R Notebook

library(tidyverse)
library(lme4)

respondents_data <- data.frame(respondent = c("Alice", "Bob", 
                           "Claudia", "Daniel"),
           gender = c("female", "male", "female", "male")) %>%
  mutate(rt_bias = runif(min=1, max=10, n=n()))
respondents_data

collected_data <- respondents_data %>% mutate(number_of_observations = 20) %>% uncount(number_of_observations) %>% mutate(reaction_time=rt_bias + rnorm(mean=10, n=n()))
collected_data

t.test(reaction_time ~ gender, data=collected_data)

    Welch Two Sample t-test

data:  reaction_time by gender
t = 6.9482, df = 48.132, p-value = 8.71e-09
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
 2.268700 4.116203
sample estimates:
mean in group female   mean in group male 
            17.09229             13.89984 

summary(lm(reaction_time ~ gender, data=collected_data))

Call:
lm(formula = reaction_time ~ gender, data = collected_data)

Residuals:
    Min      1Q  Median      3Q     Max 
-4.9314 -1.4669  0.0814  1.4191  4.1755 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  17.0923     0.3249  52.609  < 2e-16 ***
gendermale   -3.1925     0.4595  -6.948 9.88e-10 ***
---
Signif. codes:  
0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 2.055 on 78 degrees of freedom
Multiple R-squared:  0.3823,    Adjusted R-squared:  0.3744 
F-statistic: 48.28 on 1 and 78 DF,  p-value: 9.884e-10

summary(lmer(reaction_time ~ gender + (1|respondent),
             data=collected_data))

Linear mixed model fit by REML. t-tests use
  Satterthwaite's method [lmerModLmerTest]
Formula: reaction_time ~ gender + (1 | respondent)
   Data: collected_data

REML criterion at convergence: 233.3

Scaled residuals: 
     Min       1Q   Median       3Q      Max 
-2.49299 -0.44896  0.09558  0.52886  2.76354 

Random effects:
 Groups     Name        Variance Std.Dev.
 respondent (Intercept) 6.4110   2.5320  
 Residual               0.9345   0.9667  
Number of obs: 80, groups:  respondent, 4

Fixed effects:
            Estimate Std. Error     df t value Pr(>|t|)  
(Intercept)   17.092      1.797  2.000   9.512   0.0109 *
gendermale    -3.192      2.541  2.000  -1.256   0.3359  
---
Signif. codes:  
0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Correlation of Fixed Effects:
           (Intr)
gendermale -0.707

dat <- read_csv("https://github.com/LingConLab/Can-recall-data-be-trusted/raw/master/data/ITM.csv")

colnames(dat)

dat %>% group_by(year_of_birth, sex) %>% summarise(ITM=mean(`number of lang`), n = n()) %>% ggplot(aes(x=year_of_birth, y=ITM)) + geom_point(aes(size=n, color=sex), alpha=0.5)

summary(lm(`number of lang` ~ year_of_birth + sex, data=dat))

summary(lmer(`number of lang` ~ year_of_birth + sex + (1|residence), data=dat))