dependent t test

library(tidyverse)
library(tidyr)
library(dplyr)
library(effsize)

#### read data in r
data_r_w <- read.csv("读写成绩.csv")
head(data_r_w)

##   pre_test post_test
## 1       11        17
## 2       12        16
## 3        9        16
## 4       13        18
## 5       14        19
## 6       14        20

#### You have 40 participants. You want to compare whether their performance in reading and writing is different before and after "some test". The statistical method you should use is paired t-test (or dependent t-test, two names).
t.test(data_r_w$pre_test, data_r_w$post_test, paired = TRUE)

## 
##  Paired t-test
## 
## data:  data_r_w$pre_test and data_r_w$post_test
## t = -12.303, df = 39, p-value = 5.299e-15
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
##  -5.036038 -3.613962
## sample estimates:
## mean difference 
##          -4.325

The result is shown above. You can ask DeepSeek how to interpret the results. You can ask DeepSeek this question: 我做了一个paired t-test, 结果是……（省略号这里你就把上面的Paired t-tes的结果直接复制过来就好），请帮我解读一下这个结果，并告诉我在论文中应该如何报告这些结果。

#### Next, you should do a Cohen's d test. 
effect_size <- cohen.d(data_r_w$pre_test, data_r_w$post_test, paired = TRUE)
print(effect_size)

## 
## Cohen's d
## 
## d estimate: -1.978062 (large)
## 95 percent confidence interval:
##     lower     upper 
## -2.528406 -1.427719

Ask DeepSeek two questions: (1) Why do I have to do a Cohen’d test after the paired t-test? (2) How to interpret the results of Cohen’s d.