The law of normal division in sociology. Normal division Normal division in psychology
Small 1.1. Calculation scheme for standard grades (stin) for factor N 16-
factorial special nurse R.B. Cattell; Below are indicated intervals in units of 1/2 standard care
Right-handed from the middle value, the intervals are expanded, equal to 6, 7, 8, 9 and 10 walls, and the rest of these intervals are closed. From the middle value, intervals are expanded, equal to 5, 4, 3, 2 and 1 walls, and the extreme interval is also open. Now we rise to the axis of the “sirish balls”, and mark the intervals in the units of the “sirish” balls. Oskolki M = 10.2; δ=2.4, right-handed we add 1/2δ to that. 1.2 "siri" bali. In this way, the interval becomes: (10.2 + 1.2) = 11.4 “sirich” points. Then, between the intervals, which correspond to 6 walls, will extend from 10.2 to 11.4 points. In fact, it only consumes one “seere” value - 11 points. The left hand in the middle places 1/2δ and is maintained between the interval: 10.2-1.2=9. In this way, the intervals that represent 9 walls extend from 9 to 10.2. At this interval, two “siri” values are already consumed - 9 and 10. Since the last one has taken off 9 “siri” points, you now add 5 walls; If you remove 11 “ordinary” points - 6 walls, etc.
It is important that in the scale of walls there is a certain number of walls depending on the number of “plain” points. For example, for 16, 17, 18, 19 and 20 points, 10 walls will be added, and for 14 and 15 - 9 walls, etc.
In principle, the scale of the walls can be based on any data measured on an ordinal scale, with a sampling volume of >200 and a normal distribution of signs 2.
Another way to ensure an equal interval scale is to group intervals according to the principle of equality of accumulated frequencies. With normal distribution, the signs on the circle of the average value are grouped most of all, in which the intervals of the middle value appear less, narrower, and at a greater distance from the center of the stench distribution admire, (div. Fig. 1.2). Also, such a percentage scale is equal to the same interval as the accumulated frequency (Melnikov V.M., Yampolsky L.T., 1985, p. 194).
Small 1.2. Vidsotkov scale; animal to equalize the specified intervals in units of standard care
Much like a normal division of divas. Nutrition explanation 3.
Using scales of equal intervals based on data taken from the order of the scale, he guesses the trick with motorized gatherings, which S. Stevens tried. We first rise from the ramps, which are not secured to anything, and get to the ramps, which are secured. However, which way did we stumble upon it? They measured the psychological value behind the order scale, adjusted the average and standard values, and then adjusted the interval scale. “Such an illegal source of statistics can be given a pragmatic justification; in many cases it can lead to good results” (Stephens, 1960, p. 56).
Many followers do not check the stage of escape from the empirical division they have separated from the normal division, and they no longer translate the acquired significant portions of standard care or hundreds, willingly " Danimi. "Sir" is often given bevels, cuts along the edges or a double-edge. Rice. Figure 1.3 shows the distribution of the meat-willed zusilla in the selection of 102 samples. The division can be considered normal with sufficient accuracy (x 2 = 12.7 at v = 9, M = 89.75, δ = 25.1).
Small 1.3. Histogram and smooth curve to the subsection of the displayzusilla (n=102)
Rice. Figure 1.4 shows the division of the self-esteem indicator using the scale of the J. Menester - R. Koshin method “River of success, which you can already achieve at once” (n = 356). The division is significantly different from normal
(χ 2 = 58.8, with v = 7; p
Small 1.4. The histogram is smooth crooked to the bottom indicator of reliable success (n=356)
It is possible to interact with such “abnormal” divisions even more often than with classic normal ones. And the point here is not in any particular vase, but in the very specificity of psychological signs. For some methods, 10 to 20% of the following are given a rating of “zero” - for example, in their evidence there is no common verbal formulation that would reflect the motive of “hope for success” or “fear of failure” (methods ka Heckhausen). Those who sampled the assessment “zero” are normal, but the distribution of such assessments cannot be normal, as if we did not increase the sampling procedure (div. Art. 5.3).
The methods of statistical processing, presented in this manual, do not require any reversal of the difference between the obtained empirical division and the normal one. The stinks are caused by frequency adjustment and ranking. Verification is only required once the dispersion analysis has been completed. This section itself is accompanied by a description of the procedure for identifying the necessary criteria.
