Statistics is a well understood mathematic discipline. It’s weaknesses and strengths are well documented. The problem is not the math behind science, it is the persons that are intentionally trying to sell a falsehood.
There are entire books written on how to deal with alpha and beta errors which this article insinuates are not understood.
Truth!
The article is, ironically, misleading. The problem is the misuse or misunderstanding of statistics, not that the scientific method is incorrect or that statistics is incorrect.
Another issue (that I will soon write about in my blog http://libertyphysics.wordpress.com/) is that statistical correlations are very often confused with cause and effect. For example, say a statistically correct study is done showing people in countries who eat more yogurt live longer than people in countries who eat less yogurt. I'm being simplistic, of course.
That doesn't mean that eating yogurt will make you live longer, no matter how correct the statistics. The scientists who do these studies usually know better but the fawning news media does not and reports such findings as if they were a call to action.
Worse, even if the statistics is done correctly, say we discover that, on average, eating salt raises a population's blood pressure, that conclusion doesn't necessarily apply to any given individual member of the population. For example, statistically, men are stronger than women. But I can easily find a woman stronger than the average man just as I can easilly find someone who can eat salt without an increase in blood pressure.
Misuse and misunderstanding is the issue.