6.101 Turning insignificance in significance.
Every user of statistics should understand the distinction between statistical significance and practical importance.
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A sufficiently large sample will declare very small effects statistically signifcant. Consider the following randomly generated digits used to form observation pairs:
1 | 7 | 9 | 4 | 6 | 4 | 6 | 5 | 0 | 1 | |
0 | 0 | 4 | 3 | 7 | 5 | 5 | 2 | 4 | 5 |
Read the 10 ordered pair values into statistical software. We will want to test the significance of the observed correlation. Excel doesn’t provide that capability.
6.101
(a) There seems to be no relationship between and . (b) . . Yes, there is no significant correlation between and . (c) The plot is identical. The correlation is the same, . The -value is smaller (). (d) The correlation has not changed, but the -value gets smaller as increases.
-value | ||
---|---|---|
10 | 0.07565 | 0.8355 |
20 | 0.07565 | 0.7513 |
30 | 0.07565 | 0.6911 |
40 | 0.07565 | 0.6427 |
50 | 0.07565 | 0.6016 |
60 | 0.07565 | 0.5657 |
(e) . (f) Even with no relationship and a very small correlation, a big enough sample size can show statistical significance, warning us to make sure the effect is worth our attention rather than just “trusting” the statistics.
signif