### Significance of Correlations

### Values

The table below lists the correlation values that are significant at 4 significance levels and specified degrees of freedom. To perform a 1-tailed test, simply use the values in the list. For example, the 95% significance level correlation value for 40 years is listed under the .950 column for 40 degrees of freedom and is .264. For a 2-tailed test, for the significance level you want (for example 95%) use the value for thelevel+((1.000-level)/2.0) significance level.For 40 years, a correlation of +/- .3124. would be significant. These significance levels are

That is, .950+(1.000-.950)/2 or .975 levellocal. For a resolution of 144x73 gridpoints, one would assume at least .05X(144*73)=526 grids would be significant by chance at the one-sided 95% level.

### Caveats

Note that determining actual field significance is trickier than this due to the grids being correlated in space so that Monte Carlo or similar tests are usually run. for example, this paper discusses field significance calculations.

For some variables (like SST), there is year to year correlation at a region so that the number of years will be greater than the actual degrees of freedom meaning a higher correlation value is needed for significance.

(Linear) correlation makes certain assumptions about the data which can lead to spurious high correlations (or, hide real relationships). For example, the assumption is that the data is normally distributed which doesn't always hold for variables like precipitation. Also, since the method maximizes linear relationships, variables in quadrature may appear to have 0 correlation when in fact the relationship between them is exactly defined.

NOTE, CORRELATION DOES NOT IMPLY CAUSATION!!Two variables

aandbmay be highly correlated but the correlation could meanacausesb,bcausesa, the correlation is due to a third factor related to bothaandb, or, the correlation could simply arise by chance. The user should be cautious when interpreting results.A good discussion on the significance of correlations is available at graphpad software page.

### References

Livezey, R.E. and W.Y. Chen, 1983: Statistical field significance and it's determination by Monte Carlo Techniques.Mon. Wea. Review.,111, 46-59.Diaconis, P. and B. Efron, 1983: Computer Intensive methods in statistics,

Sci. Am.,248, 116-130.

Significance LevelDegrees of.950 .975 .990 .995Freedom 2 1.000 1.000 1.000 1.000 3 0.920 0.954 0.977 0.986 4 0.833 0.891 0.936 0.956 5 0.758 0.829 0.889 0.919 6 0.697 0.774 0.844 0.880 7 0.646 0.727 0.802 0.843 8 0.605 0.685 0.764 0.808 9 0.570 0.650 0.729 0.775 10 0.540 0.619 0.699 0.746 11 0.514 0.592 0.671 0.719 12 0.491 0.567 0.647 0.695 13 0.471 0.546 0.624 0.672 14 0.453 0.526 0.604 0.652 15 0.437 0.509 0.585 0.633 16 0.423 0.493 0.568 0.615 17 0.410 0.478 0.552 0.599 18 0.398 0.465 0.538 0.584 19 0.387 0.453 0.524 0.570 20 0.377 0.441 0.512 0.557 21 0.367 0.431 0.500 0.545 22 0.358 0.421 0.489 0.533 23 0.350 0.411 0.479 0.522 24 0.343 0.403 0.469 0.512 25 0.336 0.395 0.460 0.503 26 0.329 0.387 0.451 0.493 27 0.322 0.380 0.443 0.485 28 0.316 0.373 0.436 0.476 29 0.311 0.366 0.428 0.469 30 0.305 0.360 0.421 0.461 31 0.300 0.354 0.415 0.454 32 0.295 0.349 0.408 0.447 33 0.291 0.343 0.402 0.441 34 0.286 0.338 0.396 0.434 35 0.282 0.333 0.391 0.428 36 0.278 0.329 0.385 0.423 37 0.274 0.324 0.380 0.417 38 0.271 0.320 0.375 0.412 39 0.267 0.316 0.370 0.407 40 0.264 0.312 0.366 0.402 41 0.260 0.308 0.361 0.397 42 0.257 0.304 0.357 0.392 43 0.254 0.300 0.353 0.388 44 0.251 0.297 0.349 0.384 45 0.248 0.294 0.345 0.379