PIM 3133 Pengolahan Data Perikanan

PIM 3133

Pengolahan Data

Perikanan

BAHAN KULIAH

Suadi, Ph.D

Pengampu mata kuliah

Suadi

Nurfitri Ekantari

Murwantoko

Materi Kuliah I

Materi Kuliah

• Pendahuluan (pengertian, prinsip,

kegunaan)

• Pengumpulan data (sumber dan

teknik)

• Analisis data (ragam teknik analisis

data): Parametrik, non-parametrik

• Studi kasus (proyek individu atau

Kompetensi

• Memahami prinsip dan pentingnya

analisis data

• Mengetahui dan memahami teknik

pengumpulan data

• Memahami dan mampu menerapkan

analisis bivariate, univariat, dan

multivariate

Kasus 1

• Seorang peneliti melakukan penelitian tentang profil

konsumen pecel lele di DIY. Untuk menjelaskan data-data terkait (gender, umur, pendidikan, asal, jumlah

kunjungan ke warung per bulan, dan alasan memilih warung tertentu) sang peneliti meringkas data-data tersebut dalam bentuk, tabel, grafik, maupun ukuran statistik (central tendency, ukuran dispersi, maupun skewenes dan kurtosis). Statistik apa sebaiknya yang digunakan oleh si peneliti untuk menjelaskan berbagai kebutuhan informasi tersebut?

Kasus 2

• Manajer restauran seafood di Pantai Depok ingin

mengetahui profil konsumen dan sikap mereka

terhadap produk ikan olahan yang disajikan di

restaurannya. 30 tamu restauran lalu diwawancara

untuk memperoleh informasi gender, umur,

pendidikan, pekerjaan, dan preferensi mereka

terhadap produk perikanan. Apakah ada asosiasi

antara gender dengan pekerjaan konsumen?

Bagaimana hubungan antara tingkat pendidikan dan

pekerjaan berdasarkan gender dari konsumen

Kasus 3

• Ukuran pertama kali matang gonad (Lm) ikan layur

diketahui pada panjang 46.3 cm. Karena berbagai

perubahan faktor lingkungan ukuran Lm diperkirakan

semakin kecil. Penelitian yang dilakukan di 10 lokasi

pendaratan ikan di selatan Jawa mengindikasikan

rata-rata Lm dengan panjang 45 cm dengan

simpangan baku 1.25. Bagaimana saudara akan

mengambil keputusan atas data tersebut

Kasus 4

• Seorang peneliti ingin mengetahui apakah mengkonsumsi obat dari hasil ektraksi bahan aktif dari rumput laut jenis Eucheuma memberikan pengaruh yang nyata terhadap kadar gula darah dalam tubuh. Sampel sebanyak 30 orang penderita diabetes diambil darah sebelum dan

sesudah mengkonsumsi obat dan diukur kadar gula darah masing-masing. Untuk memastikan ada tidaknya

pengaruh perlakuan, uji statistik apa yang bisa digunakan?

Kasus 5

Keberhasilan program minapolitan diperkirakan akan menyebabkan over supply lele. Seorang business women melihat hal tersebut sebagai peluang untuk

mengembangkan industri baru dalam pengolahan ikan. Dua produk inovasinya dipercaya memiliki potensi pasar yang besar karena harga yang sangat kompetitif, yaitu “clarias ajifurai” dan “clarias nugget”. Sayangnya produk sejenis yang

berbahan baku tuna telah lebih dulu dikenal dan memiliki segmen pasar yang luas, yaitu masing-masing tuna ajifurai dan tuna nugget. Untuk memastikan apakah akan langsung memproduksi produk baru tersebut, sang wanita pengusaha meminta konsultan/peneliti untuk melakukan survai pasar. Penelitian lalu dilakukan di pusat perbelanjaan dengan mengambil 100 responden untuk mencicipi produk baru

tersebut dan produk yang telah ada di pasar, dengan double blind test. Empat produk diujicobakan dengan terlebih dahulu masing-masing produk diberi kode tertentu. Responden lalu diminta mencoba produk tersebut dan setelah mencicipi masing-masing produk dilakukan wawancara terkait identitas (umur, pendidikan, pekerjaan, dll) dan preferensi terhadap produk.

