Is there a set number, or a range?
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This website gives values for three levels of significance.
http://www.gifted.uconn.edu/siegle/resea…
As you can see, the more data points you have, the lower the correlation coefficient needs to be to show a connection between the variables. If the correlation coefficient is less than that shown in the table, then there is a reasonable chance that it occurred by luck even though the variables are unrelated.
Note the "How to use this table" link just under the title.
http://www.gifted.uconn.edu/siegle/resea…
As you can see, the more data points you have, the lower the correlation coefficient needs to be to show a connection between the variables. If the correlation coefficient is less than that shown in the table, then there is a reasonable chance that it occurred by luck even though the variables are unrelated.
Note the "How to use this table" link just under the title.