Power contour plot

Power contour plot visualizes the power from low (green) to high (yellow) as a function of possible sample sizes (x-axis) and effect sizes \(es\). Each sub-module plots a particular effect size (i.e correlation, eta-square, mediated effect, ect), but the interpretation of the plot does not change.

In the power contour plot, the solid line represents combinations of sample size (N) and effect size that yield the required power, such as 0.90 in this example. By interpreting the plot, you can see how power would change if you had underestimated the effect size (moving down on the y-axis) or underestimated the sample size (moving left on the x-axis). This provides a useful way to assess how sensitive your power analysis is to potential errors in estimating these key parameters.

The y-axis scale in the power contour plot, which represents values of the effect size, is designed to depict values around the input or estimated effect size. Typically, the range of the y-axis is set from approximately from \(es/3\) to \(es∗3\), where \(es\) stands for the effect size. However, in some sub-modules, adjustments to the scale may be made to enhance the readability and clarity of the plot. This ensures that the graph focuses on a meaningful range of effect sizes, making the sensitivity analysis more informative.

Power curve by effect size

The second plot we can ask is the Power curve by effect size . It portraits how the power (y-axis) chances as one increases the effect size (x-axis).

The solid line in the plot illustrates how power changes as the effect size increases, given a fixed sample size (in this example, \(N=258\)) and a fixed type I error rate (\(\alpha\)=.05). In this particular example, we observe that if the actual effect size is lower than the target value of 0.20 (represented by the white dot), the expected power will decrease rapidly. For instance, with an effect size of 0.1, the estimated power would drop significantly to around 0.30.

Power curve by N

The second plot we can ask is the Power curve by N . It portraits how the power (y-axis) chances as one increases the sample size (x-axis).

The solid line in the plot illustrates how power changes as the sample size increases, given a fixed effect size (in this example, \(es=.20\)) and a fixed type I error rate (\(\alpha\)=.05). In this particular example, we observe that if the actual sample size is lower than the target value of around 230 cases, the expected power will decrease rapidly. For instance, with one collects only around 130 cases, the estimated power would drop to around 0.60.

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