t-values and p-values in statistics
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The t statistic is basically the signal (say, a difference from the expected value) divided by the noise. The difference alone doesn’t tell you much, because you don’t know how much variation is typically encountered. When you divide by the noise, you get a dimensionless number that incorporates the comparison. If the number is low, then the noise might explain the deviation. If it’s high, then noise is a less likely explanation of the deviation.
The p value is the chance of seeing the data (again, a deviation, say) you saw (or more extreme data) if nothing unusual is happening. Consider flipping a coin repeatedly. The p-value of getting three heads in a row isn’t that low. The run of heads could easily be ascribed to chance. Twenty heads in a row? The p value of that is quite low. We’d likely start considering that the coin is weighted or even is two-headed. You could set your own threshold p value for when you wish to entertain the conclusion that things aren’t as you expected.
This is how we move forward and make a decision with limited data in the presence of uncertainty.
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