I am reading a journal article and I come across this statement:
Loneliness was associated with higher odds of having a mental health problem (OR: 1.17; CI: [1.13, 1.21], p = 0.000); and isolation was associated with higher odds of reporting one’s health as being fair/poor (OR:1.39; CI: [1.21, 1.59], p = 0.000).
I'm slightly confused. What does it mean when the p-value is 0? Does that mean 100% confidence?
Reference: Coyle, C. E., & Dugan, E. (2012). Social isolation, loneliness and health among older adults. Journal of Aging and Health, 24(8), 1346-1363.
P-values can be a tricky area. First of all a p-value does not tell you if the hypothesis is true or not, they just indicate the compatibility with a statistical model. Also, the p-value is not a measure of the confidence interval but a measure of how the data compared to the hypothesis. A p-value of close to zero (it is unlikely to be actually zero, it looks like the decimal places have been truncated in this article) means that the results were highly statistically significant and the there is strong evidence against the null hypothesis.
The ASA released an interesting statement about the use of p-values that can be found here http://www.amstat.org/asa/files/pdfs/P-ValueStatement.pdf