Dengan uji statistik apa supaya pertanyaan-pertanyaan berikut bisa terjawab: 1. Apakah responden benar-benar mengetahui perbedaan antara produk dari lele

dengan tuna?

Kasus 6

vSeorang mahasiswa ingin mengetahui apakah terdapat

perbedaan produksi per meter persegi dari lele lokal, lele

sangkuriang, dan lele dumbo. Bagaimana desain penelitian yang harus dilakukan oleh mahasiswa untuk menjawab tujuan

penelitiannya dan analisis apa yang bisa digunakan?

vSeorang peneliti ingin mengetahui apakah pola pembinaan yang

berbeda yang dilakukan terhadap pembudidaya ikan

menghasilkan produktivitas usaha yang berbeda atau tidak? Tiga kelompok masyarakat yang telah dikategorikan sebagai

kelompok pembudidaya ikan pemula, madya dan lanjut dengan jumlah masing-masing 30 orang dikaji rata-rata produksi ikan per hektar? Alat analisis apa yang dapat digunakan oleh peneliti

Kasus 7

• Seorang peneliti ingin mengetahui

pengaruh harga, promosi, dan

keragaman produk ikan terhadap

tingkat kepuasan konsumen.

– Pertanyaan?

• Bagaimana mengukur pengaruh ketiga variabel tersebut (harga, promosi, dan produk) terhadap variabel

kepuasan?

• Bagaimana mengukur pengaruh secara individu ketiga variabel tersebut (harga, promosi, dan produk) terhadap variabel kepuasan?

Tabulasi Respon Mahasiswa

Kasus Paham Tidak Ragu

1 2 3 4 5 6 7

Materi Kuliah II

Pendekatan

Pengolahan Data

Perikanan?

• Perikanan adalah semua kegiatan yang

berhubungan dengan pengelolaan dan

pemanfaatan sumber daya ikan dan

lingkungannya mulai dari praproduksi,

produksi, pengolahan sampai dengan

pemasaran, yang dilaksanakan dalam

suatu sistem bisnis perikanan (UU No.

31/2004 tentang Perikanan).

Perikanan

à

aktivitas

ekonomi

• Produksi

à

Primary sector

– Budidaya

– Penangkapan

– Ekstraksi bahan aktif

• Pengolahan

à

Produk

à

Secondary

sector

• Distribusi & pemasaran

à

Tertiary

Kebutuhan data untuk pengelolaan

perikanan

Kebutuhan Informasi Informasi Biologi Informasi Teknis Informasi habitat Informasi Sosial Informasi Ekonomi Informasi Kelembagaan

Aktor (pemangku kepentingan)

• Nelayan, pembudidaya ikan

• Pengolah dan industri pengolahan

hasil perikanan

• Pedagang pengecer

à

eksportir

• Regulator (pemerintah, legislator)

• Peneliti

Sistem Perikanan

Sumber: Charles 2001

Faktor eksternal seperti perubahan iklim

Faktor eksternal seperti kebijakan pemerintah Kebijakan dan Perencanaan Pengelolaan perikanan Pengemba-ngan perikanan Penelitian perikanan

Faktor eksternal seperti kebijakan ekonomi makro, struktur pasar, dll

Pemukiman dan komunitas Pasca Panen & pasar Nelayan dan sarana penangkapan ikan

Pertanyaan?

• Apakah perubahan dalam satu

sub-sistem atau sub-sub sub-sistem

mempengaruhi keseluruhan sistem atau

sub-sistem?

Pernyataan Penelitian

• Program minapolitan berpengaruh

terhadap perilaku pembudidaya ikan

dalam mengelola usahanya

• Bagaimana mengukur pengaruh, apa

saja yang akan dipengaruhi, data apa

saja yang dibutuhkan, bagaimana

Desain Penelitian

• Bagaimana data dikumpulkan

• Siapa yang akan menjadi responden dan berapa

banyak

• Data apa saja yang dibutuhkan

• Bagaimana memproses dan mengolah data

• Asumsi

• Hipotesis

• Apa jawaban hipotesis dan konsekuensinya

Nasir (1990): Desain penelitian dalam

pengertian sempit = pengumpulan dan analisis

data

Pengumpulan Data

– Metode pengamatan langsung

• Pengamatan berstruktur/tidak terstruktur

– Metode wawancara

• Situasi wawancara, Pewawancara, Responden, dan Konten

– Metode dengan quesioner

• Pertanyaan tentang fakta, pendapat, atau persepsi diri • Pertanyaan terstruktur , terbuka

