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Week is a Dimension in Google Analytics under the Lifetime Value and Cohorts section
Week Definition: Week offset relative to the cohort definition date. The semantics of this dimension differs based on whether lifetime value is requested or not. For a cohorts report not requesting lifetime value: This is the week offset from the cohort definition start date. For example, if cohort is defined as 2015-09-01 <= first session date <= 2015-09-07. Then, for 2015-09-01 <= date <= 2015-09-07, ga:cohortNthWeek = 0. 2015-09-08 <= date <= 2015-09-14, ga:cohortNthWeek = 1. etc. For a cohorts request requesting lifetime value: ga:cohortNthWeek is calculated relative to the users acquisition date. It is not dependent on the cohort definition date. For example, if we define a cohort as 2015-09-01 <= first session date <= 2015-09-07. And a user was acquired on 2015-09-04. Then, for 2015-09-04 <= date<= 2015-09-10, ga:cohortNthWeek = 0 2015-09-11 <= date <= 2015-09-17, ga:cohortNthWeek = 1