The study examines the pervasiveness of eight well-documented anomalies in global equity markets for the Australian stock market. After partitioning stocks into three size categories (micro, small and big), we find that none of the eight anomalies are pervasive across size groups in either sorts or cross-sectional regressions. The existence of size, value, profitability, asset growth and accruals anomalies is primarily attributable to micro-cap stocks. Momentum and asset growth predict the expected returns of big stocks, but momentum does not predict the returns on micro stocks, and asset growth does not matter for small stocks. Contrarian returns are largely explained by stock size and value dimensions. Evidence for the earnings growth anomaly contradicts the growth extrapolation hypothesis. By looking at the hedge portfolio returns of anomalies in different regimes, we also show that many anomalies tend to exist in bear markets rather than bull markets. This evidence contradicts the risk-based explanations for the existence of anomalies.