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.’

- Be aware that all parameters, as well as the option, must hae a specific valuse. The applet will not run on either a blanc, or anything else that is not a discrete or real number.
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 reported
**probability**is the proportion of scores equal to or*higher*than the reference point. - The
**option**option will make it possible to run special analyses without cluttering the menu of the applet; available options will be mentioned in the applet window if option = 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.

Mail your opinion, suggestions, critique, experience on/with the SPA

August 30, 2009
\ ben at at at benwilbrink.nl

http://www.benwilbrink.nl/projecten/spa_applet1.sa.htm