Measurement in Psychology is a complicated process involving numerous theoretical and empirical steps. Ensuring our measures are operating the same way in different groups of people is a further step referred to as Measurement Invariance testing. Measurement Invariance occurs when the factor loadings and item intercepts or thresholds of a scale operate similarly for people at the same level of the latent variable in different populations. This is commonly extended to mean the scale is measuring the same thing in those populations. Here we test the assumption of extending measurement invariance to meaning a scale is ‘measuring the same thing’ by randomly assigning American adults (N=1500) to fill out scales assessing either a coherent factor or a nonsense factor (i.e. measuring nothing). We find a nonsense scale with items measuring nothing (e.g. “I am always looking to find gavagai”) shows strong measurement invariance with a sensical scale. Furthermore, the nonsense scale shows high reliability (ω = .91) and a significant correlation with another construct (r = .25, p < .001, .37 to .14). Thus, we show that measurement invariance can occur without measurement. The implications of this for understanding psychological measurement are briefly discussed.