In solving problems, there is no need to check the degree of separation of the obtained empirical division from the normal one, and thus try to transform the ordinal scale into an equal interval. For any units there were no changes - for seconds, millimeters, degrees, number of choices, etc. - all this data can be aggregated using non-parametric criteria 3, which forms the basis of this core nothing.
An important description of the parametric criteria is given below in this section.
Scale of equal wear- this is a scale that classifies objects or subjects in proportion to the level of intensity of the controlled power. On scales, grades are indicated by numbers, which are proportional to each other: 2 goes up to 4, like 4 goes up to 8. This conveys the presence of the absolute zero point to the next. In physics, the absolute zero point tends to become narrower when there are extremes of shock or physical objects and when temperatures below the Kelvin scale are below absolute zero temperatures. It is important that in psychology the scales of equal values are used as scales of thresholds of absolute sensitivity (Steven Z, 1960; Gaida U. Do., Zakharov U. P., 1982). The capabilities of the human psyche are so great that it is important to recognize the absolute zero of any kind of psychological change. Absolute stupidity and absolute honesty are concepts rather than everyday psychology.
The same applies to the installation of equal lines: only the metaphor of everyday thought allows Ivanov to be 2 times (3, 100, 1000) wiser than Petrov.
Absolute zero, however, can come into play when a number of objects and subjects are being hydrated. For example, when choosing one of 3 alternatives, the participants did not choose alternative A every time, alternative B – 14 times, and alternative C – 28 times. In this case, we can confirm that alternative B is chosen twice as often as alternative B. However, in this case, it is not the psychological power of the people that is important, but the preference for elections among 42 individuals.
In relation to frequency displays, all arithmetic operations can be calculated: addition, subtraction, subdivision and multiplication. One change on this scale of values - 1 caution, 1 choice, 1 reaction, etc. be careful. Having tested the midpoints of the nominative scale, we can then find a scale of vimiru - a scale of differences between frequencies.
Nutrition 3 Rozed the signs. Roster parameters
The division of signs is called the pattern of people of different meanings (Plokhinsky N.A., 1970, p. 12).
In psychological investigations, there is often an attempt to establish a normal distribution.
Normal brood characterized by the fact that the extreme values of the signs tend to occur rarely, and values close to the average value tend to occur often. Such a division is called normal because it has already often become common in natural science research and appears to be the “norm” of any kind of mass episodic manifestation of a sign. This division follows the law discovered by three people at different times: Moivre in 1733. in England, by Gauss in 1809. in Nimechchina and Laplace in 1812. in France (Plokhinsky N.A., 1970, p. 17). The graph of a normal division is similar to the eye of a pre-study psychologist, the so-called bell curve (marvelous, for example, Fig. 1.1, 1.2).
The parameters of the division are the numerical characteristics that indicate how “in the middle” the values of the signs are rotated, to the extent that they are significant and minimal, and the appearance of the most important signs is avoided. The most practically important parameters are mathematical calculation, dispersion, indicators of asymmetry and excess.
In real psychological studies, we operate not on parameters, but on nearby values, on parameter estimates. This is the interconnection of the selections. The larger the sample, the closer it is possible to estimate the parameter to its true value. Nadal, speaking about the parameters, we are based on the respect of our assessments.
The arithmetic mean (assessment of mathematical calculation) is calculated using the following formula:
de x i- skin signs to watch out for;
i- Index, which indicates the serial number of a given sign value;
n- great caution;
∑ - sign of subsumption.
The dispersion estimate is calculated using the following formula:
de X i - skin significant signs that you should be careful of;
x - arithmetic mean signs;
P- be very careful.
The value that is the square root of the unbiased variance estimate (S) is called the standard variance or the mean square variance. For most predecessors, it is better to denote this quantity with the walnut letter δ (Sigma), not S. In fact, δ is the standard variation in the general population, and S is the unbiased estimate of this parameter in the vibration survey. Apart from the fragments S, the shortest estimate is δ (Fisher R.A., 1938), and this estimate is often no longer referred to as S, but as δ:
In these episodes, if there are reasons for the frequent occurrence of meanings, such as higher or lower than average, asymmetrical divisions are created. With left-sided or positive asymmetry, the subgroup often has lower sign values, and with right-sided or negative asymmetry, higher values (div. Fig. 1.5).
