HOMEWORK ASSIGNMENT 2
2025-03-29
Hyejin Roh (h12428201)
1. Find data
- Survey of Household Finances and Living Conditions (Statistics Korea, 2024)
2. Import data
mydata <- read.table("./Household.csv", header=TRUE, sep=",")3. Display data
head(mydata)## CapitalRegion Assets Liabilities NetAssets
## 1 G1 1 5300 -5299
## 2 G1 10 0 10
## 3 G1 10 0 10
## 4 G1 10 0 10
## 5 G1 10 0 10
## 6 G1 100 0 1004. Explain data
- unit: 1 household
- sample size: 60 (30 Capital, 30 NonCapital)
- CapitalRegion: living in Capital Region(Seoul, G1) or
not(G2)
- NetAssets: Net assets of a household (Assets - Liabilities)
- units of measurement: 10,000 krw
5. Data source
- Survey of Household Finances and Living Conditions (Statistics
Korea, 2024)
- URL: https://mdis.kostat.go.kr/ofrData/selectOfrDataDetail.do?survId=1005641&itmDiv=1&nPage=3&itemId=2005&itemNm=%EC%86%8C%EB%93%9D%C2%B7%EC%86%8C%EB%B9%84%C2%B7%EC%9E%90%EC%82%B0 (needs login to access)
6-1. Data manipulation
library(dplyr)##
## 다음의 패키지를 부착합니다: 'dplyr'## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, unionset.seed(2024)
mydata$CapitalRegion <- factor(mydata$CapitalRegion,
levels = c("G1", "G2"),
labels = c("Capital", "NonCapital"))
Capital <- mydata %>%
filter(CapitalRegion == "Capital", NetAssets > 0)
Capital <- Capital[sample(nrow(Capital), 30), ]
NonCapital <- mydata %>%
filter(CapitalRegion == "NonCapital", NetAssets > 0)
NonCapital <- NonCapital[sample(nrow(NonCapital), 30), ]
sample.mydata <- rbind(Capital, NonCapital)
sample.mydata <- sample.mydata[, c("CapitalRegion", "NetAssets")]
sample.mydata$LogNetAssets <- log(sample.mydata$NetAssets)
sample.mydata## CapitalRegion NetAssets LogNetAssets
## 5698 Capital 38300 10.553205
## 4645 Capital 54600 10.907789
## 3629 Capital 42552 10.658482
## 4796 Capital 66500 11.104957
## 5375 Capital 74396 11.217157
## 5009 Capital 7066 8.863050
## 2669 Capital 29400 10.288750
## 3488 Capital 40168 10.600826
## 105 Capital 102300 11.535665
## 1762 Capital 20220 9.914427
## 5119 Capital 55126 10.917377
## 5149 Capital 76740 11.248178
## 1035 Capital 150400 11.921054
## 4880 Capital 688300 13.441980
## 398 Capital 113768 11.641917
## 2978 Capital 18575 9.829572
## 3098 Capital 2420 7.791523
## 3634 Capital 426000 12.962195
## 3104 Capital 24940 10.124228
## 2773 Capital 30338 10.320156
## 4299 Capital 33000 10.404263
## 35 Capital 29740 10.300248
## 1385 Capital 16810 9.729729
## 4334 Capital 5500 8.612503
## 2641 Capital 29000 10.275051
## 3356 Capital 31266 10.350287
## 3288 Capital 36740 10.511621
## 3668 Capital 4313 8.369389
## 3548 Capital 25990 10.165467
## 1451 Capital 1800 7.495542
## 9658 NonCapital 60980 11.018301
## 8052 NonCapital 4565 8.426174
## 10516 NonCapital 7217 8.884195
## 8119 NonCapital 25400 10.142504
## 9303 NonCapital 57450 10.958670
## 6649 NonCapital 35650 10.481504
## 10858 NonCapital 64994 11.082050
## 1916 NonCapital 14913 9.609989
## 10116 NonCapital 6653 8.802823
## 9863 NonCapital 6350 8.756210
## 4020 NonCapital 22630 10.027032
## 212 NonCapital 42880 10.666161
## 1305 NonCapital 128358 11.762579
## 1849 NonCapital 138935 11.841761
## 4913 NonCapital 2656 7.884577
## 11574 NonCapital 900 6.802395
## 8026 NonCapital 32610 10.392374
## 9137 NonCapital 556 6.320768
## 3715 NonCapital 19519 9.879144
## 4249 NonCapital 23410 10.060919
## 8897 NonCapital 4560 8.425078
## 3860 NonCapital 145 4.976734
## 2441 NonCapital 12268 9.414750
## 9935 NonCapital 64336 11.071875
## 8656 NonCapital 5100 8.536996
## 4085 NonCapital 22910 10.039329
## 2234 NonCapital 5056 8.528331
## 2353 NonCapital 16200 9.692767
## 10867 NonCapital 59650 10.996249
## 1155 NonCapital 110864 11.616060- use set.seed(2024) to ensure reproducibility
- rename Capital Region code(G1, G2) to Capital,
NonCapital
- randomly select 30 households from Capital and NonCapital
- create a new dataset with CapitalRegion, NetAssets
- NetAssets > 0: for log-transform, exclude households with
negative net assets
- log(NetAssets): reduce right-skewness, improve normality of NetAssets
