Library:
> # install.packages("knitr")
> # install.packages("rmarkdown")
> # install.packages("prettydoc")
> # install.packages("equatiomatic")1 PENDAHULUAN
1.1 Latar Belakang
Di masa sekarang, di mana data menjadi salah satu aset terpenting dalam pengambilan keputusan, pemahaman mengenai faktor-faktor yang dapat meningkatkan penjualan sangatlah penting. Hal ini tentu relevan dengan industri retail, seperti penjualan sepatu, di mana persaingan sangat ketat dan preferensi konsumen dapat berubah dengan cepat. Dalam konteks ini, analisis statistik dan rancangan percobaan menjadi alat yang sangat berharga untuk membantu perusahaan memahami dan mengoptimalkan strategi pemasaran serta manajemen produk mereka.
Begitu pula dengan toko sepatu Adidas yang ingin mengetahui faktor-faktor apa saja yang mempengaruhi banyaknya penjualan sepatu mereka. Dengan memahami faktor-faktor ini, toko Adidas dapat menyusun strategi yang lebih efektif untuk meningkatkan penjualan dan mengoptimalkan pengelolaan stok produknya.
Penelitian ini bertujuan untuk mengidentifikasi dan menganalisis faktor-faktor yang mempengaruhi jumlah penjualan sepatu Adidas. Dengan menggunakan metode rancangan percobaan, penelitian ini mencoba untuk mengevaluasi pengaruh berbagai kategori produk sepatu terhadap jumlah penjualan. Adapun kategori produk yang dianalisis meliputi jenis sepatu (misalnya, sepatu olahraga, sepatu kasual, sepatu formal), harga, promosi, dan mungkin faktor lainnya seperti lokasi penjualan dan musim.
1.2 Tinjauan Pustaka
1.2.1 Rancangan Acak Lengkap
Rancangan Acak Lengkap (RAL) merupakan rancangan paling sederhana dari Rancangan Percobaan yang bertujuan untuk melihat ada tidak nya pengaruh suatu perlakukan terhadap suatu variabel \[ \text{Hipotesis:} \begin{cases} H_0 : \mu_i = \mu_{i'}=0 \\ H_1 : \text{Setidaknya ada satu } \mu_i \neq \mu_{i'} \end{cases} \] \[ \begin{align*} \text{Faktor Koreksi (FK)} &= \frac{(\sum Y_{ij})^{2}}{pr} \\ \text{JKT} &= \sum_{i}^{p} \sum_{j}^{r} Y_{ij}^{2} - FK \\ \text{JKP} &= \sum_{i}^{p} \frac{\sum_{j}^{r} Y_{ij}^{2}}{r} - FK \\ \text{JKG} &= \text{JKT} - \text{JKP} \\ \text{KTP} &= \frac{\text{JKP}}{p-1} \\ \text{KTG} &= \frac{\text{JKG}}{p(r-1)} \\ \text{Statistik F} &= \frac{\text{KTP}}{\text{KTG}}\\ \\ \text{Keterangan : }\\ \text{p} &= \text{perlakuan}\\ \text{r} &= \text{ulangan}\\ \end{align*} \]
Tabel ANOVA
> SK = c("Perlakuan", "Galat", "Total")
> DB = c("p-1", "p(r-1)", "pr-1")
> JK = c("JKP", "JKG", "JKT")
> KT = c("KTP", "KTG", " ")
> Fhit = c("KTP/KTG", " ", " ")
> anova = cbind(SK,DB,JK,KT,Fhit)
>
