IRT mini-tutorial

This is an interactive demonstration to help you better understand the 3 parameter Item Response Function:

Pij() = P(ui=1 | , ai, bi, ci) = ci + (1 - ci) / [1 + exp(-1.7 ai ( - bi)]

which states that the probability of a correct response to item i for examinee j, Pij() or P(ui=1) is a function of three item parameters, ai, bi, ci, and one examinee ability parameter . You can create imaginary test items by specifying the three item parameters ai, bi, ci. The computer will then generate two curves. The first curve will be the Item Response Function for your item as defined by equation (1). The computer will calculate the probability of a correct response to your item for values of ranging from -3.0 to +3.0 and then plot against the probability of a correct response given .

The second curve will be the Item Information Function,

I()= P()' d / [P() (1 - P()],

which shows the information provided by your item at each value of and is based on the Item Response Function. The computer will calculate values of I() for ranging from -3.0 to +3.0 and will then plot I() against .


Please pick your item parameters:  ai bi ci

What to observe

  1. The horizontal axis is the ability scale, ranging from very low (-3.0) to very high (+3.0). The vertical axis the is the probability of responding correctly to this item (defined by the three item parameters) given = .
  2. The lower asymptote is at ci. This is the probability of a correct response for examinees with very little ability (e.g. = -2.0 or -2.6). The curve has an upper asymptote at 1.0; high ability examinees are very likely to respond correctly.
  3. The bi parameter defines the location of the curve's inflection point along the theta scale. Lower values of bi will shift the curve to the left; higher to the right. The bi does not effect the shape of the curve.
  4. The ai parameter defines the slope of the curve at its inflection point. The curve would be flatter with a lower value of ai; steeper with a higher value. Note that when the curve is steep, there is a large difference between the probabilities of a correct response for a) examinees whose ability is slightly below (left) of the inflection point and b) examinees whose ability is slightly above the inflection point. Thus ai denotes how well the item is able to discriminate between examinees of slightly different ability (within a narrow effective range).
Suggested activities: (You may want to print this page rather than scrolling up and down.)

  1. Try different values for the ai parameter
    Notice that

  2. Try different values for the bi parameter
    Notice that

  3. Try different values for the ci parameter
    Notice that