# What can one say about these cor.test results?

I'm doing my project about UFOs. I computed the correlation between population (X)~observation (Y) (UFO), and I got this graphic:

Afterward, I ran the cor.test() function in R which told me:

t = 12.92, df = 49, p-value < 2.2e-16,
95 percent confidence interval: 0.7966971 0.9295809,
sample estimates: cor = 0.8792381


Can you please help me understand what I can say about this correlation? Except for cor = 0.879, I don't have a clear understanding of the coefficients.

The main idea was to find the dependency between population of US states and the number of UFO reports per state. On the X axis - population by States, on Y axis- UFO observations for all time in States. As you can see, outliers are - California, Texas and Florida, which have the largest populations and the largest numbers of UFO reports.

• Please provide some context about what you measured & what you're interested in finding out. Commented Dec 19, 2016 at 14:02
• We could answer the question you asked as you asked it but your graph raises other issues, at least for me, so it would be better if you provided the information that @Scortchi suggests. Commented Dec 19, 2016 at 14:05

First the explanation of the numbers.

The value of $t$ is provided to enable the calculation of the later values. Then you have a $p$ value $<2.2e-16$ is how it prints $2.2 \times{} 10^{-16}$, that is a very small number. So it is saying your correlation is unlikely to have arisen by chance from a population with zero correlation. The confidence interval is such that 95% of the time it contains the true value.

You refer to outliers but what your graph shows on the present scale is some states which have high leverage (the best fitting line is being pulled to go near them) and one state which is quite some way from that line (the one at $x = 20$ with a low number of UFOs).
cor.test tests whether your correlation is statistically significant away from zero. The result is highly significant at 5% or even 1% confidence level. This is also reflected in your t-statistic, which is quite high.