> paged_table(as.data.frame(anova))\[ \begin{align*} \text{Ftabel} = F_{\alpha (db1,db2)}\\ \text{Tolak } H_{0}, \text{ jika Fhit} > \text{Ftabel}\\ \text{Terima } H_{0}, \text{ jika Fhit} \leq \text{Ftabel}\\ \end{align*} \]
1.2.2 Uji Lanjut
BNT dan BNJ adalah metode uji lanjut dengan membandingkan 2 rata-rata 2 kelompok \[ \text{Hipotesis:} \begin{cases} H_0 : \mu_i - \mu_{i'}=0 \\ H_1 : \mu_i -\mu_i'\neq 0 \end{cases} \] \[ \begin{align*} \text{BNT} &= t_{\frac{\alpha}{2}, N-k} \sqrt{\text{KTG} \left( \frac{1}{n_i} + \frac{1}{n_{i'}} \right)} \\ \text{BNJ} &= q_{\frac{\alpha}{2}, k, N-k} \sqrt{\frac{\text{KTG}}{2} \left( \frac{1}{n_i} + \frac{1}{n_{i'}} \right)} \end{align*} \]
1.2.3 Asumsi
1.2.3.1 NORMALITAS RESIDUAL
Shapiro Wilk
Untuk mengetahui apakah residual terdistribusi normal dengan sampel
kecil
\[
\text{Hipotesis:}
\begin{cases}
H_0 : \text{Residual berdistribusi Normal} \\
H_1 : \text{Residual tidak berdistribusi Normal}
\end{cases}
\] \[
\begin{align*}
\text{Statistik Uji:}\\
\text{T} &= \frac{1}{D}(\sum_{i=1}^{n}ai(x_{n-i+1}-x_{i}))^{2}
\end{align*}
\] \[
\begin{align*}
\text{Keterangan:}\\
\text{D} &= \sum_{i=1}^{n}(e_{i}-\bar{e})^{2} \\
\text{ai} &= \text{Koefisien Shapiro Wilk} \\
x_{n-i+1} &= \text{Observasi ke-}(n-i+1) \\
x_{i} &= \text{Observasi ke-}i
\end{align*}
\]
1.2.3.2 Homogenitas Ragam
Uji Levene
Digunakan untuk menguji kesamaan varian dari beberapa populasi. Uji
Levene merupakan alternatf uji Bartlett. \[
\text{Hipotesis:}
\begin{cases}
H_{0}:\sigma_{i}=\sigma_{j}\\
H_{1}:\text{Setidaknya ada satu pasang }\sigma_{i}\neq\sigma_{j}
\end{cases}\\
\begin{align*}\\
\text{Statistik Uji:}\\
\text{W} &=
\frac{(n-k)}{(k-1)}\frac{\sum_{i=1}^{k}n_{i}(\bar{Z}_{i.}-\bar{Z}_{..})^{2}}{\sum_{i=1}^{k}\sum_{j=1}^{n_{i}}n_{i}({Z}_{ij}-\bar{Z}_{i.})^{2}}\sim
F_{\alpha ,k-1,n-k}\\
\text{Keterangan :}\\
\text{n} &= \text{Jumlah Observasi}\\
\text{k} &= \text{Banyak Kelompok}\\
Z_{ij} &= \left | Y_{ij}-\bar{Y}_{i.} \right |\\
\bar{Y}_{i.} &= \text{Rata-rata dari kelompok ke-i}\\
\bar{Z}_{i.} &= \text{Rata-rata dari kelompok Zi}\\
\bar{Z} &= \text{Rata-rata menyeluruh dari Z}\\
\end{align*}
\]
1.3 Data
Data yang digunakan merupakan data penjualan sepatu Adidas yang berisi rincian seperti jumlah unit yang terjual, total pendapatan penjualan, lokasi penjualan, jenis produk yang terjual, dan informasi relevan lainnya. Dengan data yang dilakukan analisis adalah variabel jenis produk dan jumlah unit yang terjual, data didapatkan dari https://www.kaggle.com/datasets/heemalichaudhari/adidas-sales-dataset
1.4 Tujuan
Tujuan analisis dilakukan antara lain ;
- Ananlisis penjualan sepatu berdasarkan kategori sepatu
- Mempermudah identifikasi penjualan sepatu
- Mencari inovasi untuk pemasaran
2 SOURCE CODE
2.2 Impor Data