• Pretest

– Metode khusus

• Proyeksi

• Content analysis

Tipe metode pengumpulan

data dalam penelitian sosial

(Somekh & Lewin 2005):

• The face-to-face interview

• Postal questionnaires

• Telephone interviews

• Online survey :

http://goo.gl/K1kCDI

•

https://www.harvestyourdata.com/prici

ng/

Pendekatan Kualitatif

• The researchers primary goal is an understanding

of social processes rather than obtaining a

representative sample’.

• The qualitative research is mainly aim to develop

an appreciation of the underlying motivations that

people have for doing what they do

– Etnografi è ‘writing about people’ è menulis tentang orang dapat

berupa diary, log books, journals, field notes or lab books

– Studi kasus à The case studies combined on-site documentary

analysis with individual interviews of key players, group interviews, observations and critical incident analysis.

– Action research à directly addresses the problem of the division

Pendekatan Kuantitatif

• The logic of such research is to:

–collect data using standardized

approaches on a range of variables;

–search for patterns of causal

relationships between these

variables;

–test given theory by confirming or

denying precise hypotheses.

Terminologi Pengoda!

• Tipe data

–Data kualitatif

•Skala nominal

•Skala ordinal

–Data kuantitatif

•Skala interval

•Skala rasio

• Populasi

• Sampel

• Parameter populasi

• Hipotesis

Populasi Sample Populasi

Simple random sampling

Stratified random sampling

Cluster sampling

Sumber data online

•

http://www.fao.org/fishery/statistics/sof

tware/fishstat/en

•

http://comtrade.un.org/

•

http://www.indexmundi.com/

Data bisu

_{Data berbicara}

Proses

statistik

Input data

Output data

Materi Kuliah III

Tipe Analisis

Sebelum menganilisis data

• Formulasi hipotesis

è

pertanyaan yang

dapat diuji

• Pengumpulan data untuk uji hipotesis

–

Variabel yang mempengarui

–

Variabel yang dipengaruhi

–

Variabel yang berasosiasi (terkait)

• Skala pengukuran

• Sesuaikan proses pengolahan dengan jenis

data yang dikumpulkan

1

• Formulasi hipotesis

2

• Kumpulkan Data untuk uji hipotesis

3

• Tentukan tipe analisis data

4

• Tentukan tingkat kepercayaan

5

• Uji statistik

6

• Bandingkan p-value dengan signifikansi level

7

• Interpretasi

Tipe Analysis Data

• Asosiasi/korelasi

Statistik Parametrik dan Non Parametrik

Descriptif

à

uji normalitas & varians

Summary Table of Statistical Tests

Level of

Measurement Sample Characteristics Correlation 1

Sample 2 Sample K Sample (i.e., >2) Independent Dependent Independent Dependent

Categorical or Nominal Χ 2_or bi-nomial Χ2 _{Macnarmar’s} Χ2 Χ 2 _{Cochran’s Q} Rank or

Ordinal Whitney UMann Matched Wilcoxin Pairs Signed

Ranks

Kruskal Wallis

H Friendman’s ANOVA Spearman’s rho

Parametric (Interval & Ratio) z test or t test t test between groups t test within

groups 1 way ANOVA between groups 1 way ANOVA (within or repeated measure) Pearson’s r

Factorial (2 way) ANOVA

Analisis Data Tipe

Kategori – Analisis

NonParametrik

Non-parametric

Analysis Procedures

Type of Analysis Type of data Parametric Analysis’s Similarity to the Type

Mann-Whitney 2 independent groups Two sampel t-test Kruskal-Wallis >2 independent _groups One-way ANOVA

Wilcoxon test 2 repeated measures Paired t-test

Friedman’s test >2 repeated _measures Repeated-measures_ANOVA

Testing for Normality

•

H

0

: The distribution of the data is

normal.

