Nearly fifty years ago, two landmark papers appeared that should have cured the problem of ambiguous uncertainty statements in published data. Eisenharts paper in Science called for statistically meaningful numbers, and Curries Analytical Chemistry paper revealed the wide range in common definitions of detection limit. A wise mentor said Believe your data, but it is wrong to impose your preconceptions on them. The recent stories of cold fusion, variable radioactive decay, and piezonuclear reactions provide cautionary examples in which prior probability has been neglected. Currie has pointed out that in any measurement campaign the number of degrees of freedom is in fact negative: there are more variables than we know, so scientific insight is essential. We show examples from our laboratory and others to illustrate that uncertainty depends on both statistics and science.