discernable” rather than significant,” but “statistically “statistically that is not widely practiced. I think that makes a lot of sense, and suggest that when you hear or read significant,” you think “statistically discernable,” to help prevent yourself from “statistically over-interpreting statistical significance. The larger the sample size, the more likely a hypothesis Caution: test will detect a small difference. Thus it’s especially important to consider practical significance when sample size is large. Connection between Type I error and significance level: A significance level corresponds to a certain value of the test α statistic, say tα, with area under the curve to the right of tα equal to α. tα is represented by the orange line in the picture of a sampling distribution below (the picture illustrates a hypothesis test with alternate hypothesis "µ > 0"), Since the shaded area indicated by the arrow is the p-value corresponding to tα, that p-value (shaded area) is α. To have p-value less than a t-value for this test must be to α, the right of tα.
“statistically discernable” rather than “statistically significant,” but that is not widely practiced. I think that makes a lot of sense, and suggest that when you hear or read “statistically significant,” you think “statistically discernable,” to help prevent yourself from over-interpreting statistical significance. Caution: The larger the sample size, the more likely a hypothesis test will detect a small difference. Thus it’s especially important to consider practical significance when sample size is large. Connection between Type I error and significance level: A significance level α corresponds to a certain value of the test statistic, say tα, with area under the curve to the right of tα equal to α. tα is represented by the orange line in the picture of a sampling distribution below (the picture illustrates a hypothesis test with alternate hypothesis "µ > 0"), Since the shaded area indicated by the arrow is the p-value corresponding to tα, that p-value (shaded area) is α. To have p-value less than α, a t-value for this test must be to the right of tα.