6-2. Data manipulation - Descriptive statistics
library(psych)
describeBy(sample.mydata$LogNetAssets, group = sample.mydata$CapitalRegion)##
## Descriptive statistics by group
## group: Capital
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 30 10.4 1.31 10.38 10.42 0.81 7.5 13.44 5.95 -0.11 0.3 0.24
## ------------------------------------------------------------
## group: NonCapital
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 30 9.57 1.63 9.95 9.74 1.62 4.98 11.84 6.87 -0.88 0.4 0.3- Capital Region
- average net assets: 10.4
- minimum net assets: 7.5
- maximum net assets: 13.44
- median net assets: 10.38 (half of the net assets are 10.38, other
net asses of households are more)
- average net assets: 10.4
- Non Capital Region
- average net assets: 9.57
- minimum net assets: 4.98
- maximum net assets: 11.84
- median net assets: 9.95 (half of the net assets are 9.95, other net
asses of households are more)
- average net assets: 9.57
- Sample Mean (\(\bar{y}\))
- Capital: 10.4, NonCapital: 9.57
- arithmetic average of observed values
- a point estimate of the population mean (\(\mu\))
- households in the capital region tend to have higher average net
assets than those in the non-capital region
- Sample Standard Deviation (s)
- Capital: 1.31, NonCapital: 1.63
- measures the dispersion of observed values around the sample mean
- estimate of the population standard deviation (\(\sigma\))
- households in the non-capital region have higher \(s\), more dispersed data than those in the
capital region
- Sample Median (\(\tilde{y}\))
- Capital: 10.38, NonCapital: 9.95
- middle value of the ordered data
- robust estimate of the population median
- households in the capital region tend to have higher median net assets than those in the non-capital region
- Capital: 10.38, NonCapital: 9.95
7-1. Statistical hypothesis test
Research Question
- Is there a difference in the average net assets between
households in the Capital Region and those in the Non Capital
Region?
Research Hypothesis
- \(H_0: \mu_{capital} =
\mu_{noncapital}\)
- \(H_1: \mu_{capital} \neq
\mu_{noncapital}\)
Assumptions
- Variable is numeric: log(Net Assets) is numeric
- Normality: check by histograms & Shapiro-Wilk
test
- For independent samples t-test:
- Independence: households in the capital/non-capital region are
independent
- Homogeneity of variance: check by Levene’s test
- Independence: households in the capital/non-capital region are
independent
library(ggplot2)##
## 다음의 패키지를 부착합니다: 'ggplot2'## The following objects are masked from 'package:psych':
##
## %+%, alphaggplot(sample.mydata, aes(x = LogNetAssets)) +
geom_histogram(binwidth = 0.5, colour="gray") +
facet_wrap(~CapitalRegion, ncol = 1) +
ylab("Amount")
- check whether the data is normally distributed (based on the
histograms)
- assume normally distributed
library(rstatix)##
## 다음의 패키지를 부착합니다: 'rstatix'## The following object is masked from 'package:stats':
##
## filtersample.mydata %>%
group_by(CapitalRegion) %>%
shapiro_test(LogNetAssets)## # A tibble: 2 × 4
## CapitalRegion variable statistic p
## <fct> <chr> <dbl> <dbl>
## 1 Capital LogNetAssets 0.954 0.215
## 2 NonCapital LogNetAssets 0.932 0.0564Shapiro Test
whether the data is normally distributed
\(H_0\): log(Net Assets) is normally distributed
\(H_1\): log(Net Assets) is NOT normally distributed
Capital Region:
- p-value = 0.215 > 0.05 \(\rightarrow\) can’t reject \(H_0\)
- data is normally distributed
- p-value = 0.215 > 0.05 \(\rightarrow\) can’t reject \(H_0\)
Non Capital Region:
- p-value = 0.057 > 0.05 \(\rightarrow\) can’t reject \(H_0\)
- data is normally distributed
- p-value = 0.057 > 0.05 \(\rightarrow\) can’t reject \(H_0\)
library(car)## 필요한 패키지를 로딩중입니다: carData##
## 다음의 패키지를 부착합니다: 'car'## The following object is masked from 'package:psych':
##
## logit## The following object is masked from 'package:dplyr':
##
## recodeleveneTest(sample.mydata$LogNetAssets, group = sample.mydata$CapitalRegion)## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 1 1.6048 0.2103
## 58Levene’s Test
- whether the variance is the same
