The result of the analysis of processes and phenomena studied using statistical methods is a set of numerical characteristics that can be classified into absolute and relative indicators.
Absolute indicators
Absolute values in terms of statistics are the number of units or amounts in the sample, which are the direct result of the summary and grouping of the analyzed data. Absolute indicators reflect, so to speak, the "physical" characteristics of the processes and phenomena under study (area, mass, volume, spatio-temporal parameters), which, as a rule, are recorded in primary accounting documents. Absolute values always have a dimension. We also note that, in contrast to the mathematical interpretation, the statistical absolute value can be either positive or negative.
Classification of absolute indicators
Absolute values are classified according to the method of presenting the dimensions of the phenomena under study into individual, group and general.
To individual include absolute indicators expressing the numerical dimensions of individual units of the population. For example, the number of employees in the organization, the gross output of the enterprise, profit, etc.
group indicators are called parameters that determine the dimensional characteristics or the number of units in a certain part of the population. Such indicators are calculated by summing up the corresponding absolute parameters of individual units of the study group or by directly counting the number of units in a sample from the general population.
Absolute indicators that describe the size of a feature in all units of the population are called common. Such parameters are the result of a summary of the results of statistical studies. These indicators include the wage fund of enterprises in the region, wheat in the state, etc.
Definition of relative value
From the point of view of statistics, a relative value is a generalizing parameter that describes the quantitative ratio of two absolute values. In other words, relative indicators characterize the relationship and interdependence of two compared absolute parameters.
Application in socioeconomic research
Relative indicators play an important role in the analysis of socio-economic processes, since the absolute characteristics themselves do not always allow a correct assessment of the analyzed phenomenon. Often, their true significance is revealed only during comparison with another absolute indicator.
Relative indicators include parameters that determine the structure of the phenomenon, as well as its development over time. With their help, it is easier to trace the trends in the development of the process under study and to make a forecast of its further evolution.
The main feature of relative values is that they make it possible to carry out processes that are incomparable in absolute terms, which, in turn, opens up opportunities for comparing the levels of development or the prevalence of various social phenomena.
The principle of calculating the relative value
In relation to absolute indicators, which are input data for statistical analysis, relative values are derived from them, or secondary. The calculation of relative indicators in general terms is performed by dividing one absolute parameter by another. In this case, the value in the numerator is called the compared, or current, and the indicator in the denominator with which the comparison is made is the basis (base) of comparison.
Obviously, it is possible to perform a comparison even of seemingly completely unrelated absolute values. Relative indicators necessary for statistical analysis should be chosen based on the objectives of a particular study and the nature of the primary data available. At the same time, it is necessary to be guided by the principles of visibility and ease of perception.
As current and basic indicators for calculation, you can use not only absolute, but also relative characteristics. Relative parameters obtained by comparing absolute characteristics are called first-order indicators, and relative parameters are called higher-order indicators.
Dimensions of relative values
Statistical analysis allows you to calculate relative indicators for both the same and opposite values. The result of the comparison of the parameters of the same name are unnamed relative values, which can be expressed in multiplicity factors, representing how many times the current indicator is greater or less than the base one (in this case, one is taken as the basis for comparison). Often in statistical studies, the comparison base is taken equal to 100. In this case, the dimension of the obtained relative indicators will be percentages (%).
When comparing dissimilar parameters, the ratio of the corresponding dimensions of indicators in the numerator and denominator is taken as the dimension of the obtained relative value (for example, the indicator of GDP per capita has the dimension of million rubles / person).
Classification of relative values
Among the variety of relative parameters, the following types are distinguished:
- indicator of dynamics;
- indicators of the plan and implementation of the plan;
- intensity indicator;
- structure index;
- indicator of coordination;
- comparison index.
Dynamic indicator (OPD)
This parameter describes the ratio of the current level of development of the phenomenon under study to some, taken as a base, the level of its development in the previous period. Expressed as a multiple ratio, the relative indicator of dynamics is called the growth factor, and as a percentage - the growth rate.
Plan Indicators (PPI) and Plan Implementation Indicators (PIP)
Such indicators are used by all economic entities involved in current and strategic planning. They are calculated as follows:
The characteristics discussed above are related by the following relationship:
OPD \u003d OPP * OPP.