Asymmetry indicator (A) calculated using the following formula:
For symmetrical divisions A = 0.
Small 1.5. Asymmetry of divisions.
A) Liva, positive
B) right, negative
In these episodes, if there are any reasons for the significant appearance of average or close to average values, a subdivision with positive excess is established. If a division prioritizes extreme values, both lower and higher, then such a division is characterized by a negative excess and a depression can be created in the center of the division, which turns it into a double-vertical one (div. Fig. 1.6).
Showcase of excess (E) indicated by the formula:
Small 1.6. Excess: a) positive; b) negative
In divisions with normal convexity E = 0.
The parameters of the division can be determined using almost all the data presented in the interval scale. As we have discussed before, the physical scales of dovzhin, hour, kuti and interval scales, and before them, we have established ways to categorize parameter estimates, from a formal point of view. Parameters for the subdivision are not covered by insurance
true psychological unevenness of seconds, millimeters and other physical units in the world.
In practice, a pre-study psychologist can determine the parameters of any given group, since only a few, who have been victorious in the past, are considered reasonable by scientific partnerships.
The law of normal division, or as it is also called - the Gauss curve, is one of the main pillars of the theory of reliability. This concept can be applied to almost all areas of modern human knowledge, from physics to philosophy. I will try, in a short look at examples, to explain how this principle can be applied when analyzing social processes in sociology.
If you want to calculate the Gauss curve more accurately, it is best to complete a complex equation, in which you will not need any knowledge of advanced mathematics. And so, let’s start with a clear understanding of why this is a sensational graphic, in the example of the image shown in the title of the article. The law of normal division shows the consistency of a given value with a distinct gradation of these values. Axis XThere are gradations in digital manifestations that go from zero on the offensive side to obvious inconsistency (or in some cases it is cruelly cut off). All Y This is an indicator of the magnitude of the probability of the value of the gradation and can range from zero to one. Important? No, everything is simple, look at this chart and everything will become clear to you.
Let’s say, you’re walking along the street, you want to ask someone reasonably from a passer-by, and you’re going crazy with people, you can be convinced that with maximum homovirality you will be a person of average intelligence, with less homovirality, you will stupid or wise and with practically minimal capacity - a genius or a stupid one.
In a word, this graph shows the incredible division of intelligence in the marriage. In this way, having looked at any position on the chart, one can say that there is confidence in sorting out people, the insight of a genius, a reasonable person, or a fool.
Actually, this graph is just an example, and may not be relevant to reality. For a real picture of this kind, an entire statistical committee may need to work on it. As can be understood from the above example, the graph can be deformed in a different way and present a different validity. The graph of the readings is called the Standard Normal Division, because this form of the balance curve is established by nature itself. And since we live in the light of the biosphere, and the different levels of diversity are assessed, it is clear that this form of the curve dominates.
In the designated ZNR, I have indicated that all X I go from both sides to inconsistency. The truth is that the assessment of any significant quantities using the method of live statistics is a phenomenon that exists only at the present time. The marriage does not stand still, it is constantly collapsing, developing and degrading, one thing at a time, another tomorrow, and then the shape and position of the Gauss curve will be different. If one does not go from the position of a standard normal division, then to demonstrate the above-mentioned fact one can lean on the same curve of the degree of intellectual depravity of marriage.
The graph is an example of assessing the intellectual development of a spouse over a period of time. The green curve, which is at zero, shows the status of the reference “earlier”. Chervona and blue curves show the moment “at once”. Two curves (red and blue) are shown only as an illustration, since in a real situation there will be only one of them, and the partnership cannot develop and degrade overnight according to one and the same evaluation criterion. Analysis of one of the curves, for example, the red one, will show the axis such a picture. The marriage became wiser on two levels, which became the reason that those people who were previously respected as reasonable ones became an extraordinary phenomenon, those who were previously respected as geniuses began to often diverge and are no longer unknown and the most extreme, and not the most reasonable people They began to look upon themselves as little more than degenerates. The overall picture will be the same as the blue curve. Before speaking, I demonstrated very well the film “Idiocracy”, in which “a person with an average mind”, having died in May, emerged as the most intelligent person on earth, because over the course of a century, the marriage of the middle mind has deteriorated. ki, that is why the degenerate has become statistically average.
