Given that a two-tailed test allots .025 of the alpha to each tail (assuming that alpha is set at .05), why does SPSS flag correlation coefficients with p values of, for example, .049 (two-tailed) as statistically significant?
The p-values for the coefficients are "two-tailed" p-values, and 0.049 < 0.05, which is the conventional level of significance.
When there is no directional relationship between X and Y (e.g., correlation), a two-tailed test should be used. However, when there is is a directional relationship between X and Y (e.g., X is positively or negatively related or affect Y), a one-tailed test can be used.
In most statistical softwares, the default for p-value is a two-tailed test (you'd better check the t-value to use a one-tailed test).
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