We conduct power analyses for the research question, “Does item format influence expected response to personality items?” by powering a balanced one-way analysis of variance. This model assumes no individual differences in response, thereby providing a more conservative estimate of the sample size needed.

# calculate each individual's average response
means = item_block1 %>% 
  group_by(proid, condition) %>% 
  summarise(response = mean(response)) %>% 
  ungroup() 

# calculate mean and variance for each condition
means = means %>% 
  group_by(condition) %>%
  summarise(m = mean(response),
            v = var(response),
            n = n()) 

# calculate ewighted variance
weighted_var = means %>% 
  mutate(newv = v*(n-1)) %>% 
  select(newv, n) %>% 
  colSums() 
weighted_var = weighted_var[[1]]/(weighted_var[[2]]-4)

# enter information into power function
power.anova.test(groups = 4, 
                 between.var = var(means$m), 
                 within.var = weighted_var,
                 power = .9, 
                 sig.level = .05)
## 
##      Balanced one-way analysis of variance power calculation 
## 
##          groups = 4
##               n = 135.3274
##     between.var = 0.009118785
##      within.var = 0.2593392
##       sig.level = 0.05
##           power = 0.9
## 
## NOTE: n is number in each group

This analysis suggests that 136 participants are needed in each condition to achieve 90% power for the differences in means found in the pilot data. To be safe, we plan to recruit 250 participants per condition.