Correlation and Causation:
A correlation is a number showing a possible relationship between two variables. It is generally stated as a fraction between minus 1 and 1. A negative correlation indicates a reverse relationship. For example, if we correlated biodiversity in countries vs percent of desert, the correlation would be expected to be negative - more desert corresponding to less biodiversity. Correlations generally have a "confidence interval" or "probability of error" attached that is largely based on consistency and sample size. The higher the correlation and the lower the error probability, the more faith we can have in the data (all other things being equal).
For example, in a study by Swanson (et al) published in the Journal of Organic Systems, Vol. 9 No 2 (2014) titled "Genetically engineered crops, glyphosate and the deterioration of health in the United States of America", time series correlations were carried out on incidence of chronic diseases vs glyphosate application data. They state the results as:
"The Pearson correlation coefficients are highly significant (< 10-5) between glyphosate applications and hypertension (R = 0.923), stroke (R = 0.925), diabetes prevalence (R = 0.971), diabetes incidence (R = 0.935), obesity (R = 0.962), lipoprotein metabolism disorder (R = 0.973), Alzheimer’s (R = 0.917), senile dementia (R = 0.994), Parkinson's (R = 0.875), multiple sclerosis (R = 0.828), autism (R = 0.989),...."
The R value is the strengrh of the correlation and the significance, (< 10-5), is a measure showing low probability of sampling error. In this case the data samples were very large. Smaller sample size would increase the error probablity.
But the standard comment back from proponents of various enviromental toxins is always "but correlation does not prove causation" and that is a true statement in general. So correlation indicates something may be amuck — but how do we determine if there is "causation"? Can you say because there is a high coorelation that glyphosate "causes" all these diseases?
No. What you can say, as these researchers did is:
"The significance and strength of the correlations show that the effects of glyphosate and GE crops on human health should be further investigated."
So we have some reason to believe glyphosate is a problem, but what has to follow is laid out in Hill's criteria