Don't think of the pink elephant
When giving instructions on a usability session:
"We are not testing you, we are testing the site"
"There are no right and wrong answers here"
"You don't need to worry that you will hurt our feelings"
Put the participant at ease by you being chill.
When we say words like "test", "wrong", "worry", or "hurt" - these will automatically activate the associated emotions and reactions in people. This is called "priming". These words prime stress, anxiety, and caution.
We can't help this. Our brain is simply a network of concepts in which one concept automatically activates all the neighboring concepts. You can't prevent someone from thinking of a pink elephant by asking them not to. Quite the contrary, you activated this image in their head yourself. "We are not testing you..." is defeating its purpose.
Inducing anxiety hurts the research because participants will start to hide their vulnerabilities and censor what they say. So we would miss out on a lot of usability issues they are experiencing.
While we can't tell our participants not to worry, we can still convey the message by acting in that spirit.
If they see that we are at ease, they will feel at ease.
If they see that we don't mind if they fail, they will not mind it either.
If they can say anything and we don't go defensive but encourage them to continue, they will know that they don't need to worry about hurting our feelings.