One of the key concepts introduced in Unit 8 (Introduction to Statistical Literacy) is the idea that the z-test and t-test statistic formulae can be appreciated as comparisons of "signal-to-noise"

"Signal"= " Observed - Expected when Null is true

Noise" Standard Error of Observed

The numerator ("signal") tells us how different the "observed" is from what we would expect if the null hypothesis is correct. Dividing this difference by the denominator ("noise") expresses this difference in units of standard error

For example, suppose the average survival time of 100 cancer patients is 46.9 months with an estimated standard error of 4.33 months. Further suppose that, when the null hypothesis is true, the expected survival time is 38.3 months.

We have 2 ways of reporting the unusualness of our data, relative to the null hypothesis:

- "Signal": The average survival time of 46.9 months is 8.6 months greater than what we would have expected under the null hypothesis (8.6 months = 46.9 months - 38.3 months)

"Signal/Noise": The average survival time of 46.9 months is 1.99 standard error units greater than what we would have expected under the null hypothesis (1.99 SE = 8.66 months / 4.33 months per SE)