We present an 850-μm map and list of candidate sources in a subarea of the Groth Strip observed using the Submillimetre Common-User Bolometer Array (SCUBA). The map consists of a long strip of adjoining jiggle-maps covering the southwestern 70 arcmin of the original Wide Field Planetary Camera 2 Groth Strip to an average 1σ rms noise level of ≥3.5 mJy. We initially detect seven candidate sources with signal-to-noise ratios between 3.0 and 3.5σ and four candidate sources with signal-to-noise ratio ≥3.5. Simulations suggest that on average in a map this size one expects 1.6 false positive sources ≥3.5σ and 4.5 between 3 and 3.5σ. Flux boosting in maps is a well-known effect and we have developed a simple Bayesian prescription for estimating the unboosted flux distribution and used this method to determine the best flux estimates of our sources. This method is easily adapted for any other modest signal-to-noise survey in which there is prior knowledge of the source counts. We performed follow-up photometry in an attempt to confirm or reject five of our source candidates. We failed to significantly redetect three of the five sources in the noisiest regions of the map, suggesting that they are either spurious or have true fluxes close to the noise level. However, we did confirm the reality of two of the SCUBA sources, although at lower flux levels than suggested in the map. Not surprisingly, we find that the photometry results are consistent with and confirm the de-boosted map fluxes. Our final candidate source list contains three sources, including the two confirmed detections and one further candidate source with signal-to-noise ratio >3.5σ which has a reasonable chance of being real. We performed correlations and found evidence of positive flux at the positions of XMM-Newton X-ray sources. The 95 per cent lower limit for the average flux density of these X-ray sources is 0.8 mJy.