Exercise: Testing the interaction in two-by-two ANOVA

Anchoring and adjustment

Items and anchor values (Jacowitz and Kahneman 1995)

• How tall is the largest coast redwood in the world? [20, 168m]
• How many member states belong to the United Nations? [14, 127 members]
• How much km/h is the maximum speed of a house cat? [11, 48km/h]

Research question

• Does time pressure (respond within 7s) increase the anchor effect?

Suggest a minimum relevant effect

• Go to https://apps.mathpsy.uni-tuebingen.de/fw/pars2eta/
• Fix the parameters of the ANOVA model

Some background

• Open anchoring quest (Röseler et al. 2022), https://osf.io/ygnvb/

Plan the study

• Pick one of the three items
• Parameter recovery
  • Make a data frame for the two-by-two design
  • With the parameter values determined before, simulate responses
  • Re-estimate the parameters
• Power simulation
  • Calculate the sample size necessary to detect the time-pressure effect

Bonus task: Verify the plausibility of your model

• Download the raw data from the open anchoring quest project
• Estimate \(\sigma\) and compare it to your value

References

Jacowitz, K. E., and D. Kahneman. 1995. “Measures of Anchoring in Estimation Tasks.” Personality and Social Psychology Bulletin 21 (11): 1161–66. https://doi.org/10.1177/01461672952111004.

Röseler, L., L. Weber, K. A. C. Helgerth, E. Stich, M. Günther, P. Tegethoff, F. S. Wagner, et al. 2022. “OpAQ: Open Anchoring Quest, Version 1.1.50.97.” https://doi.org/10.17605/OSF.IO/YGNVB.