Questions: I would like to run an experiment with a non-directional alternative hypothesis. I would like to achieve power of .8 and the effect size that I'd be interested in is 1. I assume that the distributions of scores is normal and a=.05. How many participants would I need in my study?

Solution Steps

We are conducting an experiment with the following parameters:

• Significance level (\( \alpha \)): \( 0.05 \)
• Desired power: \( 0.8 \)
• Effect size (\( d \)): \( 1 \)

To determine the required sample size, we first calculate the Z-scores corresponding to the significance level and the desired power:

• For a two-tailed test, the Z-score for \( \alpha = 0.05 \) is given by: \[ z_{\alpha} = \Phi^{-1}(1 - \frac{\alpha}{2}) = \Phi^{-1}(0.975) \approx 1.959 \]
• The Z-score for the desired power (\( 0.8 \)) is: \[ z_{\beta} = \Phi^{-1}(0.8) \approx 0.8416 \]

Using the Z-scores, we can calculate the required sample size (\( n \)) using the formula: \[ n = \left( \frac{z_{\alpha} + z_{\beta}}{d} \right)^2 \] Substituting the values: \[ n = \left( \frac{1.959 + 0.8416}{1} \right)^2 \approx (2.8006)^2 \approx 7.84 \] Rounding up to the nearest whole number, we find: \[ n = 8 \]

Final Answer