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With our t-test application, the different values of each input combination are fixed. This means that moving the sliders to change the parameters will always show the exact same results when coming back to the original settings. By interacting with this t-test application you should really get a sense of how the sample size, standard deviation, and effect size relate to the p-value in the absence of any uncertainty that randomness might introduce.

Our chi-squared application, however, does include randomness. This means that the distribution of the two groups within your sample changes every time you press the Resample button.

Now, combining both of these experiences, we are ready to look at Statistical Power (the probability of finding an effect when one exists).

The values in our Power application are like those in the t-test one, except that to make the illustration clearer, we are now looking at a "one-sample t-test" (but the overall concepts of power and randomness apply to the much more advanced tests as well).

  • First, go to the link, look at the power value (given in the text next to the Re-sample button), then the p-value. Then Re-sample a few times without changing the input parameters. Comment here whether the proportion of significant (p < 0.05) vs non-significant differences is in line with the power value.

  • Second, how does the 95% confidence interval relate to the p-value presented at the top? Can you guess whether the p-value is less than 0.05 by just looking at the confidence interval?

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