Mathematical methods in psychology are used to process research data and establish patterns between the phenomena studied. Even the simplest study cannot do without mathematical data processing.
Data processing can be carried out manually, or maybe using special software. The final result may look like a table; methods of mathematical statistics in psychology and allow you to graphically display the data. For different types of data (quantitative, qualitative and ordinal), different assessment tools are used.
Mathematical methods in psychology include both allowing to establish numerical dependencies, and methods of statistical processing. Let us dwell in more detail on the most common of them.
In order to measure data, first of all, it is necessary to determine the scale of measurements. And here such mathematical methods are used in psychology as registration and scaling , which consist in expressing the phenomena under study in numerical terms. There are several types of scales. However, only some of them are suitable for mathematical processing. This is mainly a quantitative scale that allows you to measure the severity of specific properties of the studied objects and in numerical terms to express the difference between them. The simplest example is the measurement of IQ. The quantitative scale allows the operation of ranking data (see below). When ranking, data from the quantitative scale is translated into the nominal (for example, low, medium or high value of the indicator), while the reverse transition is no longer possible.
Ranking is the distribution of data in descending (ascending) order of a sign that is being evaluated. A quantitative scale is used. Each value is assigned a specific rank (the indicator with the minimum value is rank 1, the next value is rank 2, and so on), after which it becomes possible to transfer the values from the quantitative scale to the nominal one. For example, the measured indicator is the level of anxiety. 100 people were tested, the results are ranked, and the researcher sees how many people have a low (high or medium) indicator. However, this way of presenting data entails a partial loss of information for each respondent.
Correlation analysis is the establishment of the relationship between phenomena. At the same time, it is measured how the average value of one indicator will change when the indicator changes, in relation to which it is located. Correlation is considered in two aspects: in strength and in direction. It can be positive (with an increase in one indicator, the second increases) and negative (with an increase in the first, the second indicator decreases: for example, the higher the level of anxiety of an individual, the less likely it is to occupy a leading position in the group). The dependence can be linear, or, more often, expressed as a curve. The connections that help establish a correlation analysis may not be obvious at first glance if other methods of mathematical processing are used in psychology. This is its main advantage. The disadvantages include the large complexity in connection with the need to use a considerable number of formulas and careful calculations.
Factor analysis is another statistical method that allows you to predict the likely impact of various factors on the process under study. Moreover, all impact factors are initially accepted as having equal value, and the degree of their influence is calculated mathematically. Such an analysis allows us to establish the common cause of the variability of several phenomena at once.
To display the obtained data, tabulation (creating tables) and graphical construction methods (charts and graphs that not only give a visual representation of the results obtained, but also allow to predict the process) can be used.
The main conditions under which the above mathematical methods in psychology ensure the reliability of the study are the availability of a sufficient sample, the accuracy of measurements and the correctness of the calculations.