•

Ha: The distribution of the data is not

normal.

• Kolmogorov-Smirnov and Shapiro-Wilk

test reported in the SPSS Explore

procedure can be used to test the

hypothesis that the distribution is

normal.

DESCRIBING DATA AND THE

NORMAL DISTRIBUTION

A histogram is a tool for graphically illustrating a sample's

frequency distribution and variability

DESCRIBING DATA AND THE

NORMAL DISTRIBUTION

Small vs large standard deviation

Variance

:

COMPUTING AND TESTING

KURTOSIS AND SKEWNESS FOR

SAMPLE NORMALITY

Testing for normal distribution

Prosedur Analysis Nonparametric

• Mann-Whitney U (perbandingan dua kelompok

independent): alternatif nonparametric dari uji t (dua

beda rerata independen)

• Kruskal-Wallis (perbandingan dua atau lebih kelompok

independent): alternatif nonparametric dari uji Anova

satu arah

• Sign test or Wilcoxon test (perbandingan dua kelompok

dengan pengukuran berulang atau data berpasangan):

alternatif nonparametric dari uji t berpasasangan (dua

beda rerata berpasangan)

• Friedman’s test (perbandingan dua kelompok atau lebih

dengan pengukuran berulang atau data berpasangan):

alternatif nonparametric dari Anova dua arah

• Spearman’s rank correlation (mengukur asosiasi antara

dua variabel): alternatif analisis nonparametric untuk

Pearson’s correlation

Mann-Whitney (Two Independent

Groups Test)

• Mann-Whitney test (Mann-Whitney

U) =

two-sample

t-test without the normality or equal

variance

assumption

• Data must meet the requirement that the two

samples are independent

• The sample sizes are small and normality is

questionable.

• The data contain outliers or extreme values that,

because of their magnitude, distort the mean

values and affect the outcome of the comparison.

• The data are ordinal

• Mann-Whitney test is performed on the ranked

data rather than on the actual values

1. Mann-Whitney

Conditions:

•

Required

no

normality or equal variance

assumption

•

2 independent

samples

•

Small

sample size

• The data contain outliers or extreme

values that, because of their magnitude,

distort the mean values and affect the

outcome of the comparison.

Business Statistics, 4e, by Ken Black.

© 2003 John Wiley & Sons. 17-53

Contoh Kasus

Service Health Educational Service 20.10 26.19 19.80 23.88 22.36 25.50 18.75 21.64 21.90 24.85 22.96 25.30 20.75 24.12 23.45

H0: The health service population is

identical to the educational service population on employee

compensation

Ha: The health service population is not

identical to the educational service population on employee

Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons.

17-54

Mann-Whitney

U

Test:

Small Sample Example

a _{= .05}

If the final p-value < .05, reject H0. W1 = 1 + 2 + 3 + 4 + 6 + 7 + 8

= 31

W2 = 5 + 9 + 10 + 11 + 12 + 13 + 14 + 15 = 89

Compensation Rank Group

18.75 1 H 19.80 2 H 20.10 3 H 20.75 4 H 21.64 5 E 21.90 6 H 22.36 7 H 22.96 8 H 23.45 9 E 23.88 10 E 24.12 11 E 24.85 12 E 25.30 13 E 25.50 14 E 26.19 15 E

Business Statistics, 4e, by Ken Black. © 2003 John Wiley &

17-55

Mann-Whitney

U

Test:

Small Sample Example

3 89 2 ) 9 )( 8 ( ) 8 )( 7 ( 2 ) 1 ( 53 31 2 ) 8 )( 7 ( ) 8 )( 7 ( 2 ) 1 ( 2 1 2 2 2 2 1 2 1 1 1 2 1 1 = -+ = -+ + = = -+ = -+ + =

n

n

W

n

n

n

n

U

W

n

n

n

n

U

Since U2 < U1, U = 3. p-value = .0011 < .05, reject H0.

Contoh Kasus

• Hipotesis

H0: Kedua populasi memiliki

distribusi

yang

sama

Ha: Kedua populasi memiliki distribusi berbeda

–

Kasus:

Seorang peneliti ingin menguji apakah terdapat

perbedaan antara tanaman yang diberi pupuk

merk A dan pupuk merk B. Secara acak, 7 buah

tanaman di beri pupuk A dan 6 buah tanaman

diberi pupuk B dari awal penanaman.

