The larger the sample size used to collect statistics, the more likely the sampled statistics are an accurate representation of population statistics. There is a trade-off for this accuracy: the larger the sample size, the longer it takes to collect the statistics.
You cannot use sampling to collect COLUMN statistics for the partitioning columns of row-partitioned tables and you should not use sampling to collect INDEX statistics for those columns. The collect statistics on the system-derived PARTITION or PARTITION#Ln columns.