Sample size (or number of clusters) by treatment arms
In the first experiment, each post will be randomly assigned into one of the four versions (Treatment Arms 1~3 and Control) with equal probability, so we will have approximately 600 respondents * 6 posts/respondents * .25 = 900 posts in each arm.
In the second experiment, respondents will be randomly assigned into one of the four arms, so each arm will have approximately 600 respondents * 0.25 = 150 respondents.
In the third experiment, approximately 1/3 of the respondents will be assigned to Control and 2/3 of the respondents will be assigned to Treatment, so we will have approximately 600 * 1/3 = 200 respondents in Control and 600 * 2/3 = 400 respondents in Treatment.
Update (Dec 17, 2022): Due to difficulty in recruiting a sufficient number of respondents in China by Qualtrics, we were only able to collect approximately 1,000 responses for the first three experiments. Hence, we will conduct another experiment and use Lucid to recruit another 1,000 respondents for the new experiments (see Update in the Experimental Design section). The new experiment will have approximately 200 respondents in each arm.