Method of ranking - General Psychological Workshop

Ranking method

Another fairly common method of psychological scaling is the ranking of incentives by some kind of feature. The subject is presented with a set of objects and is asked to select from this set the object most possessing some property. For example, a subject may be asked to select the most talented writer from the general list of names presented. The first object selected by the subject gets rank 1. Next, from the remaining objects, the subject again has to select the object most possessed by

estimated attribute. This incentive gets rank 2. The ranking continues until there is only one object left; he gets the last rank.

Typically, this procedure is used if the number of ranked incentives is not too large. However, there are examples of using this method and for estimating a rather large number of stimuli. As an example, we can cite a study by J. Cattell, conducted more than 100 years ago. In this study, experts were to evaluate the merits of 200 American scientists - almost all of the then-living psychologists in the United States.

The processing of the data thus obtained, as in the case of the scoring method, is reduced to averaging the obtained rank values. Retrospectively, the results given by each individual are only an ordinal scale. However, group results can be interpreted as a hidden interval scale.

The method of obtaining a scale of equal intervals on the basis of processing of group data is similar to what we already know in connection with the methods of paired comparisons and scoring. On the basis of the raw data obtained, frequency distributions are constructed, reflecting the probabilities of setting certain rank values. Then these probability values ​​are translated into z-values ​​of the interval scale.

Imagine that the expert puts the evaluated object first, assigning him rank 1. Obviously, this means that this object is preferred to all other objects whose number is n. Thus, we can designate a preference for this object as c = n - 1. Then the preference of an object having rank 2 will be evaluated as c = = < strong> n - 2. In general, the preference value of an arbitrarily chosen object can be expressed as c = n - r, where < strong> d - the rank of the object.

The same logic can be applied to group data. We will denote the average value of the preference of the object as C , and the average rank of this object as T . Obviously, the value of the preference of this object to a group of experts can be expressed in the same way as the preference for one expert. In other words, the following relation holds:

Let's translate these values ​​into the probability values ​​of the incentive preferences:

By translating these values ​​to z-units, we get values ​​on the scale of equal intervals.

Let's explain this procedure with the help of an example.

In the Cattell study, conducted at the beginning of the last century, ten experts were asked to rank the merits of ten astronomers of that time. The results are shown in Table. 8.14. Processing of ranking results should include finding the average rank for each ranking object (in our case known astronomers of the early XX century).

Then, based on these values, the average preference estimates for each object and the corresponding probabilities are calculated. The scale values ​​themselves are given in the last line of the table. These values ​​are obtained by translating the preference probabilities for each stimulus into their corresponding z-values. Note that for the astronomer A, the procedure used does not make it possible to find its place on the scale, since a hundred percent probability can not be converted to z-units. This is the limitation of the described procedure. We also note that the method of pairwise comparisons we have already examined and the procedure for scoring the law of categorical judgments also do not allow processing such cases.

Table 8.14

The results of the ranking of ten astronomers of the early XX century. ten experts

Ex -

Perth

Astronomers

/1

In

From

D

E

F

G

N

I

J

1

1

2

4

3

9

6

5

8

7

10

2

1

4

2

5

6

7

3

10

8

9

3

1

3

4

5

2

8

9

6

10

7

4

1

3

4

5

2

6

10

8

7

9

5

1

9

2

5

6

3

4

8

10

7

G

1

4

9

2

5

6

7

3

10

8

7

1

3

5

10

2

6

9

7

8

4

8

1

3

5

7

6

4

8

10

2

9

9

1

2

8

4

9

6

3

7

5

10

10

1

2

4

5

9

8

6

3

7

10

7

1.0

3.5

4.7

5,1

5.6

6.0

6.4

7.0

7.4

8.3

with

9.0

6.5

5.3

4.9

4.4

4.0

3.6

3.0

2.6

1.7

P (C )

1

0.72

0.59

0.54

0.49

0.44

0.40

0.33

0.29

0.19

2 [P (s)]

?

0.59

0.22

0.11

-0.03

-0.14

-0.25

-0.43

-0.56

-0.88

Note that if researchers do not accept negative scale values, they can easily get rid of them using a linear transformation of data like in = A + In. This transformation preserves the order and equality of the intervals, providing the desired minimums and maximums of the scale. This remark is true also in relation to methods already considered by us.

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