The stochastic experimenting plug-in supports modelling and simulation of multiple experiments with random generators like dice, coins, and urns. It contains other elements to build up a micro-world for exploring probabilistic problems through experimenting like control elements to repeat an experiment, data collectors to store the results, filters for automatic sorting or analysis e.g. in lotto experiments. Further elements support collaborative activities. Special emphasis is put on the visualisation of the outcomes in form of a table, as bar charts for absolute or relative frequency or as an estimated result. All types of stochastics problems based on urn models can be modelled and explored in an empirical way.
The palette contains an index card with several tabs to switch between the different index cards. Besides the index cards there are buttons with different types of edges, which either represent a simple connection or fulfil a special task.
The first index card offers a variety of urns. The second index card shows different drawing nodes and collectors. The third index card allocates various types of representation of results and the forth index card offers the possibility to choose a filter according to which the results or its elements should be analysed or arranged. The fifth index card contains a help function.
The plug-in “stochastic experiments” is based on the model of stochastic urns. Urns are container in which you fill elements and whose content you cannot see while drawing elements from it. You take a “blind choice”. The different types of urns differ concerning their filling; some of the urns are adjustable, some are not.
Tetrahedron, Dice, Coin
The tetrahedron, the die and the coin are non-adjustable urns. The tetrahedron can only take status 1 to 4, the die only 1-6 and the coin only the status face or versa. These three types of urns do not have to be refilled; they are always represented in their initial state.
The calendar is an urn that cannot be changed, but refilled. The initial state shows the 1st January of a normal year. After drawing the 26th February is shown on a torn off calendar sheet.
By choosing the function “refill“ the calendar is restored to the initial state.
The lotto-urn is one of four adjustable urns. You can change the population of this urn arbitrarily. The picture shows the lotto-urn containing elements 1 to 49. But you can also instantiate this urn to contain elements from e.g. 20 to 40. The lotto-urn is typically used to model a lotto game and the urn is usually left in the original setting containing elements between 1 to 49.
In addition to the lotto-urn there are three more adjustable types of urns. The first of these three types offers the possibilities to change the number of coloured balls it contains in its initial state. The second of these urns is called the "adjustable urn". By clicking on “adjust“ a window with the title “adjustable urn“ is opened. In this window you can choose if the six elements should be marked with colours (black, white, red, green etc.) or with numbers (1, 2, 3, et.)and you can also determine the quantity of each element. Zero is a possible value too. The quantity can be changed arbitrarily by drawing or typing in the desired number. Attention! The urn does only contain a maximum of 100 elements! You additionally have the possibility to change the icon that illustrates the contents of the urn. To change the icon click on the button "change icon" and a file chooser dialogue starts in which you can set a picture of you choice.Confirm with “ok“ to store your selected settings. If you use the cross to close the window the new settings are not stored and the primary settings are maintained.
Drawing Nodes and Containers¶
These different elements are combined on the second index card. Besides the urns the drawing node are an essential part of the plug-in. Besides the normal drawing node, which is not modifiable and allows "simple drawing" you can also find a drawing node which offers the possibility to repeat experiments.
Besides the drawing node this index card offers the so-called containers or collectors. These collect what was drawn and store results of experiments. The results can later be recalled. You can choose between different types of containers.
The blue collector collects what was drawn and stores results of experiments. The results can be recalled. They are collected in form of tables listing the elements of each drawing. The number of the currently shown table and the total number of collected tables are displayed. You can delete the currently shown table (red cross) or empty the collector (red double cross).
The green converter collects what was drawn and stores results of experiments. Whereas the collector stores the result of each experiment in a separate table the converter combines the results of all experiments in a single table. In this table each row consists of the elements of one experiment. The converter can be emptied (red double cross).
The violet converter is used for collaborative simulation. It cumulates the results of simulated experiments done by different group members in a shared working session.
The Bernoulli collector helps to analyse Bernoulli chains. Such chains are investigated concerning a special result e.g. face. In each experiment the frequency of the results will be determined and cumulated. The distribution can be visualsized using a display element.
A typical example of usage becomes clear when modelling a lotto game.
Nodes for representing Results¶
The size of these types of nodes can all be changed as you like. In order to change the size click on the particular node and small black quadrangles appear. Drag the view to the desired size using your mouse.
The typical representation element offers three different views. View 1 shows a numbered listing of the results of the experiments. View 2 shows the frequency distribution of the results and the absolute frequency (in brackets) in form of a bar chart. The third view shows the relative frequency as percent distribution of the results in form of a bar chart. At the top of this view on the left side you see a symbol with a disk. By choosing this symbol you can export data in CSV format. You get a text file in which the particular data sets that belong together are divided by commas and can be imported in to spread sheets or SPSS for example. By choosing the symbol that is located on the right you get a larger presentation of the nodes contents that is especially suitable for the visualisation for an audience. With the A-symbols in the middle of the window you can adjust the font size.
This table is designed for the use in shared workspaces. You can change the title of the columns. Each cooperating group reports the results of their experiments to inform the others.
The third node calculates the probability of an event defined by a filter setting.
The fourth of these nodes creates a text that documents the underlying model of the experiment. It gives information about which elements(nodes and edges) have been used and in which way they are linked to each other.
The edge mode is activated by clicking on the desired edge in the plug-in window. Thereby you differentiate between two different modes. You either choose the function “only one edge“ which means that the edge mode is automatically deactivated after drawing one or you choose an edge-type which stays activated until you deactivate it by clicking on the particular button in the plug-in window. An edge is drawn by dragging the mouse with a pressed left button from the start node to the end node. By choosing the function "delete edge" you can delete an edge by dragging the mouse with a pressed left button between the nodes. The plug-in offers you four different types of edges.
1 Draw without put back
This edge is only allowed to connect an urn and a drawing node. The number at the edge can be changed arbitrarily. It indicates, how many elements are drawn when you press “execute“ once. A “6” at the edge for example means, that 6 elements are drawn immediately when you press execute without putting the elements back into the urn. Because of this a drawn element can only occur once as a result. (Attention:
similar elements can occur several times in the urn).
2 Draw with put back
By choosing this edge an element is drawn and directly put back. This edge is only allowed to connect an urn and a drawing node! Concerning a die or a coin it does not matter which drawing edge you choose, because the number of elements stays constant.
3 Simple edge
This edge establishes a simple connection between two nodes (container, representation nodes, …).
4 Delete edge
With the help of this function the desired edge is deleted by drawing between the involved edges.
5 Separation edge
This edge allows it to split the elements of a drawing when used after the drawing node. The ordinal numbers at the edge selects the particular elements of each experiment. You can specify the elements listing up their ordinal numbers separated by “;”, you can define spans using “-“, or you can select “all”.
The plug-in provides three different possibilities to filter results and another node to combine elements.
The first filter is similar to a lotto coupon. Here you can type in your tips before you start and decide which and how many results you want to get displayed/reported. By clicking on the field with the pull down menu you are shown the different options. In the field next to it you can type in the desired number of hits.
The second filter is used to filter results with a fixed number of identical or different elements. You can choose how many elements have to be identical or use “at least” or “at most” to set boundaries.
The third filter is for sorting the drawn elements in an ascending order.
The forth node is necessary in a model if elements have been split for selective analysis with filters. To combine the elements again to a single tuple this node is used followed by a separation edge. For more details look at the description of the edges.