Clicking the Go button will start a new simulation and/or analysis using the values specified in the menu.
exception: using option 1 to leave the analysis out, and next another option, the analysis will take affect ony at the second ‘Go.’
The simulation simulates test scores for the specified number of observations or cases, assuming mastery having the value specified; the resulting distribution of test scores will be plotted as a solid green bar diagram. For larger numbers of observations the simulation will will be closer to the binomial distribution plotted in blue. If you want the analysis only, turn the simulation offf by putting the number of observations = 0.
The analysis evaluates a probability distribution function called the binomial distribution; the distribution plotted is this mathematical distribution. The binomial distribution is the theoretical distribution of test scores given a particular mastery, for the number of observations growing very large. If you want the simulation only, put option = 1 to turn the analysis off.
Mastery may be chosen between 0 and 1; mastery as a concept is defined on the set of test items that every concrete test is supposed to have been sampled from: it is the proportion of items the candidate would answer correctly if given the opportunity to try alle items in the domain.
The number of test items is the length of the test; this number is not limited.
The number of observations or runs is the number of runs for the simulation, or, equivalently, the number of cases or persons that is represented in the simulated distribution.
The reference point is a particular test score that is of interest to the user of the applet. It might be the cutoff score in pass-fail testing, the minimum score that is still considered to be a level of sufficient mastery, etcetera. It is marked by a solid vertical in the plot. Its value may be set at 0.
The horizontal scale is that of test scores obtained, the lowest score being 0.
The vertical scale as a default will be automatically chosen and depends on the highest value of the analytical distribution, this point is tabmarked. The vertical values are frequencies in the case of simulations, and probabilities in the case of analyses. Their values may be plotted using option 203 and 204, respectively. Of course frequencies and probabilities will be comparable. In fact, option 2 will plot the vertical differences separately.
The statistics reported are the mean and standard deviation for every distribution. Because the theoretical value of the binomial statistics assumes the number of observations to be infinite, there will be small differences between the actual statistics and the statistics obtained by evaluating their formulas. Simulation and analytical statistics will differ from each other, of course; the differences wil be smaller the larger the number of observations is chosen.
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