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

<div id="refs" class="references csl-bib-body hanging-indent">

<div id="ref-JacowitzKahneman95" class="csl-entry">

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>.

</div>

<div id="ref-RoeselerWeber22" class="csl-entry">

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>.

</div>

</div>