Hasil/output

è

Menulis Hasil

“Tinggi tanaman yang diberi kedua jenis

pupuk adalah

sama

atau memiliki

ditsribusi nilai tinggi yang sama

”

“Distribusi nilai tinggi tanaman yang

diberi pupuk A tidak berbeda secara

signifikan dengan pupuk B.

Mann-Whitney U = 12.5, p = 0.23.”

2. Sign Test and Wilcoxon

Signed-Rank Test for Matched Pairs

• The sign test and the Wilcoxon signed-rank test can be

used to compare paired data as nonparametric

alternatives to the paired

t-test.

• The sign test is very simple in that it counts the

number of differences that are positive and those that

are negative and makes a decision based on these

counts.

• The Wilcoxon signed-rank test goes one step further in

that it uses information about the magnitude of the

differences. Specifically, the absolute values of the

differences are ranked from smallest to largest, and

then the sum of the ranks associated with positive

differences is compared with the sum of the ranks for

the negative differences.

Hypotheses for a Sign Test or

Wilcoxon Signed-Rank Test

–

H0: The probability of a positive

difference is equal to the probability of a

negative difference.

–

Ha: The probability of a positive

difference is not equal to the probability

of a negative difference.

Hypotheses for a Sign Test or

Wilcoxon Signed-Rank Test

–

H0: The probability of a positive

difference is equal to the probability of a

negative difference.

–

Ha: The probability of a positive

difference is not equal to the probability

of a negative difference.

Contoh

kasus

Seseorang menguji apakah diet yang dilakukan 15 orang secara efektif

dapat menurunkan berat dalam 1 bulan dengan melihat data berat

Menulis Hasil

“Uji Wilcoxon digunakan untuk melihat apakah

diet efektif/berhasil menurunkan berat badan.”

“Uji Wilcoxon menunjukkan diet berjalan efektif

(berat badan turun) pada 10 dari 15 orang (

p =

Friedman’s Test

• Friedman’s test is a nonparametric

alternative to a repeated-measures analysis

of variance used to compare observations

repeated on the same subjects.

• Hypotheses for Friedman’s Test

–

H0: The distributions are the same across

repeated measures.

–

Ha: The distributions across repeated measures

are different.

Sebuah percobaan dilakukan untuk mengetahui efek 4 jenis obat yang dipercaya dapat menurunkan frekuensi ‘mendengkur’ seseorang. Delapan pasien diberikan obat secara acak selama 1 minggu dengan penilaian:

-frekuensi mendengkur per menit dihitung sebelum diberikan obat -frekuensi mendengkur

dinyatakan menurun bila <100 -frekuensi mendengkur

Output

“Friedman’s test digunakan karena

normalitas data

tidak dapat diketahui

dan

sampel

data kecil.”

“Hasil χ2(3) = 22.5 and

p < 0.001. Menunjukkan Obat 2

yang paling efektif menurunkan frekuensi mendengkur

seseorang. Tidak ada perbedaan signifikan antara Obat 2

dan 3 dengan Obat 1 dan 4”.

Kruskal-Wallis Test

• The Kruskal-Wallis test is the

nonparametric counterpart to the

one-way analysis of variance.

• Hypotheses for a Kruskal-Wallis Test

–

H

0

: There are no differences in the

distributions of the groups.

–

H

a

: There are differences in the

Example

Four groups of students were randomly

assigned to be taught with four different

techniques, and their achievement test

scores were recorded. Are the distributions

of test scores the same, or do they differ in

location?

88 62 81 79 67 78 59 3 83 69 75 2 73 87 65 1 80 89 94 4

Teaching Methods

H₀: the distributions of scores are the same Ha: the distributions differ in location

88 62 81 79 67 78 59 3 83 69 75 2 73 87 65 1 80 89 94 4 55 15 35 31 T_i (14) (2) (11) (9) (4) (8) (1) (12) (5) (7) (6) (13) (3) (10) (15) (16)

96

.

