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I have low anxiety and high anxiety participants (21 in high anxiety and 20 In low). I measured anxiety and then categorised Pts according to this.

They completed two memory tasks. In one memory task there are distractors and in another memory task there are no distractors. Tasks are exactly the same as each other, just there is distractors in one. All Participants complete both memory tasks. My DV is percentage recalled in memory task with distractors and percentage recalled in memory task without distractors.

I am predicting that those low in anxiety will have equal recall performance on both of these tasks but those high in anxiety will be worse on the tasks with distractors.

I do not know if I can do a one way ANOVA as I only two groups and I don't know if an ANOVA would be able to test for all the differences I'm interested in. But I know multiple t tests don't correct for type 1 errors.

Would it be appropriate to do a one sample t test on LOW anxiety participants to see if there is a difference between memory task without distractors and memory task with distractors? And then a one sample t test on HIGH anxiety participants to see if there is a difference between memory task without distractors and memory task with distractors?

And after that do a paired subjects t test to see if there is difference between low and high anxiety participants' performance on memory task with distractors. And then a paired subjects t test to see if there is difference between low and high anxiety participants' performance on memory task without distractors. So 4 t tests in total or is there a better way to do this?

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If I'm understanding the question, you have two factors: high/low anxiety and distractions. ANOVA can deal with those two factors and show if any of them is significant. Doing t-tests will mix the effects of the two factors.

However, if all samples weren't independent and some experiments were actually paired (same subjects or same distractions) the answer might be different.

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