- \(H_0: \sigma^2_{capital} =
\sigma^2_{noncapital}\)
- \(H_1: \sigma^2_{capital} \neq
\sigma^2_{noncapital}\)
- p-value = 0.2103 > 0.05 \(\rightarrow\) can’t reject \(H_0\)
- assume the variance is the same
7-2. Statistical hypothesis test - parametric test(Independent t-test)
t.test(sample.mydata$LogNetAssets ~ sample.mydata$CapitalRegion,
var.equal = TRUE,
alternative = "two.sided")##
## Two Sample t-test
##
## data: sample.mydata$LogNetAssets by sample.mydata$CapitalRegion
## t = 2.1785, df = 58, p-value = 0.03344
## alternative hypothesis: true difference in means between group Capital and group NonCapital is not equal to 0
## 95 percent confidence interval:
## 0.06752773 1.59635847
## sample estimates:
## mean in group Capital mean in group NonCapital
## 10.401886 9.569943- \(H_0: \mu_{capital} =
\mu_{noncapital}\)
- \(H_1: \mu_{capital} \neq
\mu_{noncapital}\)
- p-value = 0.03344 < 0.05 \(\rightarrow\) reject \(H_0\)
\(\Rightarrow\) there is a significant difference in the average net assets between households in the Capital Region and those in the Non Capital Region
library(effectsize)##
## 다음의 패키지를 부착합니다: 'effectsize'## The following objects are masked from 'package:rstatix':
##
## cohens_d, eta_squared## The following object is masked from 'package:psych':
##
## phieffectsize::cohens_d(sample.mydata$LogNetAssets ~ sample.mydata$CapitalRegion,
pooled_sd = FALSE)## Cohen's d | 95% CI
## ------------------------
## 0.56 | [0.04, 1.08]
##
## - Estimated using un-pooled SD.interpret_cohens_d(0.56, rules = "sawilowsky2009")## [1] "medium"
## (Rules: sawilowsky2009)- Based on the sample data, the average Net Assets of
households differs (p<0.034).
- Households in the Capital Region have higher average Net Assets than
those in the Non Capital Region.
- the effect size is medium, \(d\)=0.56
7-3. Statistical hypothesis test - non-parametric test(Wilcoxon Rank Sum Test)
wilcox.test(sample.mydata$LogNetAssets ~ sample.mydata$CapitalRegion,
paired = FALSE,
correct = FALSE,
exact = FALSE,
alternative = "two.sided")##
## Wilcoxon rank sum test
##
## data: sample.mydata$LogNetAssets by sample.mydata$CapitalRegion
## W = 577, p-value = 0.06043
## alternative hypothesis: true location shift is not equal to 0- \(H_0: \mu_{capital} =
\mu_{noncapital}\)
- \(H_1: \mu_{capital} \neq
\mu_{noncapital}\)
- p-value = 0.06043 > 0.05 \(\rightarrow\) can’t reject \(H_0\)
\(\Rightarrow\) there isn’t a significant difference in the average net assets between households in the Capital Region and those in the Non Capital Region
library(effectsize)
effectsize(wilcox.test(sample.mydata$LogNetAssets ~ sample.mydata$CapitalRegion,
paired = FALSE,
correct = FALSE,
exact = FALSE,
alternative = "two.sided"))## r (rank biserial) | 95% CI
## ---------------------------------
## 0.28 | [ 0.00, 0.53]interpret_rank_biserial(0.28)## [1] "medium"
## (Rules: funder2019)- Based on the sample data, the average Net Assets of
households doesn’t differ (p>0.061)
- If we calculate the effect size:
- the difference in distribution location is medium. (\(r\)=0.69)
7-4. Conclusion
- parametric test(Independent t-test) is more
suitable
- assumptions are not violated
- it has higher statistical power
- the results are more certain
- assumptions are not violated
- effect size: medium, \(d\)=0.56
- the mean difference \(\mu_d =
\mu_{capital} - \mu_{noncapital}\) corresponds to a medium effect
size
- the mean difference \(\mu_d =
\mu_{capital} - \mu_{noncapital}\) corresponds to a medium effect
size
- answer (same as the answer from the t-test):
- Based on the sample data, the average Net Assets of
households differs (p<0.034).
- Households in the Capital Region have higher average Net Assets than
those in the Non Capital Region.
- the effect size is medium, \(d\)=0.56
- Based on the sample data, the average Net Assets of
households differs (p<0.034).