8

)

17

(

3

4

55

15

35

31

)

17

(

16

12

)

1

(

3

)

1

(

12

2 2 2 2 2

=

-÷÷

ø

ö

çç

è

æ

+

+

+

=

+

-å

+

=

n

n

T

n

n

H

i i

:

statistic

Test

Rank the 16 measurements from 1 to 16, and calculate the four rank sums.

Teaching Methods

H₀: the distributions of scores are the same Ha: the distributions differ in location

96

.

8

)

17

(

3

4

55

15

35

31

)

17

(

16

12

)

1

(

3

)

1

(

12

2 2 2 2 2

=

-÷÷

ø

ö

çç

è

æ

+

+

+

=

+

-å

+

=

n

n

T

n

n

H

i i

:

statistic

Test

Rejection region: For a right-tailed chi-square test with a = .05 and df = 4-1 =3, reject H₀ if H ³ 7.81.

Reject H₀. There is sufficient evidence to indicate that there is a difference in test scores for the four teaching techniques.

Case:

Aquaculture researcher

wants to know which of four possible feeds is best in

producing weight gain for Tilapia. Twenty-eight tilapia are randomly divided into four “feed” groups. Because the groups are small, the normality of the data cannot be adequately tested.

Therefore, a Kruskal-Wallis test is used to compare the four groups.

Reporting Results for a

Kruskal-Wallis Test

• Narrative for the Methods Section

– “A Kruskal-Wallis test was used to test for

differences among feeds because normality was

questionable and sample sizes within each group

are small.”

• Narrative for the Results Section

– “The Kruskal-Wallis test for comparison of feeds

indicates that there is a statistically significant

difference in the distribution of weight gain

between the groups, χ2(3) = 24.5 and p <

0.001.”

Friedman’s Test

• Friedman’s test is a nonparametric

alternative to a repeated-measures analysis

of variance used to compare observations

repeated on the same subjects.

• Hypotheses for Friedman’s Test

–

H0: The distributions are the same across

repeated measures.

–

Ha: The distributions across repeated measures

are different.

Differences between several related

groups: Friedman's ANOVA

• Friedman's ANOVA is the non-parametric

analogue to a repeated measure ANOVA

(see

chapter 11) where the same subjects have been

subjected to various conditions.

• Example here: Testing the effect of a new diet

called 'Andikins diet' on n=10 women. Their

weight (in kg) was tested 3 times:

– Start

– Month 1

– Month 2

• Would they loose weight in the course of the

diet?

Theory of Friedman's ANOVA

• Subject's weight on each of the 3 dates is

listed in a separate column. Then ranks for

the 3 dates are determined and listed in

separate columns.

• Then, the ranks are summed up for each

Condition (

R

_i

)

_{Diet data with ranks}

Weight Weight

Start Month 1 Month 2 Start Month1 Month2 (Ranks) (Ranks) (Ranks)

Person 1 63,75 65,38 81,34 1 2 3 2 62,98 66,24 69,31 1 2 3 3 65,98 67,7 77,89 1 2 3 4 107,27 102,72 91,33 3 2 1 5 66,58 69,45 72,87 1 2 3 6 120,46 119,96 114,26 3 2 1 7 62,01 66,09 68,01 1 2 3 8 71,87 73,62 55,43 2 3 1 9 83,01 75,81 71,63 3 2 1 10 76,62 67,66 68,6 3 1 2 19 20 21 R_i Always the 3 scores are compared: The smallest one gets 1, the next 2, and the biggest

The Test statistic

F

_r

From the sum of ranks for each group, the

test statistic F

_r

is derived:

k

F

_r

= 12/Nk (k+1) Σ

_i=1

R

2 i

- 3N(k+1)

= (12/(10x3)(3+1)) (19

2

_{+ 20}

2

_{+ 21}

2

_{)) – (3x10)(3+1)}

=12/120 (361+400+441) – 120

=0.1 (1202) – 120

=120.2 - 120 =

0.2

Start Month 1 Month 2

19 20 21

Sebuah percobaan dilakukan untuk mengetahui efek 4 jenis obat yang dipercaya dapat menurunkan frekuensi ‘mendengkur’ seseorang. Delapan pasien diberikan obat secara acak selama 1 minggu dengan penilaian:

-frekuensi mendengkur per menit dihitung sebelum diberikan obat -frekuensi mendengkur

dinyatakan menurun bila <100 -frekuensi mendengkur

Output

“Friedman’s test digunakan karena

normalitas

data tidak dapat diketahui

dan

sampel

data kecil.”

