The Song dynasty is one of the two ancient flourishes in ceramic manufacture in China, the celadons from Song dynasty are especially famous for fine manufacture, jade – like appearance and various productions. The celadons from several famous kilns in Song dynasty, such as Jiao Tanxia guan kiln, Ru kiln, Xiu Neisi kiln, resemble in some aspects of appearance, thus provide proper objects in source provenance study. On the other hand, those beautiful celadons have been imitated and faked for long time, thus the celadons and their fakements can provide substantial materials in dating study. The chemical composition of various celadons and their fakements have been analyzed in this article, then multiple variable statistics was used to find the differentiation of them, which showed that they aggregated into clearly distinguished areas on factors map in principal component analysis. Thus the discrimination by chemical composition is a very useful method to classify the celadons of guan kiln from Song dynasty. Some discussion about shortage of multiple variable statistics is made when statistics are used in the differentiation of ancient celadons and their fakements. In provenance study, the celadons of Ru, Xiu Neisi and Jiao Tanxia kiln were analyzed, then the PCA (principal component analysis) method was applied to the composition data analysis, those celadons can clearly be classified in the factor’s map. Generally the compositions between the porcelains from two near kilns are almost the same, it is a little special that though the Jiao Tanxia guan kiln and Xiu Neisi guan kiln are very near, the composition between the porcelains from them can be distinguished rather clearly. In dating study, celadons of Ru kiln and their imitations made in various periods were carefully analyzed, the factor’s map reveals clearly segregated groups corresponding to ancient, Qing dynasty and modern samples. In the analysis of celadons of southern Song dynasty guan kiln and their imitations, it is much more complicated due to various imitations different in both space and time. Some special processes are introduced to the analysis by multiple variable statistics. First, the seemingly undistinguished porcelains were selected into another processing by multiple variable statistics, because some disturbing samples were get rid of, the better effect was got in the factor’s map. Second, some other elements were added to the multiple variable statistics analysis, since these elements were especially chosen to enhance the difference between ancient celadons and its fakement, very clear discrimination can be got in the new factor’s map. The above statistics analyses suggest that some special attention should be paid in the illustration of the factor’s map when the multiple variable statistic methods are used for appraisal. Because the giant difference in fakements made by various producers, they didn’t aggregate in the factor’s map, thus sometime the big difference between the ancient porcelain and some reproductions is disguised. It’s similar that though A point is far from point B in a city, looks to be close to B in the map of whole city, even they can not be distinguished in the map of the province. At last, some discussion was made about statistical methods used in decipherment of chemical composition data. It is strongly suggested that some new statistical methods should be introduced into the appraisal of ancient porcelain.