> setwd("C:/Users/HP/Documents/Semester 4/Komputasi Statistika/CSV")
> data <- read.csv("Adidas Sales.csv", header = TRUE, sep = ";")
>
> subset_data <- data.frame(Product = data$Product, Units.Sold = data$Units.Sold)
> head(subset_data)
Product Units.Sold
1 Men's Street Footwear 1200
2 Men's Athletic Footwear 1000
3 Women's Street Footwear 1000
4 Women's Athletic Footwear 850
5 Men's Apparel 900
6 Women's Apparel 10002.3 Analisis RAL
2.3.1 Dengan Cara Manual
> # Hitung DB
> N <- nrow(data)
> p <- data$Product %>% unique() %>% length()
> DBt <- N-1
> DBp <- p-1
> DBg <- N-p
>
> # Hitung JK
> perlakuan.mean <- aggregate(Units.Sold ~ Product, data, mean)[,2]
> n <- aggregate(Units.Sold ~ Product, data, length)[,2]
> grand.mean <- mean(data$Units.Sold)
>
> JKt <- sum((data$Units.Sold - grand.mean)^2)
> JKp <- sum(n*(perlakuan.mean - grand.mean)^2)
> JKg <- JKt - JKp
>
> # Hitung KT
> KTp <- JKp/DBp
> KTg <- JKg/DBg
>
> # Hitung Statistik F
> Fp <- KTp/KTg
> pVal <- pf(Fp, DBp, DBg, lower.tail = FALSE)
>
> #ANOVA
> data.frame(SK=c("Perlakuan","Galat","Total"), DB=c(DBp,DBg,DBt), JK=c(JKp,JKg,JKt),
+ KT=c(KTp,KTg,NA), Fhit=c(Fp,NA,NA), p.value=c(pVal,NA,NA))
SK DB JK KT Fhit p.value
1 Perlakuan 5 33538377 6707675.33 158.0159 6.691437e-162
2 Galat 9642 409296859 42449.37 NA NA
3 Total 9647 442835236 NA NA NA2.4 Uji Lanjut
> # BNT
> library(agricolae)
> bnt <- LSD.test(model,"Product",alpha = 0.05)
> bnt$groups
Units.Sold groups
Men's Street Footwear 368.5217 a
Men's Athletic Footwear 270.5130 b
Women's Apparel 269.7929 b
Women's Street Footwear 243.9484 c
Women's Athletic Footwear 197.5318 d
Men's Apparel 190.9608 d
> bnt$means
Units.Sold std r se LCL UCL
Men's Apparel 190.9608 169.9973 1606 5.141181 180.8830 201.0386
Men's Athletic Footwear 270.5130 216.7088 1610 5.134790 260.4478 280.5783
Men's Street Footwear 368.5217 254.2779 1610 5.134790 358.4565 378.5870
Women's Apparel 269.7929 208.7214 1608 5.137982 259.7214 279.8644
Women's Athletic Footwear 197.5318 174.8108 1606 5.141181 187.4540 207.6096
Women's Street Footwear 243.9484 199.9723 1608 5.137982 233.8769 254.0199
Min Max Q25 Q50 Q75
Men's Apparel 6 925 74 135 229.5
Men's Athletic Footwear 23 1025 111 200 350.0
Men's Street Footwear 84 1275 165 244 545.0
Women's Apparel 38 1100 115 200 350.0
Women's Athletic Footwear 0 925 75 136 250.0
Women's Street Footwear 14 1100 104 175 323.5
> plot(bnt)
>
> #BNJ
> TukeyHSD(model,conf.level = 0.95)
Tukey multiple comparisons of means
95% family-wise confidence level
Fit: aov(formula = f, data = data)
$Product
diff lwr
Men's Athletic Footwear-Men's Apparel 79.552271 58.84154
Men's Street Footwear-Men's Apparel 177.560967 156.85023