The relative indicator of the plan determines the intensity of the task compared to the previous period, and the implementation of the plan determines the degree of its implementation.
Structural Index (SIR)
This relative indicator shows the structural composition of the population and is expressed in relation to the size of the absolute attribute of the structural part of the object under study to the size of the attribute of the population as a whole. In other words, the calculation of structure indicators consists in calculating the specific weight of each part of the population:
OPS are usually expressed as fractions of a unit (coefficients) or percentages. The sum of the specific weights of the structural parts of the studied population should be equal to one or one hundred percent, respectively.
Such coefficients are used in the study of the structure of multicomponent complex phenomena, for example, in the study of emissions of harmful substances by vehicles of a traffic flow, separating them by the type of fuel used (gasoline, diesel, gas) or by purpose (cars, trucks, buses), etc.
Index of Coordination (CPI)
This parameter characterizes the ratio of the characteristics of some part of the statistical population to the characteristics of the base part. The relative indicator of coordination is used in statistical analysis for a more visual representation of the relationship between the individual parts of the population under study.
The part of the population with the maximum specific gravity or being a priority is chosen as the basic one.
Intensity Index (IIR)
This characteristic is used to describe the propagation of the phenomenon (process) under study in its own environment. Its essence lies in the comparison of oppositely named quantities related to each other in some way.
An example is indicators of the level of GDP per capita, demographic indicators of natural increase (decrease) of the population per 1000 (10000) people, etc.
Comparison indicator (CFR)
This parameter describes the ratio of the same absolute characteristics of different objects:
The relative comparison indicator can be used for comparative analysis, for example, the population of different countries, prices for the same goods of different brands, labor productivity at different enterprises, etc.
The calculation of relative characteristics is an important step in statistical analysis, however, considering them regardless of the primary absolute indicators, one can come to unreliable conclusions. Consequently, a correct assessment of various socioeconomic processes and phenomena should be based on a system of parameters, which includes both absolute and relative indicators.
Intensive indicators are used when it is necessary to estimate the prevalence of the phenomenon under study in the environment with which it is associated. In other words, the relative values of the frequency answer the question of how often the phenomenon under study occurs in the environment in which it occurs. Relative frequency values can be calculated on various bases - 100, 1000, 10,000, etc.
The methodology for calculating intensive indicators is based on the proportion:
Typical intensive indicators are indicators of fertility, mortality, morbidity in certain groups of people and at a certain time.
Example: Calculate the morbidity rates of workers with acute respiratory infections, if 512 diseases were registered in the reporting year. The number of employees at the enterprise is 1676 people.
2. Extensive indicators.
Relative distribution values are used when it is necessary to quantify the distribution of a whole into its constituent parts. In other words, the relative values of the distribution answer the question of what proportion (%) of the entire phenomenon as a whole, taken as 100%, is occupied by any component of it.
The method for determining the relative values of the distribution is based on the elementary proportion:
The absolute value of the phenomenon under study is 100%
The value of any component of the phenomenon is X%.
Hence the relative value of distribution X:
Example:
Distribution of infectious diseases of workers of the enterprise by types of diseases
|
Diagnosis of the disease |
Absolute number of cases |
Relative distribution values (structure) in % |
|
Other SARS | ||
|
Dysentery | ||
|
infectious hepatitis | ||
|
Other infectious diseases | ||
|
Total |
Calculation method:
An extensive indicator characterizes the share of some part of the phenomenon under study in the total population and does not say anything about the size of this part.
Extensive indicators can characterize the distribution of births by sex, height, weight; distribution of the dead by age, sex and causes of death; distribution of patients according to nosological forms, according to the terms of hospitalization; composition of the population by sex and age. In some cases, it is possible to use only extensive indicators, for example, the formula of white blood elements.
A characteristic feature of extensive indicators is their interconnectedness, which causes automatic shifts, since their sum is always 100%. So, when studying the structure of morbidity, the proportion of a particular disease may increase:
a) with its true growth, i.e. with an increase in absolute values and an intensive indicator;
b) at the same level - if the number of other diseases decreased during this period;
c) with a decrease in the level of this disease, if the decrease in the number of other diseases occurred at a faster pace.