Based on this understanding, you can draw up these schedules, you can also evaluate the collapse of the marriage in the past, and make plans for the future based on the knowledge of how things are going to happen. For example, it was decided that the problem of alcoholism in marriage, which I considered the other day, can be oriented around this form. (This is my subjective thought, formed not by mathematical statistics, but by what I especially think about for myself.)
Here is the rigidity of the axis X , Behind the boundaries of this, the dimness of the crooked one lies blindly. On the drawn graph, I identified the clear boundaries of the observed phenomenon - from an ideological non-drinker to a binge alcoholic. It is clear that an attempt to estimate the point of the curve beyond this range is impossible due to the lack of value of the estimate. The rose flower development, of course, is also between the range, but it is true that it is so great that it is easier to mean it as inconsistency, rather than as limited in size. Also on the graph you can see the deformation of one of the curves, which is the natural state of the described object.
And so, on the graph of the red curve, the approximate state of the Russian Federation coping with alcoholism at this moment is shown. The green line demonstrates the level of speech about drinking alcohol “as it would be” in a normal (healthy and thinking) marriage. In such a manner, mi bachimo even more summary camp of speeches at this moment. As we begin to sort out people one by one, it is clear that the most common among them are passive alcoholics (a term I defined in the last article “Alcohol Arithmetic with Pictures”, which means a person regularly (every other day, once a week, once a month). those that you should like and sit on) that drink regardless of how much you drink). Those who allow themselves to drink (that is to say, vip, will not) and alcoholics will be equally likely to be involved. With even less confidence, drunken alcoholics are completely blinded. A person who does not drink in such a state of speech is a major relapse, and an ideological person who does not drink food, so the phenomenon has burned out in the extreme. (The ideal non-nourisher is a person who not only follows a sound way of living, but carries with it an ideology, for example, directly declares the principles of a healthy marriage.)
In a normal marriage (green curve), twilight may be the norm. With a minimal amount of water, a truly non-drinking person may come out. And the axis of the people’s life, which allows you not to be afraid of the glass, going to the area of relapse, and to become a little bit of a threat to marriage. As you understand, there are no passive alcoholics in that marriage, so the stench cannot be eliminated from anyone (they will be the open enemies of the people, through those who reduce the ethics and demography of the marriage). The remainder is expressed by the deformation of the green Gauss curve.
Pevna rich, in this crap text it is simply impossible to include the full range of possible options for establishing the law of normal division in sociology. Well, I’m sure that I’ve given you some ground for thought.
In my opinion, knowing this law, a mother, be a human being, is guilty of wanting to think a little about her future. And, as you know, it’s its own future, it’s right to lie down before the future marriage with the zhalom, i.e., the middle part in which we live. And since we know the skin, where, and the firebrand needs to go, then this is already a guarantee of success that we will go as far as possible.
________________________________________ ________________________________________ ____
One of the most important concepts in mathematical statistics is the concept of normal division. The normal distribution (also called the Gaussian division) is characterized by the fact that the extreme values of the signs tend to be rare, and the values close to the average value are frequent. The normal division is due to the fact that the fallout value is given due to the large number of independent fallout values, the skin of which plays an insignificant role in the light of all.
A normal division has a ring form, the values of the mode, the median and the arithmetic mean are equal to each other. It has been established that there are a lot of biological parameters of similar divisions (growth, moisture, etc.). Over the years, psychologists have realized that most psychological factors (indicators of intelligence, temperamental characteristics, abilities and other mental phenomena) also form a normal division. This principle underlies the standardization of test methods. With more sampling, the more rejections, the empirical distribution approaches the normal one.
The characteristic power of the normal division lies in the fact that 68.26% of all of them always lie in the range of ± 1 standard change from the arithmetic mean (no matter the value of the standard change). 95.44% - for borders ± two standard pads and 99.72 - for borders ± three standard pads.
A normal division - you understand. Classification and features of the category "Normal division" 2017, 2018.
