of the test item as a reaction pattern for the analysis target, and
From the reaction pattern, the ability estimation step of estimating the ability score of the analysis target by reducing the influence of item dependence due to the item difficulty level and item discriminating ability of the item, and
The ability score to be analyzed is referred to as a ranking in the reference distribution (hereinafter referred to as "ability score conversion order") based on a distribution determined for ranking the ability score (hereinafter referred to as "reference distribution"). Converted to an ordinal scale, and further created based on the "correspondence relationship between the ability score conversion order and the ability score" created based on the reference distribution, the item discriminating ability of the item, and the item difficulty level. The item characteristic function indicating "the correspondence between the ability score and the probability that the analysis target satisfies the item of the test (hereinafter referred to as" satisfaction rate ")" is combined with "the ability score conversion order". It is provided with a scale conversion step for generating data of "correspondence with the sufficiency rate" .
User of the data generated the "corresponding relationship between the ability score converted ranking and the fulfillment rate" is the ability score transform, characterized in that it enables conversion between the ability score converted ranking and the fulfillment rate Method. Ability score conversion method performed by a computer system
In the test performed on the analysis target, an acquisition step of acquiring the result of the test item as a reaction pattern for the analysis target, and
From the reaction pattern, the ability estimation step of estimating the ability score of the analysis target by reducing the influence of item dependence due to the item difficulty level and item discriminating ability of the item, and
Based on the distribution determined for ranking the ability scores (hereinafter referred to as "reference distribution"), the ability score to be analyzed is ranked in the reference distribution (hereinafter referred to as "ability score conversion order"). The scale conversion step to convert to the ordinal scale,
The analysis is based on an arithmetic process in which the rank difference between the "target rank set as a target in the reference distribution" and the "ability score conversion rank" is divided by the "magnitude of the ability score conversion rank". Ability score conversion method characterized by having a cost calculation step for finding a target achievement cost. The ability score conversion method according to claim 2.
The cost calculation step uses the target achievement cost as a measure showing the actual labor such as the actual time required for the consideration of the target achievement cost based on the past statistical processing between the target achievement cost and the actual labor. Ability score conversion method characterized by conversion. The ability score conversion method according to any one of claims 2 to 3.
In the cost calculation step, for items belonging to a desired field that determines the priority order for achieving the target, the target achievement cost for the analysis target is obtained for each field, and the target achievement cost for each field is sorted by a sorting rule. Ability score conversion method characterized by finding the priority of the above-mentioned field to be achieved by the means. The ability score conversion method according to any one of claims 1 to 4.
The scale conversion step, as the reference distribution,
(1) Unified distribution: Distribution defined for unified ranking of the ability score (2) Partial distribution: Select the distribution defined for ranking in the predetermined subgroup to which the analysis target belongs. Ability score conversion method characterized by being possible. The ability score conversion method according to any one of claims 1 to 5.
It is characterized by having a simulation step in which a time change of the ability score conversion order is obtained in a plurality of tests conducted in a time series, and a future change of the ability score conversion order is obtained as a simulation based on the time change. Ability score conversion method to do. An ability score conversion program comprising causing a computer system to execute the ability score conversion method according to any one of claims 1 to 6. In a test conducted on an analysis target, an acquisition unit that acquires the results of the test items as a reaction pattern for the analysis target, and
An ability estimation unit that estimates the ability score of the analysis target by reducing the influence of item dependence due to the item difficulty level and item discriminating ability of the item from the reaction pattern.
The ability score to be analyzed is referred to as a ranking in the reference distribution (hereinafter referred to as "ability score conversion order") based on a distribution determined for ranking the ability score (hereinafter referred to as "reference distribution"). Converted to an ordinal scale, and further created based on the "correspondence relationship between the ability score conversion order and the ability score" created based on the reference distribution, the item discriminating ability of the item, and the item difficulty level. The item characteristic function indicating "the correspondence between the ability score and the probability that the analysis target satisfies the item of the test (hereinafter referred to as" satisfaction rate ")" is combined with "the ability score conversion order". It is equipped with a scale conversion unit that generates data "correspondence with the sufficiency rate" .
User of the data generated the "corresponding relationship between the ability score converted ranking and the fulfillment rate" is the ability score transform, characterized in that it enables conversion between the ability score converted ranking and the fulfillment rate apparatus. In a test conducted on an analysis target, an acquisition unit that acquires the results of the test items as a reaction pattern for the analysis target, and
An ability estimation unit that estimates the ability score of the analysis target by reducing the influence of item dependence due to the item difficulty level and item discriminating ability of the item from the reaction pattern.
Based on the distribution determined for ranking the ability scores (hereinafter referred to as "reference distribution"), the ability score to be analyzed is ranked in the reference distribution (hereinafter referred to as "ability score conversion order"). The scale conversion part that converts to the ordinal scale,
The analysis is based on an arithmetic process in which the rank difference between the "target rank set as a target in the reference distribution" and the "ability score conversion rank" is divided by the "magnitude of the ability score conversion rank". Ability score conversion device characterized by having a cost calculation unit for calculating the target achievement cost.

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