= Significant and nonsignificant results need not differ significantly
For independent effect estimates $1.01$ with <standard error> $0.50$, and $0.99$ with standard error $0.51$, one two-sided <Wald test> is significant at five percent and the other is not. But their difference is $0.02$ with standard error $\sqrt{0.50^2+0.51^2}\approx0.714$, giving a negligible test statistic. Hence different significance labels do not establish an <interaction> or <between-study heterogeneity>; compare the effects directly.<The Difference Between Significant and Not Significant is not Itself Statistically Significant by Andrew Gelman and Hal Stern>[Printed p. 328, Introduction; pp. 328–329, theoretical example]{ref}
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