It is impossible to draw conclusions about the intensity of the phenomenon in different populations on the basis of their shares.
Relative statistics It is customary to call a generalizing characteristic, expressed as a numerical measure of the ratio of two compared absolute values. These indicators are used to study the structure of the phenomenon under study, to compare its level of development with the level of development of another phenomenon, to assess the changes taking place in the phenomenon under study, etc.
A relative statistical indicator is obtained by dividing one absolute indicator by another.
In general, the formula for a relative statistical indicator will look like this:
OP=
Relative indicators can be expressed as coefficients, percentages, ppm and decimille.
If the base of comparison is taken as a unit, then the relative indicator is expressed in the form of a coefficient. If the base of comparison is taken as one hundred units, then the relative indicator is expressed as a percentage. If the comparison base is taken as a thousand units, then the relative indicator is expressed in ppm (a tenth of a percent), if for ten thousand - in a decimill (hundredth of a percent).
Speakers;
plan and execution of the plan;
structures;
coordination;
Intensity and level of economic development;
Comparisons.
Relative indicator of dynamics characterizes the change in the phenomenon under study over time and is a ratio of indicators characterizing the phenomenon in the current period and the previous (or base) period.
OPD =
The indicator calculated in this way is usually called the growth (decrease) coefficient. It shows how many times the indicator of the current period is more (less) than the indicator of the previous (base) period. Expressed as a percentage, the relative indicator of dynamics is usually called the rate of growth (decrease).
T p \u003d (y i / y i-1) * 100%
T p \u003d (y i / y o) * 100%
Example: population of the Russian Federation according to the 2002 census. amounted to 145181.9 thousand people, according to the 1989 census. - 147021.9 thousand people Determine the coefficient and rate of growth (decrease).
T p = 
98, 7%
Consequently, the population decreased by 1.3%.
Relative indicator of the plan (forecast) (OPP) and the implementation of the plan (OPVP) are used by all subjects of financial and economic activities that carry out current and strategic planning and are calculated according to the formula:
The relative indicator of the plan characterizes the intensity of the plan task, and the relative indicator of the plan's implementation characterizes the degree of its implementation.
Example: the actual turnover of the company for 2008ᴦ. amounted to 2 billion rubles. Market analysis showed that for 2009ᴦ. it is possible to bring the turnover up to 2.6 billion rubles. Actual turnover for 2009ᴦ. amounted to 2.5 billion rubles. Define AKI and OPVP.
OPP==130% or 1.3 times
OPVP==96%
Calculations show that the target for 2009 is 1.3 times higher than the actual level for 2008, but the plan for 2009 was only 96% fulfilled.
Relative indicators of the structure(OPS) characterize the shares (specific weights) of the constituent parts of the population in its total volume. Οʜᴎ characterize the structure of the population and its structure.
OPS=
(*100%)
OPVs are usually expressed in the form of coefficients or percentages. The sum of the coefficients should be 1, and the sum of the percentages should be 100%, since the specific weights are reduced to a common base.
The set of relative values of the structure shows the structure of the set.
Relative indicators of coordination(OPK) characterize the ratio of parts of a given statistical population to one of them, taken as the basis for comparison. Οʜᴎ show how many times one part of the population is larger than the other, or how many units of one part of the population account for one, ten, one hundred, etc. units of another population.
For the base of comparison, the part that has the largest share is selected, or is a priority in this population.
Relative indicators of the intensity and level of economic development(OPI) characterize the degree of distribution or the level of development of the studied phenomena or processes in a certain environment. Οʜᴎ are formed as a result of comparing oppositely named, but in a certain way related quantities.
This indicator is calculated per hundred, thousand, ten thousand, etc. units of the studied population and is used in cases where it is impossible to determine the scale of the phenomenon by the value of the absolute indicator. For example, when studying demographic processes, indicators of birth rate, mortality, natural increase (decrease) of the population are calculated as the ratio of the number of births (deaths) or the amount of natural increase per year to the average annual population of a given territory per 1,000 or 10,000 people.
K r =‰
K m=‰
to natural growth =‰
Relative indicators of the level of economic development characterize the efficiency of resource use and production efficiency. These are indicators of production output, costs per unit of output, efficiency in the use of production assets, etc.
