In a study that investigated the relationship between television watching habits

Question

In a study that investigated the relationship between television watching habits and work productivity, researchers asked respondents three items related to their TV watching: However, when the researchers ran their item response analyses, they realized they never learned how to interpret them - so they called you. Your task is to describe what is happening in the figure below. Specifically: (a) briefly describe what we are looking at - what do "discrimination" and "ability (or theta)" represent in the context of the study? interpret the three curves for someone at theta = -2, and describe to the researchers what that means; (c) describe how we would determine whether a curve reflects "good" discrimination; and (d) based on that information, suggest to the researchers which item(s) they should keep and which item(s) they should remove, and be sure to explain why you are offering those suggestions

Explanation / Answer

(a) Discrimination provides evidence on how well an item successfully divides people of a particular aptitude on the hypothesis. Discrimination is measured by examining the slope of each item characteristic curves. An item having a steep slope which points more vertically is more efficient in separating participants’ response on the factor. On the flipside, an item having a slope similar to a horizontal line is useless in discerning performance levels in the hypothesis. Whereas, Theta or ability factor ranges on a continuum from low to high, ranking participants in terms of overall performance on teh ability factor.

So in the context of teh study, the slope of item 1 is similar to a horizontal line, that of item 3 has teh steepest slope and that of line 2 intermediate to item 1 and 3.

Thus item 1 is useless in distinguishing the effect of work performance on the televison watching participants. Whereas item 3 has the highest relation of work performance on the televison watching participants.

(b) With Theta in the center of the graph, assuming that Theta = -2 is somewhere closer to the left end of the chart.

At Theta = -2, the point on the line of item 1 will be higher placed than those of item 2 with line 3 being the lowest. This would imply that the response to item 1 will have more affirmative responses than response of item 2 and item 3, repectively.

(c) As defined above, "An item having a steep slope which points more vertically is more efficient in separating participants’ response on the factor. On the flipside, an item having a slope similar to a horizontal line is useless in discerning performance levels in the hypothesis."

(d) Therefore, by definition, item 3 has the best vertical slope so the curve for item 3 reflects "good" descrimination while the other two curves (i.e. item 2 and item 1) are moderate and bad decriminators respectively. Researchers should definitely keep item 3 and get rid of item 1.

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