### Significance of Correlations

### Values

That is, .950+(1.000-.950)/2 or .975 level

**local**. 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 **a** and **b** may be highly correlated but
the correlation could mean **a** causes **b**, **b**
causes **a**, the correlation is due to a third factor related
to both **a** and **b**, 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

*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