Another element in understanding reliability is assessing item and test information using item response theory (IRT; Ayearst & Bagby, 2010). Higher information on items and tests (i.e., scales in this context) indicates greater measurement precision and lower measurement error. We focus on test information in this section as it applies to the reliability (precision of measurement) of the scales. Item information was a contributing factor in the item selection phase and development of the Conners 4 scales (see chapter 6, Development, for more information). One of the benefits of item and test information is the recognition that the degree of precision in measurement can vary across the trait level (i.e., an assessment may be more precise in measuring individuals who are at a certain level of the construct, and less precise in other ranges). In contrast, classical test theory (CTT) reliability assumes the test works equally well across all levels of the trait (Ayearst & Bagby, 2010). For the Conners 4, test information at higher levels of the trait or construct being measured, specifically approaching and exceeding 1.5 SD above the mean, was prioritized. The purpose of the Conners 4 is to assess clinically significant symptoms, associated features, and functional impairments or outcomes related to having ADHD—which is represented by scores that fall 1.5 SD above the mean (i.e., Elevated T-score range)—rather than to measure the full spectrum of behaviors associated with attention and activity.

Test information is assessed using a test information function (TIF), which plots the precision of the test across all levels of the construct being measured. The inverse of the TIF is the conditional SEM (for a detailed explanation of SEM, see Standard Error of Measurement in this chapter). Therefore, the least amount of error in a test is at the peak of the TIF (Ayearst & Bagby, 2010; Embretson & Reise, 2000). Guidelines for interpreting test information suggest values greater than 10 indicate high precision, values below 10 are moderately precise, and values close to 5 are considered adequate. These recommended guidelines (above 10, between 5 and 10, and less than 5) are approximately set at standard errors of .44, .39, and .32, and reliability coefficients of .90, .85, and .80, respectively (Flannery, Reise, & Widaman, 1995; Reeve & Fayers, 2005).

An analysis of test information was conducted on the Total Sample (i.e., all general population and all clinical cases combined; see chapter 6, Development, for a description of the samples), to provide maximum information in estimating these functions via the mirt package in R (Chalmers, 2012). As seen in Figure 8.1, the Parent and Teacher forms of the Conners 4 demonstrate high precision across all scales. The Self-Report form ranges from adequate precision for the Family Relations scale, to precision that is moderate to high across other scales. The peak of the curve for most scales is at approximately 2 SD above the mean, and the area under the test information functions (or curves) is wide, such that precision is fairly consistent from average levels of the construct (i.e., when theta, on the x-axis, is at 0) to 2 to 3 SD above the mean, depending on the scale. Additionally, the peak of the curve extends well beyond information values of 10 for Parent and Teacher forms, which indicates very high precision of measurement, or reliability, for each scale. The high degree of precision and small degree of error at the target ranges, as demonstrated by the test information functions in Figure 8.1, provide further evidence of the reliability of the Conners 4 scales.

Figure 8.1. Test Information Functions by Scale: Conners 4

a) Inattention/Executive Dysfunction	b) Hyperactivity
c) Impulsivity	d) Emotional Dysregulation
e) Depressed Mood	f) Anxious Thoughts
g) Schoolwork	h) Peer Interactions
i) Family Life	j) DSM ADHD Inattentive Symptoms
k) DSM ADHD Hyperactive/Impulsive Symptoms	l) DSM Total ADHD Symptoms
m) DSM Oppositional Defiant Disorder Symptoms	n) DSM Conduct Disorder Symptoms