The classic normal division THE NORMAL LAW OF THE ROSSIDAL GROWTH TO VIEW Lecture 6 The normal division or the Gaussian division is the most universal, simple and widely used. It matters what... .
Let's look at example 2, in which the X value is represented by a vibration (xi). These data were taken away by the operator under the hour of extinction of power and for help. The value of A is unchanged. The rapid drilling at the input and output of CI resulted in (xj) powdering in the range D = xmax -... .
Equal division Acts of absolutely uninterrupted distribution Meaningful. An equal division into a section is called a division with thickness. Meaning. A normal division with parameters and is called a division with strength. Ist...
Meaning 1. A non-interrupted variable value is called log-normally divided (lognormal), since it is a logarithm of suborders to the normal law of division. The fragments are uneven and equivalent, then the function of the division of the lognormal division... .
Value 7. The non-interruptible drop value has a normal division with two parameters a, s, and s>0. (5) The fact that the fall value is a normal division can be briefly written in the form X ~ N(a;s). Let us show that p(x) is thick (shown in... .
Value 7. The non-interruptible drop value has a normal division with two parameters a, s, and s>0. (5) The fact that the fall value is a normal division can be briefly written in the form X ~ N(a;s). Let us show that p(x) is the thickness (shown in...
Most experimental studies related to experiments, including those in psychology, which produce practically any values at a given interval (which is based on the sample size) are described by the model of periodic continuous quantities and in Supposedly – uninterrupted division.
One of the permanent divisions that plays a major role in mathematical statistics is the normal (or Gaussian) division. The normal division is the most important in statistics, which is explained by low reasons:
It has a ringing shape, symmetrical to the point M=X, with dots along the bend, the abscises of which stand in front of +.
For a normal division, mathematically, the dispersion and standard variation of the population is equal to (sigma).
The normal division is determined by two parameters: mathematical calculations (average) and standard calculations.
mode, median and arithmetic mean of the normal subdivision are avoided and equal to the mathematical calculation of M.
A lot of experimental precautions can be successfully described for the benefit of a close to normal population.
Most divisions knitted from the fall selection, with increased effort, proceed to the normal division.
The normal division is characterized by low friendly mathematical authorities, which provides plenty of information for their widespread stagnation among statistics:
Based on the fact that the normal distribution is generally determined by two parameters Mі (sigma), then, with these parameters being different, it is possible to identify a whole range of normal curves. In order to avoid the incompetence associated with disorders for a specific skin condition, psychology is called so-called normalized(or more often standard) normal brood, In order to standardize scales (psychometric lines)
The standard distribution is normal, with parameters M = 0 and = 1, and has a ringing form.
The peculiarity of this curve is that the area under the curve has a constant value (as shown in figure 1). This feature is fundamental for the standard interpretation in empirical studies using the method of making a psychological diagnosis: so, with the development of any signs, if the individual result falls within the range, it becomes 68.2% in and all types (that is, in 68.2% of the total population sampled, stage show the traced sign itself will be in this range), which can be assessed as the average manifestation of the traced sign and be interpreted as norm, show signs.
Fig.1. The 100-fold distribution of drops under the normal curve.
Standardized scales.
The indicators of psychometric tests, based on practical psychology, using the method of making a psychological diagnosis, are translated from the original ones ("sirish" - not subject to processing) and those tested after this test from standard indicators, which can be determined on the basis of a linear or non-linear transformation of the primary indicators (with the division of a close to the normal law). Moreover, historically there has been the emergence of a number of the most extensive standard indicators associated with peculiarities re-creation, i zvіdsi – the revelation of the “homeland” of standard scales, which are translated one into one and not reduced to the Z-scale.
The Z-scale is established as a result of centering, which is understood as a linear transformation of sign values, in which the average value of the subdivision becomes equal to zero, and the normalization procedure using additional mean-square changes.
The Z-score consists of a continuous continuum of Z-indicators, which are determined by the difference between individual initial results and the average values for the general population, divided into a standard division.
de X - neobrobleni, siri bali,
- Seredne,
– standard care.
When this is done, the Z-scale is set to the midpoint M = 0 and one vimiru (scale) 1 standard (single) normal subdivision, as shown in figure 2.
