i would like to help but i need you to be more precise about few things:
1) which version/s of the ANT are you referring to?
2) are you comparing groups (control vs clinical)? or you have only repeated measurements?
3) it seems like somebody already dealt with (at least part of) this problem; check out these papers:
a) Ishigami and Klein: Repeated measurement of the components of attention using two versions of the Attention Network Test (ANT): Stability, isolability, robustness, and reliability. Journal of Neuroscience Methods, 2010
b) McConnel and Shore:. Mixing Measures: testing an assumption of the attention network test. Attention, Perception, Psychophysics 2011.
To put it simply, I want to know how reliable the test is just as a general measure of attention. I am not interested in assessing orienting and alerting as separate components.
as MacLeod et al (2010) reported ---> three years ago:
[.. Since the initial description of the ANT (Fan et al., 2002), attention network function of many special populations has been examined using this task, including individuals with dyslexia (Bednarek et al., 2004), schizophrenia (Wang et al., 2005), borderline personality disorder (Rogosch & Cicchetti, 2005), depression (Murphy & Alexopoulos, 2006), attention-deficit hyperactivity disorder (ADHD; Adolfsdottir et al., 2008), and 22q11 deletion syndrome (Bish et al., 2005). It also has been used to examine the heritability of attention networks (Fan et al., 2003; Fossella et al., 2006; Fossella, Sommer, Fan, Pfaff, & Posner, 2003), and the effectiveness of mindfulness training (Jha et al., 2007; Tang et al., 2007; Zylowska et al., 2008). Many studies have used ANT results to claim that a clinical population demonstrates an attentional deficit in a specific attentional subsystem, rather than a general attention deficit....]
Of course this doesn't mean that the test is 100% "reliable" (some authors have argued against the use of the ANT because of the low test-retest coefficient found in the original paper) but it is widely used and literature is increasing exponentially.
If you are not interested in assessing INDEPENDENTLY orienting and alerting, then my suggestion is to use the ANT-R version (Fan et al., 2009; Mackie et al., 2013) created to test the behavioural interaction and integration of the attentional networks.