pilot a testing

# loading libraries
library(dplyr)

## 
## Attaching package: 'dplyr'

## The following objects are masked from 'package:stats':
## 
##     filter, lag

## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union

# reading data
data <- read.csv("PilotA.csv")

# preparing data
difficult_data <- subset(data, Condition == "Brush")
easy_data <- subset(data, Condition == "Arial")

# z-test for proportion of "2" answers
prop_difficult_2 <- mean(difficult_data$Distorted == "2")
prop_easy_2 <- mean(easy_data$Distorted == "2")

#combined standard error
n_difficult <- nrow(difficult_data)
n_easy <- nrow(easy_data)
p_combined <- (sum(difficult_data$Distorted == "2") + sum(easy_data$Distorted == "2")) / (n_difficult + n_easy)
se_combined <- sqrt(p_combined * (1 - p_combined) * (1/n_difficult + 1/n_easy))

#z-test
z_score <- (prop_difficult_2 - prop_easy_2) / se_combined
p_value <- 2 * (1 - pnorm(abs(z_score)))

cat("Z-score for comparison of '2' answers:", z_score, "\nP-value:", p_value, "\n")

## Z-score for comparison of '2' answers: -0.58554 
## P-value: 0.5581846

# meta-analysis using rosenthal's methods
z_values <- c(3.26, 2.89, 2.5, 2.45)
combined_z <- sqrt(sum(z_values^2))
combined_p_value <- 2 * (1 - pnorm(combined_z))

cat("Combined Z-score using Rosenthal's method:", combined_z, "\nCombined P-value:", combined_p_value, "\n")

## Combined Z-score using Rosenthal's method: 5.588578 
## Combined P-value: 2.28937e-08

# making the plots

library(ggplot2)

proportions <- data.frame(
  Condition = c("Difficult", "Easy"),
  Proportion = c(prop_difficult_2, prop_easy_2)
)

ggplot(proportions, aes(x = Condition, y = Proportion, fill = Condition)) +
  geom_bar(stat = "identity", position = "dodge") +
  ylim(0, 1) +
  labs(title = "Proportion of '2' Answers by Font Condition",
       x = "Font Condition",
       y = "Proportion of '2' Answers") +
  theme_minimal()