The Z-score can have both positive and negative values. Most of the differences (99.72%) of the values of indicators change at intervals -3 
, de Zp - re-creations of a standard display; b - standard treatment of the reconstituted rose; Z - Z-score; A is the average value of the reconstituted subdivision. Such a transition is legitimate, since the standard scale is an interval scale, which allows linear transformations to be eliminated, so that the constants are real numbers.
Let's look at the procedure for re-creating standard displays on the bottom of the butts:
An empirical study of the level of learning performance was carried out (institutional hospital Reizas - 0-90) on a sample of teachers (50 people) from various schools in M. Novgorod. As a result of the initial statistical analysis, the following results were obtained:
The division of the initial results ("siry scores") is close in shape to the normal division (after grouping procedures and analysis of the distribution curve - the frequency range).
The characteristics for this sample have been calculated –
It is proposed to carry out a linear transformation and calculate for different scales the value of one primary result X = 45 (the “serial score” of one of the last ones).
Change to Z-score follow the formula:
de Z-standard Z-score;
X is the first result of the test simulation;
M x – the average value of the sampling results (at the median);
S x – standard variation of this sample. Find the opposite sign on the Z-scale (Figure 2) and make a note about the appearance of the following sign that is being observed.
Conversion to T-scale for McCall's incubators is carried out using the already known formula (Zp = A + bZ), introducing the substitution of constants A = M = 50; 45) for standard T-balls according to the formula:
Thus, the result is 25 points (standard points).
Transformation to the stanina scale Gilford (English standardnine - standard nine), where assessments are given values ranging from 1 to 9, with M = 5, = 2, vibrating according to the formula:
In this case, the result of the trial will be 1 stanine (the result of C = 0 will be removed in the interval of the 1st stanine).
This C-scale has such miraculous power (magnificent little ones 2), that in the 1st and 9th stages it consumes 4% of the last selections, in the 2nd and 8th stages - 7% each, etc. In this way, with a ranked increase in the primary test results of the normal (or close to normal) division, the first 4% of the data are assigned 1 stanine, the next 7% of the data - the 2nd stanine, the next 12% of the data - the 3rd stanine And so on, in this way, the data will be ordered into a scale that corresponds to the standard frequency of the result.
Change to scalesten Kettel (from the English standardten - standard ten) for the 16PF incubator, where the ratings are assigned values ranging from 1 to 10, with M = 5; = 2 vibrate the formula:
Once again, the result of the test is lost in the interval of the 1st stage.
The intelligence tested has normalized scales:
Wechsler scale represented by IQ-standard scores:
Amthauer Intelligence Structure Scale following the formula:
To help interpret the data, lighting practitioners can use the Lehnert scale:
ScaleLinert's school grades:
Fig.2. The curve and standard indicators are normal.
Vibrant values are associated with significant differences. It’s worth talking about the fallacy when it seems impossible to unambiguously convey the result that can be seen in other minds.
Let's say we throw in a coin. Please note, the result of this procedure is not uniquely significant. It is possible to confirm with success that one of two things will happen: either “heads” or “tails”. Be that as it may, you will fall into disrepair. You can enter a variable that describes the result of this phase. Obviously, in this change we will take two discrete values: “heads” and “tails”. We definitely cannot transfer the fragments from behind, since we can accept the changeable values from two possible values, it is possible to solidify, in which case we can be to the right of the random values.
It is now acceptable that experiments are carried out to evaluate the reaction time of the tested presentation of any stimulus. As a rule, it turns out that what to do if the experimenter survives all trials before standardizing the experimental minds, minimizing or reducing to zero possible variations in the presented stimulus, The names of the magnitude of the reaction time of those tried all the same vary. It seems that the time of the reaction of the tested substance is described by a drop value. The fragments, in principle, in the experiment we can remove whatever the value of the reaction time is - there are no possibilities, the value of the reaction time that can be removed as a result of vimirvania appears to be infinite - to speak about continuity these are fall-off values.
Nutrition is to blame: what patterns can be discerned in the behavior of seizure values? The food appears to be solid.
