Global analyses of monthly sea surface temperature (SST) anomalies from 1856 to 1991 are produced using three statistically based methods: optimal smoothing (OS), the Kalman filter (KF) and optimal interpolation (OI). Each of these is accompanied by estimates of the error covariance of the analyzed fields. The spatial covariance function these methods require is estimated from the available data; the time-marching model is a first-order autoregressive model again estimated from data. The data input for the analyses are monthly anomalies from the United Kingdom Meteorological Office historical sea surface temperature data set (MOHSST5) <Parker et al., 1994> of the Global Ocean Surface Temperature Atlas (GOSTA) <Bottomley et al., 1990>. These analyses are compared with each other, with GOSTA, and with an analysis generated by projection (P) onto a set of empirical orthogonal functions (as in Smith et al. <1996>). In theory, the quality of the analyses should rank in the order OS, KF, OI, P, and GOSTA. It is found that the first four give comparable results in the data-rich periods (1951--1991), but at times when data is sparse the first three differ significantly from P and GOSTA. At these times the latter two often have extreme and fluctuating values, prima facie evidence of error. The statistical schemes are also verified against data not used in any of the analyses (proxy records derived from corals and air temperature records from coastal and island stations). We also present evidence that the analysis error estimates are indeed indicative of the quality of the products. At most times the OS and KF products are close to the OI product, but at times of especially poor coverage their use of information from other times is advantageous. The methods appear to reconstruct the major features of the global SST field from very sparse data. Comparison with other indications of the El Ni¿o-Southern Oscillation cycle show that the analyses provide usable information on interannual variability as far back as the 1860s. ¿ 1998 American Geophysical Union