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UW Libraries has a whole guide, Savvy Info Consumers: Evaluating Information, which discusses different types of sources and how to approach evaluating their credibility/reliability.
What it means for a source to be credible/reliable can vary depending on the context of its use. Generally, a credible or reliable source is one that experts in your subject domain would agree is valid for your purposes. This can vary, so it is best to use one of the source evaluation methods that best fits your needs. Do remember that credibility is contextual!
It is important to critically evaluate sources because using credible/reliable sources makes you a more informed writer. Think about unreliable sources as pollutants to your credibility, if you include unreliable sources in your work, your work could lose credibility as a result.
There are certain frameworks that information professionals have put together to help people think critically about the information provided.
Some of the methods that UW Libraries suggest are:
5 W Questions (5Ws): This method means thinking critically about each of your sources by answering five questions to determine if the source is credible/reliable. The acceptable answers to these questions will vary depending on your needs. The questions are:
SMART Check: This method is particularly good at evaluating newspaper sources. Like the 5Ws method it also involves answering critical questions about your source. The criteria are:
CRAAP Test: This method provides you with a set of criteria that make a source more or less credible. The criteria are: