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We present a model‐independent investigation of the  Wilkinson Microwave Anisotropy Probe (WMAP)  data with respect to scale‐independent and scale‐dependent non‐Gaussianities (NGs). To this end, we employ the method of constrained randomization. For generating so‐called surrogate maps a well‐specified shuffling scheme is applied to the Fourier phases of the original data, which allows us to test for the presence of higher order correlations (HOCs) also and especially on well‐defined scales.  Using scaling indices as test statistics for the HOCs in the maps we find highly significant signatures for NGs when considering all scales. We test for NGs in four different  l ‐bands Δ l , namely in the bands Δ l =[2, 20], [20, 60], [60, 120] and [120, 300]. We find highly significant signatures for both NGs and ecliptic hemispherical asymmetries for the interval Δ l =[2, 20] covering the large scales. We also obtain highly significant deviations from Gaussianity for the band Δ l =[120, 300]. The result for the full  l ‐range can then easily be interpreted as a superposition of the signatures found in the bands Δ l =[2, 20] and [120, 300]. We find remarkably similar results when analysing different ILC‐like maps based on the  WMAP  3‐, 5‐ and 7‐year data. We perform a set of tests to investigate whether and to what extent the detected anomalies can be explained by systematics. While none of these tests can convincingly rule out the intrinsic nature of the anomalies for the low‐ l  case, the ILC map making procedure and/or residual noise in the maps can also lead to NGs at small scales.  Our investigations prove that there  are  phase correlations in the  WMAP  data of the cosmic microwave background. In the absence of an explanation in terms of Galactic foregrounds or known systematic artefacts, the signatures at low  l  must so far be taken to be cosmological at high significance. These findings would strongly disagree with predictions of isotropic cosmologies with single field slow roll inflation.  The task is now to elucidate the origin of the phase correlations and to understand the physical processes leading to these scale‐dependent NGs – if it turns out that systematics as a cause for them must be ruled out.

Scale‐dependent non‐Gaussianities in the WMAP data as identified by using surrogates and scaling indices