Relative Comparison Index OPS r characterizes the comparative sizes of absolute indicators of the same name relating to different objects or territories, but for the same period of time.
They are obtained as partial divisions of the absolute indicators of the same name characterizing different objects belonging to the same period or point in time.
OPS r=
Using these indicators, you can compare labor productivity in different countries, compare prices for various goods and compare economic indicators for various enterprises.
Relative indicators of intensity(OPI) in
legal statistics are called indicators that characterize the degree of prevalence or the level of development of a particular feature in the observed population. Relative intensity indicators are used to characterize the degree of prevalence of civil disputes, crime in various cities, regions, countries, to reflect the provision of the population with law enforcement personnel, etc.
Opi An indicator characterizing the social and legal phenomenon
An indicator characterizing the environment for the spread of this phenomenon
140 Relative indices of intensity are calculated by comparing quantities of different names characterizing various phenomena that are in a certain relationship with each other. These indicators are usually determined per 100, 1000, etc. units of the denominator indicator (for example, per 100 hectares of land, per 1000 population, etc.). Intensity indicators are used to reflect the degree of development of a phenomenon in a particular environment.
When comparing the number of civil lawsuits with the total population in the regions being compared, one can obtain data on the intensity of lawsuits per 10,000 or 100,000 people.
In criminal law statistics, among the relative indicators of intensity, an important place is occupied by crime rate(KP). It is calculated as the ratio of the facts of crimes or the number of persons who committed crimes to the total population or to the population that has reached the age of criminal responsibility.
t "P x 100 000
where P- the absolute number of registered crimes or the number of persons who committed them;
H- the total population or the population aged 14 years and over.
Both indicators (the number of registered crimes or persons who committed crimes and the total population) are taken in the same temporal and territorial volume. The crime rate is usually calculated as the number of crimes per 100,000 people in the population. But with small numbers of crimes and the population, it can be calculated per 10 thousand or per 1 thousand of the population, while 100 thousand, 10 thousand and 1 thousand mean the dimension of the coefficient.
Comparison of the crime rates of different regions or countries makes it possible to objectively judge in which territory the intensity of crime is higher or lower, since it eliminates the influence of the size and growth of the population on the change in crime.
When calculating and evaluating intensity factors in legal statistics, it is necessary to take into account some features of the compared indicators:
The numbers of crimes, detected offenders, criminal and civil cases, lawsuits brought, etc., taken over a certain period (usually a year), are interval series of dynamics characterizing the sum of facts or events of a phenomenon throughout the year. While the population is usually characterized on a certain date (beginning or end of the year) and represents moment row. It will be more correct if the crime rate and other intensity factors are calculated in relation to the average annual population, which is taken as half the sum of the population at the beginning or end of the year.
In population statistics, there are permanent and cash population. This division of the population into categories is of particular importance in legal statistics when calculating intensity factors for regions with a high level of temporary population, such as Moscow. The difference between the permanent and actual population in Moscow in 2002 was more than 3 million people, which cannot be ignored when calculating crime rates, because from a third to a half of crimes in Moscow are committed by temporary residents.
When comparing the intensity coefficients for regions with significantly different birth rates, it is more correct to calculate the coefficients for the population that has reached a certain age, from which comes criminal liability (i.e. 14 years of age and older). Since the proportion of minors in countries with high and low birth rates is very different. In practice, due to the frequent lack of data on the population by age categories 14-16 years old, as well as in international comparisons, when criminal liability occurs from different ages (from 10, 12, 14, 16 years old), the crime rate is usually calculated in relation to the entire population.
When calculating the intensity coefficients, instead of the total number of persons who committed crimes, the number of convicts can be taken, and then we get conviction rate. If we take the number of victims in the numerator, we get victimization rate, if the number of prisoners, then - prize money ratio(from the English word prison- a prisoner). When calculating the ratio of prisoners, it must be taken into account that the number of prisoners
2 is also a moment series, like the population. Therefore, when calculating this coefficient, either the average annual number of prisoners or their number at the end of the year is taken (the number of the entire population in this case should also be taken at the end of the year). The prisoner rate can also be calculated per 100,000 reported crimes or perpetrators identified, showing intensity of repressiveness judicial system.
