You looked up your degrees of freedom, found the critical value, and your r exceeds it. Congratulations! You’ve cleared the lowest bar in statistics. Statistical significance is necessary but nowhere near sufficient. With a large enough sample, a correlation of .08 becomes “significant.” But it explains less than 1% of the variance. Your committee will ask: “So what?” And if you don’t have an answer about practical significance and effect size, you’re in trouble.
The tipping point isn’t crossing the critical value threshold. It’s the moment you move from “is this significant?” to “does this matter?” Report r². Interpret the magnitude. Context is what separates a result from a finding.
Significance gets you past the table. Interpretation gets you past your committee. That’s the tipping point.

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|
1-tailed | |||
| 0.05 | 0.025 | 0.005 | |
|
2-tailed | |||
| N | 0.1 | 0.05 | 0.01 |
| 1 | 0.988 | 0.997 | 0.999 |
| 2 | 0.900 | 0.950 | 0.990 |
| 3 | 0.805 | 0.878 | 0.959 |
| 4 | 0.729 | 0.811 | 0.917 |
| 5 | 0.669 | 0.754 | 0.875 |
| 6 | 0.621 | 0.707 | 0.834 |
| 7 | 0.584 | 0.666 | 0.798 |
| 8 | 0.549 | 0.632 | 0.765 |
| 9 | 0.521 | 0.602 | 0.735 |
| 10 | 0.497 | 0.576 | 0.708 |
| 11 | 0.476 | 0.553 | 0.684 |
| 12 | 0.458 | 0.532 | 0.661 |
| 13 | 0.441 | 0.514 | 0.641 |
| 14 | 0.426 | 0.497 | 0.623 |
| 15 | 0.412 | 0.482 | 0.606 |
| 16 | 0.400 | 0.468 | 0.590 |
| 17 | 0.389 | 0.456 | 0.575 |
| 18 | 0.378 | 0.444 | 0.561 |
| 19 | 0.369 | 0.433 | 0.549 |
| 20 | 0.360 | 0.423 | 0.537 |
| 21 | 0.352 | 0.413 | 0.526 |
| 22 | 0.344 | 0.404 | 0.515 |
| 23 | 0.337 | 0.396 | 0.505 |
| 24 | 0.330 | 0.388 | 0.496 |
| 25 | 0.323 | 0.381 | 0.487 |
| 26 | 0.317 | 0.374 | 0.479 |
| 27 | 0.311 | 0.367 | 0.471 |
| 28 | 0.306 | 0.361 | 0.463 |
| 29 | 0.301 | 0.355 | 0.456 |
| 30 | 0.296 | 0.349 | 0.449 |
| 35 | 0.275 | 0.325 | 0.418 |
| 40 | 0.257 | 0.304 | 0.393 |
| 45 | 0.243 | 0.288 | 0.372 |
| 50 | 0.231 | 0.273 | 0.354 |
| 60 | 0.211 | 0.250 | 0.325 |
| 70 | 0.195 | 0.232 | 0.303 |
| 80 | 0.183 | 0.217 | 0.283 |
| 90 | 0.173 | 0.205 | 0.267 |
| 100 | 0.164 | 0.195 | 0.254 |
| 150 | 0.134 | 0.159 | 0.208 |
| 300 | 0.095 | 0.113 | 0.148 |
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