# 載入 haven 套件，用於讀取 SPSS 資料
library(haven)
# 載入 psych 套件，用於描述性統計分析
library(psych)
# 載入 car 套件，用於變異數同質性檢定
library(car)## Loading required package: carData##
## Attaching package: 'car'## The following object is masked from 'package:psych':
##
## logit# 匯入 PISA 2022 資料
PISA <- read_sav("PISA_tawian2022_trimmed_lab.sav")
# 查看資料的基本摘要
summary(PISA)## CNT CNTSTUID NatCen Gender
## Length :5599 Min. :15800002 Length :5599 Min. :1.000
## N.unique : 1 1st Qu.:15802092 N.unique : 1 1st Qu.:1.000
## N.blank : 0 Median :15804235 N.blank : 0 Median :2.000
## Min.nchar: 3 Mean :15804221 Min.nchar: 6 Mean :1.503
## Max.nchar: 3 3rd Qu.:15806338 Max.nchar: 6 3rd Qu.:2.000
## Max. :15808413 Max. :2.000
## AGE ESCS REPEAT MISSSC
## Min. :15.33 Min. :-3.8421 Min. :0.000000 Min. :0.00000
## 1st Qu.:15.58 1st Qu.:-0.9395 1st Qu.:0.000000 1st Qu.:0.00000
## Median :15.83 Median :-0.2368 Median :0.000000 Median :0.00000
## Mean :15.81 Mean :-0.2701 Mean :0.007323 Mean :0.02375
## 3rd Qu.:16.08 3rd Qu.: 0.4393 3rd Qu.:0.000000 3rd Qu.:0.00000
## Max. :16.33 Max. : 4.2070 Max. :1.000000 Max. :1.00000
## SKIPPING WORKPAY MATHMOT RELATST
## Min. :0.0 Min. : 0.0000 Min. :0.00000 Min. :-6.2677
## 1st Qu.:0.0 1st Qu.: 0.0000 1st Qu.:0.00000 1st Qu.:-0.3331
## Median :0.0 Median : 0.0000 Median :0.00000 Median : 0.1440
## Mean :0.1 Mean : 0.6269 Mean :0.04608 Mean : 0.3006
## 3rd Qu.:0.0 3rd Qu.: 0.0000 3rd Qu.:0.00000 3rd Qu.: 0.8408
## Max. :1.0 Max. :10.0000 Max. :1.00000 Max. : 3.1654
## BELONG STRESAGR GROSAGR TEACHSUP
## Min. :-3.25830 Min. :-5.24990 Min. :-3.5994 Min. :-2.9095
## 1st Qu.:-0.48610 1st Qu.:-0.39990 1st Qu.:-0.3061 1st Qu.:-0.3322
## Median :-0.24820 Median :-0.00690 Median :-0.0144 Median :-0.1002
## Mean : 0.01419 Mean :-0.04094 Mean : 0.1384 Mean : 0.2342
## 3rd Qu.: 0.41630 3rd Qu.: 0.29860 3rd Qu.: 0.7798 3rd Qu.: 1.5558
## Max. : 2.75620 Max. : 5.58370 Max. : 3.3724 Max. : 1.5558
## ANXMAT MATHPERS PV1MATH PV1READ
## Min. :-2.3945 Min. :-3.13190 Min. :219.1 Min. :167.4
## 1st Qu.:-0.2758 1st Qu.:-1.08650 1st Qu.:460.4 1st Qu.:439.2
## Median : 0.3378 Median :-0.52750 Median :541.6 Median :515.9
## Mean : 0.3078 Mean :-0.51540 Mean :537.8 Mean :509.2
## 3rd Qu.: 0.7889 3rd Qu.:-0.02115 3rd Qu.:618.8 3rd Qu.:582.0
## Max. : 2.6350 Max. : 2.83150 Max. :917.4 Max. :864.8
## PV1SCIE
## Min. :194.7
## 1st Qu.:462.5
## Median :536.1
## Mean :530.8
## 3rd Qu.:602.8
## Max. :882.7# 計算全體學生數學成績的均值
mean(PISA$PV1MATH, na.rm = TRUE)## [1] 537.822# 計算全體學生數學成績的標準差
sd(PISA$PV1MATH, na.rm = TRUE)## [1] 109.7305# 依性別分組計算數學成績的描述性統計
# Gender：1 為女生，2 為男生
describeBy(PISA$PV1MATH, PISA$Gender)##
## Descriptive statistics by group
## group: 1
## vars n mean sd median trimmed mad min max range skew
## X1 1 2780 535.84 102.26 538.56 536.99 108.38 227.79 821.56 593.77 -0.11
## kurtosis se
## X1 -0.4 1.94
## ------------------------------------------------------------
## group: 2
## vars n mean sd median trimmed mad min max range skew
## X1 1 2819 539.78 116.62 546.54 541.26 125.62 219.06 917.38 698.32 -0.1
## kurtosis se
## X1 -0.51 2.2# 將性別轉換為類別變項
PISA$Gender <- as.factor(PISA$Gender)
# 查看不同性別的樣本數
summary(PISA$Gender)## 1 2
## 2780 2819# 使用 Levene 檢定判斷兩組母體變異數是否相等
# H0：兩組母體變異數相等
# H1：兩組母體變異數不相等
# center = "mean" 表示以平均數為中心
leveneTest(
PISA$PV1MATH ~ PISA$Gender,
center = "mean"
)## Levene's Test for Homogeneity of Variance (center = "mean")
## Df F value Pr(>F)
## group 1 59.342 1.557e-14 ***
## 5597
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Levene 檢定結果為 F(1, 5597) = 59.34， p < 0.001，達顯著水準，表示兩組具有變異數異質性。
# 因變異數異質，採用不合併變異數的 t 檢定
# var.equal = FALSE 表示不假設兩組變異數相等
# 採用調整後的自由度進行雙尾檢定
t.test(
PISA$PV1MATH ~ PISA$Gender,
var.equal = FALSE
)##
## Welch Two Sample t-test
##
## data: PISA$PV1MATH by PISA$Gender
## t = -1.3461, df = 5521.6, p-value = 0.1783
## alternative hypothesis: true difference in means between group 1 and group 2 is not equal to 0
## 95 percent confidence interval:
## -9.688443 1.799944
## sample estimates:
## mean in group 1 mean in group 2
## 535.8361 539.7803檢定結果為 t(5521.60) = -1.35， p = 0.18，未達顯著水準。
本研究以雙獨立樣本 t 檢定比較台灣男生與女生 在 PISA 2022 數學成績的均值差異。
由於 Levene 變異數同質性檢定達顯著水準， 因此採用不合併變異數的 t 檢定。
結果顯示 p = 0.18 > 0.05， 因此不拒絕虛無假設， 表示男生與女生的數學成績均值 未達統計上的顯著差異。