We analyze the uncertainties in the amplitudes of the spatial correlation functions estimated from angular correlations in a sample from the Automatic Plate Measuring Facility (APM) Galaxy Survey, with bJ = 17-20. We model the uncertainties in the selection function and in the evolution of clustering. In particular, we estimate σAPM₈, the rms galaxy number fluctuation in spheres of radius at 8 h⁻¹ Mpc, from the measured angular variance in the APM. The uncertainty in σAPM₈ has three main contributions: 8% from sampling and selection function uncertainties, 7% from the uncertainty in the evolution of clustering, and 3% from the uncertainty in the value of Ω₀. Including all these contributions, we find that σAPM₈ is in the range 0.78-1.08. If the galaxy clustering in the APM evolves as expected from gravitational clustering of matter fluctuations, then σAPM₈= 0.95±0.07 (1.00±0.08) for Ω₀ ≌ 1 (Ω₀ ≌ 0), close to the values for nearby optical samples. On the other hand, if we assume that clustering evolution is fixed in comoving coordinates, then σAPM₈ = 0.83±0.05 (0.87±0.06), closer to the results for nearby IRAS samples. The final uncertainty in the range of values for the hierarchical amplitudes SJ = ζbarJ/ζbarJ-1₂ is typically twice the estimated sampling errors, with the highest values for the case of less clustering evolution. We compare our estimates with other results and discuss the implications for models of structure formation.
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E. Gaztañaga (1995) studied this question.