So, if you throw an infinitely large number of coins, you can find that the number of skins on both sides of the coin will appear approximately the same, since, of course, the coin is not counterfeit and not bent. In order to understand this pattern, introduce the concept of the likelihood of a fallout. It is clear that when a coin is tossed, one of two possible options will inevitably become available. This is due to the fact that the total reliability of these two approaches, otherwise called complete reliability, is equal to 100%. If we assume that the differences between the two approaches associated with the testing of the coin are obtained with equal parts of the reliability, then the reliability of the skin result appears to be equal to 50%. Thus, theoretical measurements allow us to describe the behavior of this variable value. Such a description in mathematical statistics is designated by the term "division of subadult size".
This is a complex situation with a drop in value, which has a clearly defined value for the set, then. appears uninterrupted. Once again, we can name some important patterns of behavior. Thus, by conducting an experiment based on the reaction time of the tested product, it can be determined that different intervals of the test reaction of the tested product are assessed at different levels of toxicity. Shvidshe for everything, rarely, if you try to react to that shvidko. For example, in the case of semantic solution testing, it is practically impossible to respond more accurately with a speed of less than 500 ms (1/2 s). Similarly, it is unlikely that when you try, strictly following the instructions of the experimenter, you greatly delay your response. In semantic decision tasks, for example, reactions that are estimated to take more than 5 s are therefore considered unreliable. Proteus with 100% consistency can be allowed until the reaction time of the tested product appears in the range from Pro to + s. In addition, the severity is determined by the consistency of the skin-surrounding value of the epithelial value. Therefore, the division of the non-interruptible phase value can be described in terms of the non-interruptible function y = f (X ).
As we have on the right with a discrete variable value, if all possible values are known in advance, as in the case of a coin, the model of its section, as a rule, appears not very foldable. It is enough to introduce just a few reasonable steps, as we have done in the butt. A complex situation with a division of uninterrupted quantities takes on an unknown number of values. Actually, if we, for example, developed a theoretical model that describes the behavior of the experimentally tested reaction at the highest level of semantic decision, it could be tested on the basis of this model write a theoretical breakdown of the specific values of the time of reaction of the same test manifested by the same stimulus. However, this is not always possible. Therefore, the experimenter is tempted to assume that the division of the fallout value, which is what he is talking about, is described by some kind of law that has already been studied later. Most often, although it is possible and always appears to be absolutely correct, for these purposes the name of the normal division is used, which appears as a manifestation of the division of any kind, regardless of its nature. This division was first described mathematically in the first half of the 18th century. de Moivre.
Normal brood This may be the case when it is clear to us that there is an influx of an infinite number of variable factors that are equal to each other. Formally, a normal division, as de Moivre showed, can describe such relationships:
de X This is a significant value for us, the behavior of which we monitor; R - The value of the balance is related to the value of the drop; π ta e – Here are the mathematical constants that describe the relationship between the diameter and the basis of the natural logarithm; μ and σ2 – parameters of the normal subdivision of the fall value – clearly mathematically calculated and dispersion of the fall value X.
To describe a normal division, it is necessary and sufficient to measure the parameters μ and σ2.
Therefore, since we have a unique value, the behavior of which is described by equations (1.1) with sufficient values of μ and σ2, we can designate it as Ν (μ, σ2), without the memory of all the details of this quest.
Small 1.1.
Any division can be submitted in person according to the schedule. Graphically, a normal division looks like a ringing curve, the exact shape of which is determined by the parameters of the division, then. mathematical calculations and dispersion. The parameters of the normal division can be taken at almost any value that appears on the scale that is measured by the experimenter. Theoretically, the values of the mathematical calculation can be adjusted to any number in the range of numbers from -∞ to +∞, and the variance – to any non-negative number. Therefore, there are no different types of normal division and there are no curves to represent it (there may, however, be a similar ringing form). It’s clear that it’s impossible to describe them. However, depending on the parameters of a particular normal division, it can be transformed into the so-called to a single normal subdivision, Mathematical calculation of each is equal to zero, and dispersion is equal to one. Such a normal division is also called standard or else z-rozpodilom. The graph of a single normal division is shown in Fig. 1.1, it is obvious that the top of the ringing curve of the normal division characterizes the value of the mathematical calculation. Another parameter of a normal distribution – dispersion – characterizes the stage of “spreading” of a ring-like curve along the horizontal (abscis axis).