Plasma wave data are compared with ISEE 1's position in the electron foreshock for an interval with unusually constant (but otherwise typical) solar wind magnetic field and plasma characteristics. For this period, temporal variations in the wave characteristics can be confidently separated from sweeping of the spatially varying foreshock back and forth across the spacecraft. The spacecraft's location, particularly the coordinate Df downstream from the foreshock boundary (often termed DIFF), is calculated by using three shock models and the observed solar wind magnetometer and plasma data. Scatterplots of the wave field versus Df are used to constrain viable shock models, to investigate the observed scatter in the wave fields at constant Df, and to test the theoretical predictions of linear instability theory. The scatterplots confirm the abrupt onset of the foreshock waves near the upstream boundary, the narrow width in Df of the region with high fields, and the relatively slow falloff of the fields at large Df, as seen in earlier studies, but with much smaller statistical scatter. The plots also show an offset of the high-field region from the foreshock boundary. It is shown that an adaptive, time-varying shock model with no free parameters, determined by the observed solar wind data and published shock crossings, is viable but that two alternative models are not. Foreshock wave studies can therefore remotely constrain the bow shock's location. The observed scatter in wave field at constant Df is shown to be real and to correspond to real temporal variations, not to unresolved changes in Df. By comparing the wave data with a linear instability theory based on a published model for the electron beam it is found that the theory can account qualitatively and semiquantitatively for the abrupt onset of the waves near Df=0, for the narrow width and offset of the high-field region, and for the decrease in wave intensity with increasing Df. Quantitative differences between observations and theory remain, including large overprediction of the wave fields and the slower than predicted falloff at large Df of the wave fields. These differences, as well as the unresolved issue of the electron beam speed in the high-field region of the foreshock, are discussed. The intrinsic temporal variability of the wave fields, as well as their overprediction based on homogeneous plasma theory, are indicative of stochastic growth physics, which causes wave growth to be random and varying in sign, rather than secular.¿ 1997 American Geophysical Union