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The probability of solving a crime drops dramatically when there are no witnesses of any kind.
These two parameters relate negatively (θi – δi), because the probability of solving an item increases with the person's ability but decreases with greater item difficulty (Wright & Stone, 1979).
It can also become a concern if certain tasks require a large set of skills, as one might claim that the probability of solving a task decreases with an increasing number of necessary skills.
We wanted to check whether different types of instruction differentially influence the probability of solving single items, which would ultimately change the meaning of the underlying construct that should be unambiguously measured independent of type of instruction.
In a pre-post instruction design, students complete the bMCU test repeatedly, as a pre- and as a posttest, which would be problematic if re-testing differentially influenced the probability of solving single items.
The probability of solving an item depends only on the respondent's ability, or proficiency, and two item parameters characterizing the properties of the item (item difficulty and item discrimination).
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If assigning an extra worker to m2 produces a greater marginal gain in the total probability of solving the problem than assigning her to m1, then the worker should be assigned to m2.
For a dichotomous item in the Rasch model, the item information is P i × (1 − P i ), where P i is the probability of correctly solving item i. Accordingly, the maximum value of each item information curve in the dichotomous Rasch model is 0.25 at P i = .50.50
Consequently, if a specific person's ability B n complies with a specific item's difficulty D i, the person's probability of solving this item is P ni = .50.50
So although humans will hopefully save us (we do, in fact, desperately need brilliant people to develop scaleable technology to remove carbon from the air, for instance), the solution to this cannot be to have as many babies as possible, with the hope that this raises our probability of solving the problem.
But if he/she has a skill-deficit in at least one of the skills needed for a particular task, he/she has only a low probability of solving the task correctly.
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