Women's Apparel-Men's Apparel 78.832138 58.11498
Women's Athletic Footwear-Men's Apparel 6.570984 -14.15262
Women's Street Footwear-Men's Apparel 52.987611 32.27045
Men's Street Footwear-Men's Athletic Footwear 98.008696 77.31085
Women's Apparel-Men's Athletic Footwear -0.720133 -21.42442
Women's Athletic Footwear-Men's Athletic Footwear -72.981288 -93.69202
Women's Street Footwear-Men's Athletic Footwear -26.564660 -47.26894
Women's Apparel-Men's Street Footwear -98.728829 -119.43311
Women's Athletic Footwear-Men's Street Footwear -170.989983 -191.70072
Women's Street Footwear-Men's Street Footwear -124.573356 -145.27764
Women's Athletic Footwear-Women's Apparel -72.261155 -92.97832
Women's Street Footwear-Women's Apparel -25.844527 -46.55524
Women's Street Footwear-Women's Athletic Footwear 46.416627 25.69946
upr p adj
Men's Athletic Footwear-Men's Apparel 100.263004 0.0000000
Men's Street Footwear-Men's Apparel 198.271699 0.0000000
Women's Apparel-Men's Apparel 99.549302 0.0000000
Women's Athletic Footwear-Men's Apparel 27.294592 0.9456676
Women's Street Footwear-Men's Apparel 73.704774 0.0000000
Men's Street Footwear-Men's Athletic Footwear 118.706544 0.0000000
Women's Apparel-Men's Athletic Footwear 19.984150 0.9999987
Women's Athletic Footwear-Men's Athletic Footwear -52.270555 0.0000000
Women's Street Footwear-Men's Athletic Footwear -5.860377 0.0034945
Women's Apparel-Men's Street Footwear -78.024545 0.0000000
Women's Athletic Footwear-Men's Street Footwear -150.279251 0.0000000
Women's Street Footwear-Men's Street Footwear -103.869073 0.0000000
Women's Athletic Footwear-Women's Apparel -51.543991 0.0000000
Women's Street Footwear-Women's Apparel -5.133811 0.0050659
Women's Street Footwear-Women's Athletic Footwear 67.133790 0.00000002.5 Asumsi
> # Normalitas Galat
> library(tseries)
> model$residual %>% jarque.bera.test()
Jarque Bera Test
data: .
X-squared = 4008.9, df = 2, p-value < 2.2e-16
>
> # Asumsi Homogenitas Ragam
> library(car)
> leveneTest(Units.Sold ~ Product, data)
Levene's Test for Homogeneity of Variance (center = median)
Df F value Pr(>F)
group 5 57.338 < 2.2e-16 ***
9642
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 13 HASIL DAN PEMBAHASAN
3.1 ANOVA
3.1.1 Hipotesis
\[ \text{Hipotesis:} \begin{cases} H_0 : \mu_i - \mu_{i'}=0 \\ H_1 : \mu_i -\mu_i'\neq 0 \end{cases} \]
3.1.2 Statistik Uji
> anova <- data.frame(SK=c("Perlakuan","Galat","Total"), DB=c(DBp,DBg,DBt), JK=c(JKp,JKg,JKt),
+ KT=c(KTp,KTg,NA), Fhit=c(Fp,NA,NA), p.value=c(pVal,NA,NA))
> paged_table(as.data.frame(anova))p-value ≤ α (0,05), maka H0 ditolak
Dengan taraf nyata 5%, dapat disimpulkan produk memberikan pengaruh yang
nyata terhadap banyak nya penjualan.
