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Writing testable user stories helps to conclude the development. Testable is one of the attributes for a User story. In agile software development, if a user story is too big (compound user story), we can split the story, create multiple shorter stories and put them in an epic. To conclude a story development, it must be tested successfully. So every user story should be testable.
Non-functional user stories are good examples for untestable. The following user story is not testable because it is not written from a testing point of view.
“As a user, I want a good user experience and usability on Homepage.”
You can rephrase the story as “Home page should comply with usability checklist” to make it testable. If a user story is testable, you can identify acceptance tests before the story is implemented.