Compute propensity scores $p(condition = treatment | covariates)$ with logistic regression model: `condition ~ 10 covariates` (see below for covariates).
# those who completed both days
N = 275
```r
condition N
1: accuracy 183
2: interest 92
```
Probability of being assigned to treatment condition is higher in the treatment (accuracy) than control (interest) condition.
```r
# logistic regression predicting treatment assignment with covariates
m0 <- glm(conditiond ~ age + gender + region + country + domain + role + tenuredays + aot + covid_concern + conspiracy, d00, family = "binomial")
d00$propensity_glm <- predict(m0, type = 'response')
# t-test
> summaryh(t.test(propensity_glm ~ condition, d00))
results
1: t(174) = 8.60, p < .001, r = 0.55
# multilevel model with counterbalance as clustering variable
> summaryh(m1 <- lmer(propensity_glm ~ condition + (1 | counterbalance), d00))
term results
1: (Intercept) b = 0.70, SE = 0.04, t(6) = 16.21, p < .001, r = 0.99
2: conditioninterest b = −0.18, SE = 0.06, t(7) = −2.90, p = .024, r = 0.75
```
There's quite a bit of overlap in the propensity score distributions for treatment and control groups, so we should be good (but maybe match on propensity scores)?
![[_temp.png]]
Propensity scores for different conditions (8 conditions for counterbalancing).
![[_temp 2.png]]
# extra check: those who completed only day 1 or both days
N = 360
```r
condition N
1: accuracy 245
2: interest 115
```
```r
# logistic regression predicting treatment assignment with covariates
m0 <- glm(conditiond ~ age + gender + region + country + domain + role + tenuredays + aot + covid_concern + conspiracy, d00, family = "binomial")
d00$propensity_glm <- predict(m0, type = 'response')
# t-test
> summaryh(t.test(propensity_glm ~ condition, d00))
results
1: t(232) = 8.62, p < .001, r = 0.49
# multilevel model with counterbalance as clustering variable
> summaryh(m1 <- lmer(propensity_glm ~ condition + (1 | counterbalance), d00))
term results
1: (Intercept) b = 0.70, SE = 0.04, t(6) = 18.42, p < .001, r = 0.99
2: conditioninterest b = −0.14, SE = 0.05, t(7) = −2.52, p = .042, r = 0.70
```
![[_temp 1.png]]
![[_temp 3.png]]