Hypothesis testing in linear models

The database HBSC24_S4 from package hecedsm contains data for Study 4 of Huang et al. (2024).

Code 
remotes::install_github("lbelzile/hecedsm")
data(HBSC24_S4, package = "hecedsm")
?hecedsm::HBSC24_S4
# Fit regression for effect of mindset on perceived authenticity
mod <- lm(authenticity ~ cond, data = HBSC24_S4)
(emm <- emmeans::emmeans(mod, specs = "cond"))
emm |>
  contrasts(
    method = list(C1 = c(), # fill in Contrast 1 here
                  C2 = c()))  # fill in Contrast 2 here

The following results are extracted from Section D Authenticity and Social Learning Behavior of the Supplementary material.

We ran a regression with contrast coding to examine the role of mindset on perceived authenticity. Participants who reflected on their goal attainment as a transformation perceived their current state to be more authentic \((M = 5.98\), \(\text{SD} = .82)\) compared to participants who wrote about distancing from old state or arriving at a new state \((M_{\text{old}} = 5.62\), \(\text{SD} = 1.18\); \(M_{\text{new}} = 5.74\), \(\text{SD} = 1.07\), contrast 1: \(b = .10\), \(\text{SE} = .04\), \(t(259) = 2.21\), \(p = .028).\)

Further, there was no difference between participants who reflected on their goal attainment as distancing from an old state compared to arriving at a new state (contrast 2: \(b = .06\), \(\text{SE} = .08\), \(t(259) = .79\), \(p = .433).\)

We next examined how perceived authenticity affects information sharing. As expected, authenticity positively predicted information sharing (\(b = 6.84\), \(\text{SE} = 1.87\), \(t(260) = 3.66\), \(p <.001\)).

  1. Using the description from the text, write down the weights for the two contrasts listed above if the order of the conditions is change, new and old.
  2. Perform a global test for the authenticity as a function of experimental condition (cond)
  3. Compute contrasts and report the values of the tests. Check the marginal means and the test statistics: can you reproduce the output of the authors.
  4. Perform a simple linear regression of words on authenticity and check whether the correlation is significant.

References

Huang, S., Brucks, M. S., Song, J., & Campbell, M. C. (2024). Beyond achievement: Transformation mindset enhances authenticity after goal success. Motivation Science, 10(3), 171–181. https://doi.org/10.1037/mot0000340