3.2 Uji Lanjut
BNT
> bnt$groups
Units.Sold groups
Men's Street Footwear 368.5217 a
Men's Athletic Footwear 270.5130 b
Women's Apparel 269.7929 b
Women's Street Footwear 243.9484 c
Women's Athletic Footwear 197.5318 d
Men's Apparel 190.9608 d- Rata-rata penjualan sepatu dengan produk “Men’s Street Footwear”
berbeda nyata terhadap rata-rata penjualan sepatu dengan produk “Men’s
Athletic Footwear”
- Rata-rata penjualan sepatu dengan produk “Men’s Athletic Footwear”
tidak berbeda nyata terhadap rata-rata penjualan sepatu dengan produk
“Women’s Apparel”
- Rata-rata penjualan sepatu dengan produk “Men’s Athletic Footwear”
dan “Women’s Apparel” berbeda nyata terhadap rata-rata penjualan sepatu
dengan produk “Women’s Street Footwear”
- Rata-rata penjualan sepatu dengan produk “Women’s Street Footwear”
berbeda nyata terhadap rata-rata penjualan sepatu dengan produk “Women’s
Athletic Footwear”
- Rata-rata penjualan sepatu dengan produk “Women’s Athletic Footwear”
berbeda nyata terhadap rata-rata penjualan sepatu dengan produk “Men’s
Apparel”
- Rata-rata penjualan sepatu tertinggi adalah kategori sepatu “Men’s Street Footwear”
BNJ
> TukeyHSD(model,conf.level = 0.95)
Tukey multiple comparisons of means
95% family-wise confidence level
Fit: aov(formula = f, data = data)
$Product
diff lwr
Men's Athletic Footwear-Men's Apparel 79.552271 58.84154
Men's Street Footwear-Men's Apparel 177.560967 156.85023
Women's Apparel-Men's Apparel 78.832138 58.11498
Women's Athletic Footwear-Men's Apparel 6.570984 -14.15262
Women's Street Footwear-Men's Apparel 52.987611 32.27045
Men's Street Footwear-Men's Athletic Footwear 98.008696 77.31085
Women's Apparel-Men's Athletic Footwear -0.720133 -21.42442
Women's Athletic Footwear-Men's Athletic Footwear -72.981288 -93.69202
Women's Street Footwear-Men's Athletic Footwear -26.564660 -47.26894
Women's Apparel-Men's Street Footwear -98.728829 -119.43311
Women's Athletic Footwear-Men's Street Footwear -170.989983 -191.70072
Women's Street Footwear-Men's Street Footwear -124.573356 -145.27764
Women's Athletic Footwear-Women's Apparel -72.261155 -92.97832
Women's Street Footwear-Women's Apparel -25.844527 -46.55524
Women's Street Footwear-Women's Athletic Footwear 46.416627 25.69946
upr p adj
Men's Athletic Footwear-Men's Apparel 100.263004 0.0000000
Men's Street Footwear-Men's Apparel 198.271699 0.0000000
Women's Apparel-Men's Apparel 99.549302 0.0000000
Women's Athletic Footwear-Men's Apparel 27.294592 0.9456676
Women's Street Footwear-Men's Apparel 73.704774 0.0000000
Men's Street Footwear-Men's Athletic Footwear 118.706544 0.0000000
Women's Apparel-Men's Athletic Footwear 19.984150 0.9999987
Women's Athletic Footwear-Men's Athletic Footwear -52.270555 0.0000000
Women's Street Footwear-Men's Athletic Footwear -5.860377 0.0034945
Women's Apparel-Men's Street Footwear -78.024545 0.0000000
Women's Athletic Footwear-Men's Street Footwear -150.279251 0.0000000
Women's Street Footwear-Men's Street Footwear -103.869073 0.0000000
Women's Athletic Footwear-Women's Apparel -51.543991 0.0000000
Women's Street Footwear-Women's Apparel -5.133811 0.0050659
