A right–left dichotomy of olfactory processes has been recognized on several levels of the perception or processing of olfactory input. On a clinical level, the lateralization of components of human olfaction is contrasted by the predominantly birhinal olfactory testing. The present analyses aimed at investigation of the relation of such side-differences related with the subject's age, sex and with the cause or degree of olfactory loss. The detection of 12 different odors from a validated clinical standard test of human olfactory function was assessed separately for both nostrils in a cohort of 6016 subjects who had reported for olfactory loss associated with different etiologies. In 26.8% of all odor identification tasks, the same odor was correctly identified only when using one but not the other nostril. Beside the subjects’ age, associated with reduced olfactory performance, the analysis identified additional modulators of the agreement between nostrils, quantified as Cohen's kappa. Classical hierarchical clustering and machine-learning based deep clustering resulted in a consistent cluster structure of odors. This structure could be interpreted as possibly owing to different familiarity of the odors. The observation particularly owed to olfactory loss attributed to head trauma, which may hint at a different impact on the left or right hemisphere processing of olfactory input. Thus, between-nostrils agreement in odor identification is limited and the common unilateral olfactory testing probably misses important information. Lateral differences owe to age, sex, kind of odor and etiology of olfactory loss.