Aplikasi Komputer - 10 - Statistik di MatLab

1. 1
Aplikasi Statistik
Dalam MATLAB
Arif Rahman, ST MT

2. 2
Pemusatan Data
Mencari Rata-rata
mean(Datavector)
Mencari Rata-rata Geometrik
geomean(Datavector)
Mencari Rata-rata Harmonik
harmmean(Datavector)
Mencari Rata-rata tanpa outlier
trimmean(Datavector,percent)

3. 3
Pemusatan Data
Mencari Nilai Tengah
median(Datavector)
Mencari Nilai Paling Sering Muncul
mode(Datavector)

4. 4
Penyebaran Data
Variansi
var(Datavector)
Simpangan Baku
std(Datavector)
Rentang
range(Datavector)
Kuartil
quantile(Datavector, rank)
Persentil
prctile(Datavector,rank)

5. 5
Ukuran Distribusi
Kemiringan
skewness(Datavector)
Keruncingan
kurtosis(Datavector)

6. Statistik Deskriptif
Summary
summary(Datavector)
Tabulasi Tabel Frekuensi
tabulate(Datavector)
Tabulasi Silang
crosstab(x1,x2,x3,...)
Stratifikasi
grpstats(Datavector,groupvars)
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7. Matriks
Korelasi
corr(Datavector)
Koefisien Korelasi
corrcoef(Datavector)
Kovarian
cov(Datavector)
Kovarian Korelasi
corrcov(Datavector)
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8. Grafik
Balok rentang  boxplot(x,group)
Pencar  scatter(x,y), scatter3(…)
Garis  plot(x,y), plot3(…), plotyy(…)
Batang  bar(x,y), barh(…), bar3(…)
Histogram  hist(y,x), hist3(…)
Venn  pie(x), pie3(…)
Pareto  pareto(y, name)
8

9. 9
Pengujian Hipotesis
Uji Rata-rata σ diketahui
[h,p] = ztest(Datavector,µ,σ)
[h,p] = ztest(Datavector,µ,σ,α,tail)
h
Hipotesa yang diterima
p
Probabilitas tingkat signifikansi

10. 10
Pengujian Hipotesis
Uji Rata-rata σ tidak diketahui
[h,p] = ttest(Datavector,µ)
[h,p] = ttest(Datavector,µ,α,tail)
h
Hipotesa yang diterima
p
Probabilitas tingkat signifikansi

11. 11
Pengujian Hipotesis
Uji Dua Rata-rata
[h,p] = ttest2(x,y)
[h,p] = ttest2(x,y,α,tail)
h
Hipotesa yang diterima
p
Probabilitas tingkat signifikansi

12. 12
Pengujian Hipotesis
Uji satu variansi
[h,p] = vartest(Datavector,σ2
)
[h,p] = vartest(Datavector,σ2
,α,tail)
h
Hipotesa yang diterima
p
Probabilitas tingkat signifikansi

13. 13
Pengujian Hipotesis
Uji dua variansi
[h,p] = vartest2(x,y)
[h,p] = vartest2(x,y,α,tail)
h
Hipotesa yang diterima
p
Probabilitas tingkat signifikansi

14. 14
Pengujian Hipotesis
Uji beberapa variansi
p = vartestn(Datavector,group)
p = vartestn(Datavector,group,α,tail)
p
Probabilitas tingkat signifikansi

15. 15
Pengujian Hipotesis
Uji Chi Square χ2
Tingkat Signifikansi
• CHITEST(DataRange1; DataRange1)
χ2
hitung
• CHIINV(SignLvl;df)
χ2
tabel
• CHIINV(α;df)

16. Uji Nonparametrik
signtest - Sign test (paired
samples).
ranksum - Wilcoxon rank sum test
(independent samples).
signrank - Wilcoxon sign rank test
(paired samples).
kruskalwallis - Kruskal-Wallis test
(nonparametric one-way anova).
friedman - Friedman's test
16

17. Peta Kontrol
controlchart - Shewhart control chart.
capability - Capability indices.
capaplot - Capability plot.
runstest - Runs test for randomness.
17