Women's Street Footwear-Women's Athletic Footwear 67.133790 0.0000000- Rata-rata penjualan kategori sepatu Men’s Athletic Footwear dan
Men’s Apparel berbeda nyata
- Rata-rata penjualan kategori sepatu Men’s Street Footwear dan Men’s
Apparel berbeda nyata
- Rata-rata penjualan kategori sepatu Women’s Apparel dan Men’s
Apparel berbeda nyata
- Rata-rata penjualan kategori sepatu Women’s Athletic Footwear dan
Men’s Apparel tidak berbeda nyata
- Rata-rata penjualan kategori sepatu Women’s Street Footwear dan
Men’s Apparel berbeda nyata
- Rata-rata penjualan kategori sepatu Men’s Street Footwear dan Men’s
Athletic Footwear berbeda nyata
- Rata-rata penjualan kategori sepatu Women’s Apparel dan Men’s
Athletic Footwear tidak berbeda nyata
- Rata-rata penjualan kategori sepatu Women’s Athletic Footwear dan
Men’s Athletic Footwear berbeda nyata
- Rata-rata penjualan kategori sepatu Women’s Street Footwear dan
Men’s Athletic Footwear berbeda nyata
- Rata-rata penjualan kategori sepatu Women’s Apparel dan Men’s Street
Footwear berbeda nyata
- Rata-rata penjualan kategori sepatu Women’s Athletic Footwear dan
Men’s Street Footwear berbeda nyata
- Rata-rata penjualan kategori sepatu Women’s Street Footwear dan
Men’s Street Footwear berbeda nyata
- Rata-rata penjualan kategori sepatu Women’s Athletic Footwear dan
Women’s Apparel berbeda nyata
- Rata-rata penjualan kategori sepatu Women’s Street Footwear dan
Women’s Apparel berbeda nyata
- Rata-rata penjualan kategori sepatu Women’s Street Footwear dan Women’s Athletic Footwear berbeda nyata
3.3 Uji Asumsi
3.3.1 Normalitas Residual
\[ \begin{align*}\\ \text{Hipotesis :}\\ H_{0} &: \text{Residual berdistribusi normal}\\ H_{1} &: \text{Residual tidak berdistribusi normal}\\ \end{align*} \]
> model$residual %>% jarque.bera.test()
Jarque Bera Test
data: .
X-squared = 4008.9, df = 2, p-value < 2.2e-16p-value ≤ α (0,05), maka H0 ditolak
Dengan taraf nyata 5%, dapat disimpulkan residual tidak berdistribusi
normal.
3.3.2 Homogenitas Ragam
\[ \begin{align*}\\ \text{Hipotesis :}\\ H_{0} &: \text{Ragam Homogen}\\ H_{1} &: \text{Ragam Tidak Homogen}\\ \end{align*} \]
> leveneTest(Units.Sold ~ Product, data)
Levene's Test for Homogeneity of Variance (center = median)
Df F value Pr(>F)
group 5 57.338 < 2.2e-16 ***
9642
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1p-value ≤ α (0,05), maka H0 ditolak
Dengan taraf nyata 5%, dapat disimpulkan ragam tidak homogen.
4 KESIMPULAN
- Kategori Sepatu berpengaruh terhadap banyak nya Penjualan
- Rata-rata penjualan sepatu tertinggi adalah kategori sepatu “Men’s
Street Footwear”
- Residual tidak berdistribusi normal, maka data tidak berdistribusi normal
5 DAFTAR PUSTAKA
Sari, D. E., & Khafid, J. (2022). Analisa Pengaruh Pemasaran
Melalui Media Sosial Terhadap Penjualan AMC Media Menggunakan Desain
Acak Lengkap . INDONESIAN COUNCIL OF PREMIER STATISTICAL SCIENCE,
20-25
Uji lavene. (2013). Retrieved from https://www.slideshare.net/mmubaraq/uji-lavene-20049868
SUmber data https://www.kaggle.com/datasets/heemalichaudhari/adidas-sales-dataset