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Description: Inhomogeneities in climate data are the main source of uncertainty for secular warming estimates. To reduce the influence of inhomogeneities in station data statistical homogenization compares a candidate station to its neighbors to detect and correct artificial changes in the candidate. Many studies have quantified the performance of statistical break detection tests used in this comparison. Also full homogenization methods have been studied numerically, but correction methods by themselves have not been studied much. We analyze the so-called ANOVA joint correction method, which is expected to be the most accurate published method. We find that, if all breaks are known, this method produce unbiased trend estimates and that in this case the uncertainty in the trend estimates is not determined by the variance of the inhomogeneities, but by the variance of the weather and measurement noise. For low signal-to-noise ratios and high numbers of breaks, the correction may also worsen the data by increasing the original random unbiased trend error. Any uncertainty in the break dates leads to a systematic undercorrection of the trend errors and in this more realistic case the variance of the inhomogeneities is also important.