“Hasil χ2(3) = 22.5 and

p < 0.001. Menunjukkan

Obat 2 yang paling efektif menurunkan frekuensi

mendengkur seseorang. Tidak ada perbedaan

signifikan antara Obat 2 dan 3 dengan Obat 1

dan 4”.

Spearman’s Rho

• Spearman’s rho measures the strength of

an increasing or decreasing relationship

between two variables.

• Design Considerations for Spearman’s Rho

–

Data Benefits from Ranking

–

Data Observed as Ordinal Variables.

–

Sample Size Too Small.

•

Notes:

–

Verify Results With a Graph

–

Correlation Does Not Imply Cause and Effect.

Hypotheses for Spearman’s

Rho

–

H

0

: There is no monotonic relationship

between the two variables.

–

H

a

: There is a monotonic relationship

Case:

An educator wants to know how

attendance (recorded as the percentage

of classes attended) is related to the

final letter grade received by freshmen

students in an American history class at

a community college. Because the

grades are given as A, B, C, D, and F

(recorded as 1, 2, 3, 4, and 5),

Spearman’s rho is used to measure the

association.

Hasil

“Korelasi Spearman’s rho digunakan untuk melihat

hubungan antara kehadiran dan nilai siswa”

“Nilai uji Spearman’s rho = –0.85,

p < 0.001.

Hal ini

menjelaskan bahwa siswa yang jarang hadir memiliki

nilai yang rendah”

Analisis Korelasi Data Tipe

Kategori

• Tipe data: nominal dan/atau ordinal

• Tabel Frequensi atau Tabulasi silang

•

Contingency Table Analysis (r × c)

– a common method of analyzing the association

between two categorical variables.

– The r × c crosstabulation or contingency table

has r rows and c columns consisting of r × c cells

containing the observed counts (frequencies) for

each of the r × c combinations.

– a contingency table analysis and is usually

accomplished using a chi-square statistic

à

Chi

square tests

• Two separate sampling strategies lead to

the chi-square contingency table analysis

–

Test of Independence

à

A single random

sample of observations is selected from the

population of interest, and the data are

categorized on the basis of the two variables

of interest.

–

Test for Homogeneity

à

Separate random

samples are taken from each of two or more

populations to determine whether the

responses related to a single categorical

variable are consistent across populations.

• Use Counts—Do Not Use Percentages

• Each Subject Is Counted Only Once

• Explain Significant Findings

• Hypotheses for a Contingency Table

Analysis

–

Test of Independence

•

H0: There is no association between the two

variables.

•

Ha: The two variables are associated.

–

Test for Homogeneity

• H0: The distribution of the categorical variable

is the same across the populations.

• Ha: The distribution of the categorical variable

differs across the populations.

Case:

In 1909, Karl Pearson conducted a now classic study involving the

relationship between

criminal behavior and the drinking of alcoholic

beverages. He studied 1,426 criminals, and the data in Table show the

drinking patterns in various crime categories. This table is made up of counts in 6 × 2 cells, and, for

example, 300 subjects studied were abstainers who had been convicted of stealing.

• Narrative for the Methods Section

– “A chi-square test was performed to test the null

hypothesis of no association between type of crime and incidence of drinking.”

• Narrative for the Results Section

– “An association between drinking preference and type of crime committed was found, χ2 (5, N = 1,426) = 49.7, p < 0.001.”

• Or, to be more complete,

– “An association between drinking preference and type of crime committed was found, χ2 (5, N = 1,426) = 49.7, p < 0.001. Examination of the cell frequencies showed that about 70% (144 out of 207) of the criminals convicted of fraud were abstainers while the percentage of abstainers in all of the other crime categories was less than 50%.”

Bahan Rujukan

•

Elliott, A.C. & W.A. Woodward, 2007,

Statistical analysis quick reference