While hundreds of loci have been identified as reflecting strong-positive selection in human populations, connections between candidate loci and specific selective pressures often remain obscure. This study investigates broader patterns of selection in African populations, which are underrepresented despite their potential to offer key insights into human adaptation. We scan for hard selective sweeps using several haplotype and allele-frequency statistics with a data set of nearly 500,000 genome-wide single-nucleotide polymorphisms in 12 highly diverged African populations that span a range of environments and subsistence strategies. We find that positive selection does not appear to be a strong determinant of allele-frequency differentiation among these African populations. Haplotype statistics do identify putatively selected regions that are shared across African populations. However, as assessed by extensive simulations, patterns of haplotype sharing between African populations follow neutral expectations and suggest that tails of the empirical distributions contain false-positive signals. After highlighting several genomic regions where positive selection can be inferred with higher confidence, we use a novel method to identify biological functions enriched among populations' empirical tail genomic windows, such as immune response in agricultural groups. In general, however, it seems that current methods for selection scans are poorly suited to populations that, like the African populations in this study, are affected by ascertainment bias and have low levels of linkage disequilibrium, possibly old selective sweeps, and potentially reduced phasing accuracy. Additionally, population history can confound the interpretation of selection statistics, suggesting that greater care is needed in attributing broad genetic patterns to human adaptation.