Scale of equal intervals, Scale of relations - General Psychological Workshop

The scale of equal intervals

If the researcher builds a scale where the requirement of interval equivalence is met, he gets a metric scale of equal intervals. As a typical example of such a scale, we can cite the previously mentioned temperature scales of Celsius and Fahrenheit. The value of one degree in both scales is fixed unchanged throughout the scale. Therefore, if in one day the temperature rises, say, five degrees, and on the second day by as much, we can assert that there is a uniform, linear change in temperature.

The interval scale is a truly measuring scale. It allows almost any mathematical operations with numbers corresponding to the elements of this scale, and also allows the calculation of

almost any statistics - both parametric and non-parametric.

An important advantage of the interval scale is the ability to translate measurement results from one scale to another. The transfer of one interval scale to another is carried out on the basis of general linear transformations. So, for example, to convert degrees Celsius (C) to degrees Fahrenheit (F), you can use the following linear relationship:

These temperature scales demonstrate a general approach to the construction of scales of equal intervals. The choice of the origin of the scale and the unit of measure in the construction of such scales is largely arbitrary. So, in the Celsius scale, the freezing point of water is set as the reference point, and as a unit of measurement, one hundredth of the difference between this temperature and the boiling point of water. On the Fahrenheit scale, the reference point is the freezing point of a mixture of water, salt and ammonia, and the unit of measurement is 1/96 of the difference between this temperature and the normal temperature of the human body. On the Delil scale of temperature, the boiling point of water was taken as the reference point. Thus, the reference points on the scale of intervals are chosen relatively arbitrarily, and the unit is taken to divide the range between them into equal intervals. How many such intervals should be between the reference points, the researcher also chooses arbitrarily.

In psychology, an example of an interval scale can serve as a scale in which units of standard deviation are used as units of measurement. We have already cited, as an example, the scale of intelligence proposed by Wechsler, where, as an analog of zero value, there is a point corresponding to the median distribution of the success of this test in the population. It is set at 100 points. As a unit of measure, recall, a value corresponding to 1/15 of the unit of standard deviation for this indicator is used. However, this method of constructing an interval scale is indirect, and therefore the researcher may have doubts in a number of cases whether the scale constructed is really an interval. That is why many researchers are not inclined to consider the results of psychodiagnostic measurements exactly in accordance with the interval scale.

Thanks to Stephens' efforts in psychology, methods have been developed that make it possible to obtain a scale of intervals directly. We shall consider these methods in Ch. 9 Direct Scaling Methods .

Relationship Scale

The relative and arbitrary location of the zero value of the interval scale does not allow it to establish equality of relations, for example, A/B = C/D , i.e. does not allow you to draw conclusions about how many times the severity of the measured quality in one person is higher than that of another, or how many times is it lower in one situation than in another. Indeed, if yesterday there were five degrees of heat on the street, and today it is ten, this does not mean that today it is twice as warm. This equality can be established only for the relations between the intervals, and not for the points themselves on the scale.

The ability to determine equality of relations appears only when the scale has an absolute zero value. As an example of such a scale, we give the absolute temperature scale of Kelvin. Most physical measurements involve the construction of relationship scales describing the size, weight, density, electrical resistance.

The only possible mathematical permutation for such scales is the operation of multiplying by some amount. For example, in this way we can convert meters to feet, kilograms to pounds, millimeters of mercury to millibars.

In psychology, such scales are still very few. A rare example is the scales of sensations developed by Stevens - for example, a scale for the evaluation of auditory senses, or a scale of weights that reflects the sensation of weight. So, in the scale of the SOPs for a zero value, the value of the sensation of sound at a frequency of 1000 Hz is assumed, the power of which corresponds to the lower absolute threshold. One dream corresponds to a sensation of sound at a height of 1000 Hz, whose power by 4 Bells exceeds the absolute threshold.

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