The method of minimal changes and its varieties, Measurement...

Minimal change method and its variants

The procedure for the method of minimal changes directly reproduces the very notion of a sensory threshold. In this method, the threshold is represented as the boundary between perceived and non-perceived stimuli. Therefore, this method is customarily called the boundary method. It involves a gradual change in the stimulus that affects the subject, or the difference between the two stimuli, until the subject feels or disappears from the stimulus or the difference between the stimuli. The subject himself should evaluate his feelings on the principle of "I see - I do not see", "I hear - I do not hear", "I feel - I do not feel". When comparing two stimuli, the answers are "more," less than and is & quot ;. The researcher is interested in when the subject first changes the category of the answer.

The specific procedure for the minimal change method is slightly different, depending on which threshold we want to measure: absolute or differential.

Absolute threshold measurement

Procedure. In the case of measuring the absolute threshold by the method of minimal changes, the researcher presents the physical stimuli descending and ascending by rows, alternating them. The subject is instructed to answer "yes" in the case of an incentive, and no if it is impossible to detect it. The answer is also "I do not know, I'm not sure". As a rule, the procedure for assessing the threshold is preceded by training tests, the purpose of which is to make it clear to the subject what exactly is required of it, since in a number of cases the verbal instruction may be poorly understood by the subject when assessing the absolute threshold.

The experiment, as a rule, begins with a descending series of stimuli. The first subject is presented with a stimulus, the magnitude of which certainly exceeds the value of the absolute threshold. Then the researcher gradually reduces the stimulus value to some small value, each time asking the subject whether he is able to detect this stimulus. A number of incentives change until the subject changes the category of the answer.

In the classical work of E. Titchener, an example is given of estimating the lower absolute threshold for detecting the pitch of sound. The experiment began with the presentation of a sound pitch 24 Hz high, and then the sound pitch was reduced by 1 Hz. In Table. 6.1 shows the data collected by Titchener.

Table 6.1

Determination of the lower absolute threshold of sensation of pitch by the method of minimal changes

Frequency

(Hz)

Alternating ascending and descending series

24

Yes

23

Yes

22

Yes

Yes

21

Yes

Yes

20

Yes

Yes

Yes

End of the table. 6.1

Frequency

(Hz)

Alternating ascending and descending series

19

Yes

Yes

Yes

18

Yes

Yes

Yes

Yes

Yes

17

Yes

Yes

Yes

Yes

Yes

16

Yes

Yes

Yes

Yes

Yes

Yes

15

Yes

No

Yes

Yes

Yes

Yes

Yes

Yes

Yes

14

No

No

No

No

?

No

?

Yes

?

No

13

No

No

No

No

No

12

No

No

No

No

No

11

No

No

No

No

10

No

No

No

9

No

No

8

No

No

7

No

No

In the first, the descending series, the researcher incrementally reduces the sound tone value by 1 Hz to 14 Hz. Here there is a change in the category of the respondent's response - he ceases to hear the sound. Thus, we can assume that the lower absolute threshold is passed. Obviously, it is between 15 and 14 Hz.

Evaluating the absolute threshold in the descending series, the researcher proceeds to estimate the threshold in the ascending row. This is necessary because the subject in the experiment may be inclined to commit one of two systematic errors: a waiting error and an addiction error.

The error of waiting, or anticipating, is that the subject aspires to change the category of the answer before the threshold value is passed. Thus, the estimated value of the sensor threshold will be overestimated. The opposite effect will take place due to the error of habituation. In this case, the subject tries to maintain his answer even when the threshold has already been passed. In order to obtain a more accurate threshold value, the minimal change method assumes an alternation of descending and ascending series.

In the example we are considering, from the work of Titchens, the second series begins with a stimulus whose magnitude is certainly below the threshold value of 7 Hz. Then the researcher gradually increases the stimulus value by 1 Hz at each step until the subject's response changes again. As can be seen, this time this happens at a stimulus value of 16 Hz. Thus, in this series, the absolute threshold value is between 15 and 16 Hz.

In order to get a more accurate threshold value, the experiment procedure consisting of descending and ascending series is repeated

repeatedly, as a rule, from 20 to 200 times. The required number of rows is determined on the basis of an estimate of the required accuracy of the measurement and the degree of variability of the threshold itself.

It is assumed that sometimes the subject may give an uncertain answer. In Table. 6.1 such a response is indicated by a question mark. In this case, the threshold is also considered passed, and the researcher proceeds to the next row. However, in the general case, such answers should be avoided and the subject should be asked to answer "yes" or no .

We also pay attention to the fact that as the threshold value is clarified during the procedure of its measurement, the series of stimuli themselves can be shortened. In other words, if we follow the results of the experiment presented in Table. 6.1, there is no need to start the descending series with 24 Hz each time, and the ascending one from 7 Hz. In subsequent downward series, the starting stimulus can be reduced to 22 Hz or even to 19 Hz, and in the ascending rows the researcher can start the series already from 10 Hz, 11 Hz or even 12 Hz.

Processing of results. The processing of data obtained by the method of minimum changes begins with the determination of the threshold in each row. The value of the threshold is taken as the average arithmetic value of the stimulus in two adjacent samples, where the subject's response changes. Thus, in the example under consideration (Table 6.1), the value of the threshold in the first row turns out to be 14.5 Hz, since it appears to be between the stimuli of 14 and 15 Hz, in the second row it is 15.5 Hz, here the threshold is between the stimuli at 15 and 16 Hz, etc.

After that, the value of the absolute threshold over all series is calculated and the degree of its variability is estimated. There are three possible calculations.

In the first case (this is, apparently, the most common variant), the absolute threshold value ( RL ) is calculated as the arithmetic mean of the estimated threshold values ​​in each row:

(6.1)

where L i - the threshold value in the i -th row; N - number of rows.

The degree of variation in threshold values ​​is determined by the standard deviation ( SD RL ):

(6.2)

Another option for calculating the threshold value involves calculating the average value for each pair consisting of the ascending and descending series. Then, for the values ​​obtained, the arithmetic mean and the standard deviation value are also calculated. It is clear that the very

the threshold value RL will be the same as in the previous case, but the standard deviation will be slightly less.

Finally, another version of the threshold estimate assumes a separate estimate of its magnitude for the ascending and descending series. This option allows you to assess the presence of two types of systematic errors in the answers of the subject - the error of expectation and the error of habituation. If in the descending series the threshold is above the threshold in the ascending series, then this fact obviously indicates the presence in the judgments of the subject of the error of expectation. If, on the contrary, in the descending series the threshold is below the threshold in the ascending series, this indicates an error of habituation.

The reliability of the absolute threshold measurements is calculated by calculating the standard error value:

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