4 Important Types of Item Characteristic Curve (ICC)

Introduction

Item Characteristic Curve (ICC) is a graphical representation of relationship between the probability of correct P(θ) response and a test takers ability (θ).  It is used to evaluate the psychometric properties of tests like reliability, difficulty, and discriminatory power

The term “Item Characteristic Curve” was coined by Ledyard Tucker in 1946. It is one of the main IRT concepts. These approaches allow for a deeper understanding of individual test items and their contribution to assessing latent traits, such as abilities or attitudes, in test-takers.

Also known as Item Response Function (IRF).

ICC is a mathematical equation that describes the relation between the amount of a latent trait an individual possesses and the probability that he or she will give a designated response to a test item designed to measure that construct.

Item Characteristic Curve (ICC) graphically depict the relationship between an individual’s ability level and their probability of answering an item correctly, while IRT provides a theoretical framework for understanding item behavior and improving the efficiency and validity of assessments.

Read More- Psychological Test

Item Characteristic Curve (ICC)

The ICC is a fundamental tool in item analysis. It provides a graphical representation of how an individual test item performs across varying levels of a latent trait. The curve illustrates the probability that an examinee with a specific ability level will answer the item correctly.

Structure and Components of ICCs

The ICC is plotted with the total test score, an approximation of the latent trait, on the horizontal (X) axis, and the proportion of test-takers answering the item correctly on the vertical (Y) axis (Aiken, 2008).

• Horizontal (X) axis- the total test score is plotted on – test takers ability (θ).
• Vertical (Y) axis – the proportion of examinees who get the items correct- probability of correct P(θ) response.

The X-axis represents the examinees’ estimated ability, while the Y-axis shows the likelihood of success on a given item. Each test item generates a unique curve that reveals its characteristics, such as difficulty and discriminability (Guion & Ironson, 1983).

The curve is bounded between 0 and 1.

It is monotonically increasing, and is commonly assumed to take the shape of a logistic function.

Each item in a test has its own item characteristic curve.

Purpose of Item Characteristic Curve (ICC)

The ICC serves multiple purposes in test development. First, it provides insights into how well an item measures the intended construct. For example, a well-performing item should show a gradual increase in the probability of correct responses as the examinee’s ability increases (Holland & Hoskens, 2003).

Second, ICCs help identify items that may not function as expected, such as those that fail to discriminate between different ability levels or that unfairly favor certain groups of test-takers.

Drawing Item Characteristic Curve (ICC)

To construct an ICC, test-takers’ scores are grouped into discrete categories, which can be as specific as individual test scores or broader intervals, depending on the sample size (Penfield, 2003a). The proportion of test-takers in each category who answered the item correctly is then plotted against the corresponding ability level. Smoother curves can be obtained by using fewer categories or by increasing the sample size.

Item Characteristic Curve ICC for several items

For example- consider an item on a math test. To draw its ICC, researchers calculate the proportion of test-takers with scores in the range of 65–70 who answered the item correctly, then repeat this calculation for other score intervals. The resulting data points are plotted and connected to form the curve.

Read More- Reliability

Types of Item Characteristic Curves (ICC)

ICCs vary depending on how well an item performs. Several types of curves illustrate different item characteristics-

1. Good Items-

These items show a steady upward curve, indicating that the probability of answering correctly increases as ability increases. Such items effectively discriminate across all ability levels (Yanai, 2003).

Item Characteristic Curves (ICC) for a Good Item

2. Items with Limited Discrimination-

Some items only discriminate at certain ability levels. For instance, an item might perform well for lower ability levels but fail to distinguish between moderate and high ability levels.

3. Poor Items-

Poor items produce flat or irregular curves. A flat curve suggests that test-takers at all ability levels have an equal chance of answering correctly, indicating the item does not measure the intended trait. An irregular curve may indicate a flaw, such as a trick question or ambiguous wording (Reise & Waller, 2003).

Item Characteristic Curves (ICC) for a Poor Item

4. Problematic Items-

Occasionally, ICCs show a downward slope at high ability levels, which may occur when highly knowledgeable test-takers overthink or misinterpret the item. For instance, “none of the above” options in multiple-choice questions can confuse highly skilled examinees (Hayes, 2000).

Applications of ICCs

ICCs are invaluable in test development and evaluation. By analyzing ICCs, test developers can:

1. Identify and Remove Poor Items- items that fail to discriminate effectively or show bias can be eliminated, enhancing the test’s validity and reliability (Schmidt & Embretson, 2003).
2. Improve Test Sensitivity- ICCs highlight the ability ranges where items are most sensitive, allowing test developers to include items that cover a broad spectrum of abilities (Meijer, 2003).
3. Optimize Difficulty Levels- items with moderate difficulty (i.e., a 30%-70% passing rate) and good discrimination are ideal for most tests. ICCs help in selecting such items (Guion & Ironson, 1983).
4. Evaluate Bias- ICCs can reveal whether an item functions differently for subgroups of test-takers, aiding in the detection of bias (Holland & Hoskens, 2003).

Read More- Validity

Conclusion

Item Response Theory and Item Characteristic Curves have revolutionized the field of assessment by offering precise tools for understanding item performance and measuring latent traits. ICCs provide valuable insights into item discrimination and difficulty, while IRT allows for the development of more reliable, valid, and adaptive tests. Despite its challenges, IRT’s benefits far outweigh its limitations, making it a cornerstone of modern psychometric research and practice.

References

Aiken, L. R. (2008). Psychological Testing and Assessment. Boston: Allyn and Bacon.

Guion, R. M., & Ironson, G. H. (1983). “Item analysis and test construction.” Annual Review of Psychology, 34, 73-101.

Gregory, R. J. (2014). Psychological Testing: History, Principles, and Applications (7th ed.). Pearson.

Kaplan, R. M., & Saccuzzo, D. P. (2018). Psychological Testing: Principles, Applications, and Issues (9th ed.). Cengage Learning.

Hayes, J. R. (2000). The Complete Problem Solver. Philadelphia: Taylor & Francis.

Holland, P. W., & Hoskens, M. (2003). “Classical test theory and item response theory.” Handbook of Psychological Testing.

Meijer, R. R. (2003). “Computerized adaptive testing: Advances and challenges.” Applied Psychological Measurement, 27(3), 181-194.

Penfield, R. D. (2003a). “Examining the assumptions of IRT models.” Educational and Psychological Measurement, 63(6), 906-913.

Reise, S. P., & Waller, N. G. (2003). “How many IRT parameters are enough?” Psychological Methods, 8(2), 164-181.

Schmidt, F. L., & Embretson, S. E. (2003). “Modern measurement: The promise and pitfalls of IRT.” Psychological Science in the Public Interest, 4(2), 103-120.