If we correlate the number of crimes with the number of persons who committed them, we get coefficient of criminogenic activity of criminals, showing how many crimes each criminal commits on average.
In the numerator of the intensity coefficients, the total number of solved crimes, preliminary arrests, all convicted, sentenced to imprisonment and other indicators can also be taken.
For minors, women, men, previously convicted, unemployed, military personnel and other groups of the population, specialized crime rates. In this case, the numerator of the coefficient will include the number of crimes committed by a particular population group, and the denominator - the total population of this group in a certain territory.
To assess the intensity of certain groups and types of crimes, the coefficients of economic, violent, mercenary acts, intentional murders, thefts, etc. are calculated.
The use of various intensity factors contributes to a more objective assessment of the level of crime and its individual types, allowing them to be compared in time (by years) and in space (by territory).
There are four types of relative values: intensive, extensive, ratio indicators, visibility indicators.
Intensive indicators - show frequency phenomena in the environment. The medium is usually a certain set of objects (population, patients, cases), some of which have some kind of phenomenon. Calculated using the following formula:
I.p. = phenomenon/environment*coefficient.
The coefficient is used for the convenience of presenting the indicator, it represents various powers of the number 10 and usually takes the values 100, 1000, 10,000, 100,000. Its value depends on the frequency of occurrence of the phenomenon: the less common, the greater the coefficient. Thus, the birth rate, mortality, general morbidity of the population are usually calculated per 1000 people. When calculating maternal mortality, as a much rarer event, a factor of 100,000 is used. Conversely, the frequency of such a common event as temporary disability is calculated per 100 workers.
An example of calculating an intensive indicator:
During the year, 360 surgical operations were performed at the N. hospital. In 54 cases, various complications were observed in the postoperative period. Find the frequency of postoperative complications per 100 operations.
Solution: The frequency of postoperative complications is an intensive indicator that can be calculated as the ratio of the phenomenon to the environment. The environment is a set of performed operations (360), of which in 54 cases, as follows from the conditions of the problem, a phenomenon occurred - postoperative complications were noted. In this way:
Postoperative Complication Rate = (Number of Postoperative Complications) / (Number of Operations Performed) * 100 = (54 / 360) * 100 = 15.
The value of the coefficient is taken equal to 100, since the condition of the problem asks for the frequency calculated for 100 performed operations.
Answer: The frequency of postoperative complications in the N. hospital for the year was 15 cases per 100 operations performed.
Extensive indicators - characterize structure phenomena are measured as a percentage, less often - in ppm or fractions of a unit. Extensive values show what part is a separate group of units in the structure of the entire population. Calculated according to the formula:
E.p. = part/whole*100%.
An example of calculating an extensive indicator:
In a study of the effectiveness of the treatment of pneumonia using a new antibiotic, 200 patients took part, of which 90 were men. It is necessary to determine the proportion of men among the subjects, the result is expressed in%.
Solution: Male patients represent a part of the total population of the study. Therefore, we must use the formula for calculating extensive indicators:
The proportion of male patients among all studied = (number of men) / (number of all patients) * 100% = (90 / 200) * 100% = 45%.
Answer: The proportion of patients in the structure of the study is 45%.
Ratio indicators - characterize the ratio of two unrelated sets. These aggregates can be measured in the same quantities, the main condition is that their changes must occur independently of each other. Usually, various indices, coefficients, indicators are presented in this form. security population. Calculated using the following formula:
P.s. = (first population) / (second population)*coefficient
The coefficient usually takes the values 1 (for indexes) or 10,000 (for indicators of the provision of the population).
An example of calculating the ratio indicator:
In one of the districts of the Republic of Tatarstan, 40,000 people live. 384 inpatient beds have been deployed in the medical and preventive institutions of this district. What is the provision of the population with beds in the district?
Solution: We have two populations: population and inpatient beds. Changes in the population number do not depend on changes in the number of inpatient beds and vice versa, and therefore we conclude that the populations presented are not related. Calculate the indicator of provision of the population with inpatient beds:
Provision of the population with beds = (number of beds) / (population) * 10,000 = (384 / 40,000) * 10,000 = 96.
Answer: The provision of the population with inpatient beds is 96 per 10,000 population.
