A comprehensive understanding of data quality is the cornerstone of measurement studies in social media research. This paper presents in-depth measurements on the effects of Twitter data sampling across different timescales and different subjects (entities, networks, and cascades). By constructing complete tweet streams, we show that Twitter rate limit message is an accurate indicator for the volume of missing tweets. Sampling also differs significantly across timescales. While the hourly

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... ng rate is influenced by the diurnal rhythm in different time zones, the millisecond level sampling is heavily affected by the implementation choices. For Twitter entities such as users, we find the Bernoulli process with a uniform rate approximates the empirical distributions well. It also allows us to estimate the true ranking with the observed sample data. For networks on Twitter, their structures are altered significantly and some components are more likely to be preserved. For retweet cascades, we observe changes in distributions of tweet inter-arrival time and user influence, which will affect models that rely on these features. This work calls attention to noises and potential biases in social data, and provides a few tools to measure Twitter sampling effects.