In this study, we classified SNS into open and closed types, and empirically examined in which SNS activity the privacy paradox holds. The idea comes from the argument that privacy paradox may be observed differently in the open SNS, which is more vulnerable to the leakage of personal information due to public profiles, and the closed SNS, which is relatively less vulnerable by limiting the range of acquaintances, The results of the empirical analysis are as follows. First, in case of SNS usage, the privacy paradox holds in the overall SNS activities, but different conclusions are drawn according to open and closed SNS. In particular, it is found that as privacy concerns increase, individuals respond in a reasonable and desirable way to reduce SNS activity in the open SNS, which is more susceptible to infringement. Second, in the case of SNS activity intensity, (i) heavy users are more seriously aware of the probability of privacy infringement than light users, so there is a reasonable response to reducing the intensive margin with increasing privacy concerns, and (ii) this tendency is more clearly observed in open SNS, which is more vulnerable to privacy infringement. Accordingly, insisting that the privacy paradox is empirically established by observing only the overall SNS activities without distinguishing them into open and closed SNS may be interpreted as a "Fallacy of Composition."