If the F-value in ANOVA produces a significantly high p-value (a.k.a. "Sig." in SPSS) of 0.11 or more, then it is appropriate to proceed with a post-hoc test (e.g., Duncan).

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A high p-value (e.g., 0.11) indicates that there is no statistically significant difference between group means, so a post-hoc test is not warranted. Post-hoc tests are only conducted when the ANOVA shows significant results (typically p < 0.05).

If the F-Value in ANOVA Produces a Significantly High P-Value