18. Uji Distribusi
dfittool
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19. Uji Distribusi
disttool
19

20. Uji Distribusi
cdfplot(Datavector)
histfit(Datavector)
normplot(Datavector)
probplot(Distribution, Datavector)
chi2gof(Datavector)
kstest(Datavector,CDF,alpha,tail)
lillietest(x,alpha)
jbtest(x,alpha)
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21. Anova
anova1 - One-way analysis of
variance.
anova2 - Two-way analysis of
variance.
anovan - n-way analysis of variance.
multcompare - Multiple comparisons of
means and other estimates.
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22. Regresi Linier
regress - Multiple linear regression using
least squares.
regstats - Regression diagnostics.
lsline - Add least-square fit line to scatter
plot.
robustfit - Robust regression model fitting.
polyfit - Least-squares polynomial fitting
corr - Linear correlation coefficient.
partialcorr - Linear partial correlation
coefficient.
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23. Statistik Multivariate
clusterdata - Construct clusters from
data.
factoran - Factor analysis.
princomp - Principal components
analysis from raw data.
rotatefactors - Rotation of FA or PCA
loadings.
barttest - Bartlett's test for
dimensionality.
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24. Probability density function
betapdf - Beta density.
binopdf - Binomial density.
chi2pdf - Chi square density.
exppdf - Exponential density.
fpdf - F density.
gampdf - Gamma density.
geopdf - Geometric density.
hygepdf - Hypergeometric density.
lognpdf - Lognormal density.
nbinpdf - Negative binomial density.
normpdf - Normal (Gaussian) density.
poisspdf - Poisson density.
tpdf - T density.
unidpdf - Discrete uniform density.
unifpdf - Uniform density.
wblpdf - Weibull density.
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25. Cumulative distribution function
betacdf - Beta cumulative distribution function.
binocdf - Binomial cumulative distribution function.
chi2cdf - Chi square cumulative distribution function.
expcdf - Exponential cumulative distribution function.
fcdf - F cumulative distribution function.
gamcdf - Gamma cumulative distribution function.
geocdf - Geometric cumulative distribution function.
hygecdf - Hypergeometric cumulative distribution function.
logncdf - Lognormal cumulative distribution function.
nbincdf - Negative binomial cumulative distribution function.
normcdf - Normal (Gaussian) cumulative distribution function.
poisscdf - Poisson cumulative distribution function.
tcdf - T cumulative distribution function.
unidcdf - Discrete uniform cumulative distribution function.
unifcdf - Uniform cumulative distribution function.
wblcdf - Weibull cumulative distribution function.
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26. Inverse Distribution Function
betainv - Beta inverse cumulative distribution function.
binoinv - Binomial inverse cumulative distribution function.
chi2inv - Chi square inverse cumulative distribution function.
expinv - Exponential inverse cumulative distribution function.
finv - F inverse cumulative distribution function.
gaminv - Gamma inverse cumulative distribution function.
geoinv - Geometric inverse cumulative distribution function.
hygeinv - Hypergeometric inverse cumulative distribution function.
logninv - Lognormal inverse cumulative distribution function.
nbininv - Negative binomial inverse distribution function.
norminv - Normal (Gaussian) inverse cumulative distribution function.
poissinv - Poisson inverse cumulative distribution function.
tinv - T inverse cumulative distribution function.
unidinv - Discrete uniform inverse cumulative distribution function.
unifinv - Uniform inverse cumulative distribution function.
wblinv - Weibull inverse cumulative distribution function.
26

27. Random Generator
betarnd - Beta random numbers.
binornd - Binomial random numbers.
chi2rnd - Chi square random numbers.
frnd - F random numbers.
gamrnd - Gamma random numbers.
geornd - Geometric random numbers.
hygernd - Hypergeometric random numbers.
lognrnd - Lognormal random numbers.
nbinrnd - Negative binomial random numbers.
normrnd - Normal (Gaussian) random numbers.
poissrnd - Poisson random numbers.
unidrnd - Discrete uniform random numbers.
unifrnd - Uniform random numbers.
wblrnd - Weibull random numbers.
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28. Parameter Estimation
betafit - Beta parameter estimation.
binofit - Binomial parameter estimation.
expfit - Exponential parameter estimation.
gamfit - Gamma parameter estimation.
lognfit - Lognormal parameter estimation.
nbinfit - Negative binomial parameter estimation.
normfit - Normal parameter estimation.
poissfit - Poisson parameter estimation.
unifit - Uniform parameter estimation.
wblfit - Weibull parameter estimation.
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29. Distribution Fitting Test
dfittool - Distribution fitting tool.
chi2gof - Chi-square goodness-of-fit test.
jbtest - Jarque-Bera test of normality.
kstest - Kolmogorov-Smirnov test 1 sample.
kstest2 - Kolmogorov-Smirnov test 2 samples.
lillietest - Lilliefors test of normality.
29

30. Most Likelihood Estimation (MLE)
mle - Maximum likelihood estimation.
betalike - Negative beta log-likelihood.
explike - Negative exponential log-likelihood.
gamlike - Negative gamma log-likelihood.
lognlike - Negative lognormal log-likelihood.
nbinlike - Negative binomial log-likelihood.
normlike - Negative normal likelihood.
wbllike - Negative Weibull log-likelihood.
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31. 31
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