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Histogram of distribution.
Distribution of values of parameters supplies an important information about probability for it to appear in any given numerical interval. Visually distribution of one parameter usually is presented in form of histogram. To create initial raw data of distribution of one parameter the following procedure have to be performed:
The examined interval where appearance of the measured number is supposed to be relevant (most logical it is interval between minimum and maximum of observed numbers but can be larger or smaller for some special reasoning) is divided by equal subintervals, bins. Although number of subintervals could be any positive integer there is intuitively obvious demand that some sort of optimum between conflicting needs in most possible reveling situation in any part of whole domain and number of cases fallen into each of subintervals. LeoStatistic provides ability for user or to select number of subintervals by arbitrary decision or by choosing optimum automatically by algorithm incorporated into program.
To create histogram of one parameter set state of all examined parameters as "Value". In case of two variables these are belonged two the same series this scheme is not available and three dimensional distribution will be presented instead. To get nevertheless x-y histogram of two variables import outside data two times creating two series choosing at first one variable from available and then other.
If as is given by default the presenting scheme is array with equal steps, to switch it to histogram style go to "View" tab of the control panel and press on button. To manage conditions of histogram building go to "Statistics" tab of control panel:
It permits to perform following operations:
Conditional parameters in LeoStatistic can be defined as a array of "filters" each of them characterized by: parameter to apply, logical operation to perform and interval in parameter values valid to. "Logical operation" is the only concept here that is not quite self-explanatory. There are four values user can choose from:
To determine is the conditions are true the software at first will check all or style conditions and assign true as soon at least one of them is fulfilled; then all and conditions is checked and if any of them will be false whole expression will will be assigned to false. Note that if there will be only one or style condition it will act in the same way as one and condition.
User has a choice manually add conditions one by one or to use automatic algorithm to find set of conditions that create subset of parameters with maximum probability not random selection.
In LeoStatistic a probability that conditional selection is not random is calculated by empirical procedure. The main idea of the algorithm is in calculation of mean and standard deviation of randomly selected subsets of examined parameter and compare these with mean of checking subset. The farther if from average of randomly selected selected subsets the more probable that is not random by itself. The numerical value of probability is calculated on the base presumption of student distribution. The actual algorithm implemented in LeoStatistic is slightly more sophisticated taking into consideration possible symmetry in non random selection.
When analyzing experimental data each record contains two parameters, two major cases should be considered. One of them is described in other place when on the chart with x-y Cartesian coordinates points are grouping around some curve. Other is the map like situation when any area of the chart can be characterized by concentration of the points. If divide the area where data are by perpendicular grid creating mesh with rectangular elements and calculate number of points fall in each of them we will fulfill this task. LeoStatistic is doing exact this, producing a value Nij(x,y) - number of cases belonged to the intervals from xi till xi+stepx and from yj till yj+stepy where x and y are examined parameters; stepx and stepy - widths of mesh elements along both coordinates; i and j - indexes of the mesh.
Leo Statistic offers an options to display Nij(x,y) either in form three dimensional mesh or as a color map these can be switched by user in the "View" tab..
Number of intervals area divided by both coordinates can be modified in the tab "Statistics" of the control panel:
Except of modifying level of resolution for observing distribution of data the search of area with "maximum density" of points concentration can be performed by checking up a corresponding control.
Screenshots of the LeoStatistic software:
click on picture to enlarge
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