Item Characteristic Curves

This chapter provides an overview of the psychometric properties of the HSOPSC using both classical test theory (CTT) and the modem approach, often referred to as Item Response Theory (IRT). To enhance the understanding and importance of IRT, the basic principles will first be introduced. In partictrlar, three fundamental outcomes of the IRT approach will be highlighted (1) item characteristic curves, (2) measurement information, and (3) invariance. Moreover, this chapter will present data that have been previously analysed and... 

Item Characteristic Curve (ICC) IRT is a group of measurement models that describe the mathematical relationship between underlying latent construct of safety culture and the uKhviduaPs performance (observed item responses) as a logistic function called an item characteristic curve (ICC). Each single item in a 5-point Likert-type response format is characterised by an ICC defined by the estimated slope parameter and 4 item location parameters representing the movement from the lower options to the higher options of the Likert scale. 

Figure 8.1 Hypothetical Item Characteristic Curves (ICCs) based on estimated item discrimination a (slope parameter) and item difficnity b (fonr location parameters)...

The amount of measurement information can be derived from the item characteristic curves by providing a number that represents an item s ability to assess individual differences at each level of patient safety culture. In particular, items with location parameters spread across the full range of the underlying safety culture scale provide measurement information throughout the measured construct. Moreover, items with higher discrimination power provide more measurement information than those with lower slope parameters. 

A third fundamental of IRT is related to invariance, which has two implications. Firstly, the person parameter G (cf Table 8.1) can be estimated from responses by an individual to any set of items with known item characteristic curves (Reise et al. 2005). Secondly, the estimated item slope and location parameters are independent of the sample under study (Reise et al. 2005). This invariance is displayed below, where individuals with low levels (Figure 8.2a) and with high levels (Figure 8.2b) of safety culture perceptions responded to the same item. 

Figure 8.2a Item Characteristic Curves (ICCs) fitted to a group with low levels of safety culture perceptions...

Table 3.3 shows the operating characteristics for a normal inspection level sampling plan with a sample size (i.e. number of items examined) of n = 200 at three different AQLs. This table shows that if a product has 3% nonconforming items (p) then, using an AQL of 2.5%, approximately 95% of lots would be expected to be accepted. Operating characteristics curves are given in ISO 2859-1. 

This equation describes an operating characteristic" curve—the relationship between the percentage of contaminated items in the universe and the probability of accepting or rejecting the universe on the basis of finding at least one contaminated item in a sample of a specified size (N). 

Stress—Strain Curve. Other than the necessity for adequate tensile strength to allow processibiUty and adequate finished fabric strength, the performance characteristics of many textile items are governed by properties of fibers measured at relatively low strains (up to 5% extension) and by the change ia these properties as a function of varyiag environmental conditions (48). Thus, the whole stress—strain behavior of fibers from 2ero to ultimate extension should be studied, and various parameters should be selected to identify characteristics that can be related to performance. 

Acceptance sampling is a widely used technique for economically assessing the quality of a lot of items. A single-sampling attributes plan of the form (n, c) specifies that n items wiU be sampled and the lot will be accepted if no more than c < n defective items are discovered. The values of n and c are chosen based on the operating characteristic (OC) curve they imply. The OC curve is the probability of accepting a lot as a function of the lot quality, where quality is usually stated in terms of the probability of a defective item (see Chapter 69 of the Handbook). 

The Operating Characteristic function and curve represent the probability of accepting a product over a range of nonconforming items or proportions. 

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