PIM 3133 Pengolahan Data

Perikanan

BAHAN KULIAH

Suadi, Ph.DLab. Sosial Ekonomi Perikanan

Pengampu mata kuliah

SuadiNurfitri Ekantari

Murwantoko

Materi Kuliah I

Pendahuluan

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

kelompok)

Kompetensi• Memahami prinsip dan pentingnya

analisis data• Mengetahui dan memahami teknik

pengumpulan data• Memahami dan mampu menerapkan

analisis bivariate, univariat, danmultivariate

• Dapat merancang cara analisis data

Kasus 1• Seorang peneliti melakukan penelitian tentang profil

konsumen pecel lele di DIY. Untuk menjelaskan data-data terkait (gender, umur, pendidikan, asal, jumlahkunjungan ke warung per bulan, dan alasan memilihwarung tertentu) sang peneliti meringkas data-data tersebut dalam bentuk, tabel, grafik, maupun ukuranstatistik (central tendency, ukuran dispersi, maupunskewenes dan kurtosis). Statistik apa sebaiknya yang digunakan oleh si peneliti untuk menjelaskan berbagaikebutuhan informasi tersebut?

Kasus 2• Manajer restauran seafood di Pantai Depok ingin

mengetahui profil konsumen dan sikap merekaterhadap produk ikan olahan yang disajikan direstaurannya. 30 tamu restauran lalu diwawancarauntuk memperoleh informasi gender, umur, pendidikan, pekerjaan, dan preferensi merekaterhadap produk perikanan. Apakah ada asosiasiantara gender dengan pekerjaan konsumen? Bagaimana hubungan antara tingkat pendidikan danpekerjaan berdasarkan gender dari konsumenrestauran tersebut?

Kasus 3• Ukuran pertama kali matang gonad (Lm) ikan layur

diketahui pada panjang 46.3 cm. Karena berbagaiperubahan faktor lingkungan ukuran Lm diperkirakansemakin kecil. Penelitian yang dilakukan di 10 lokasipendaratan ikan di selatan Jawa mengindikasikanrata-rata Lm dengan panjang 45 cm dengansimpangan baku 1.25. Bagaimana saudara akanmengambil keputusan atas data tersebut(menerima/menolak hipotesis)?

Kasus 4

• Seorang peneliti ingin mengetahui apakah mengkonsumsiobat dari hasil ektraksi bahan aktif dari rumput laut jenisEucheuma memberikan pengaruh yang nyata terhadapkadar gula darah dalam tubuh. Sampel sebanyak 30 orang penderita diabetes diambil darah sebelum dansesudah mengkonsumsi obat dan diukur kadar gula darahmasing-masing. Untuk memastikan ada tidaknyapengaruh perlakuan, uji statistik apa yang bisadigunakan?

Kasus 5Keberhasilan program minapolitan diperkirakan akan menyebabkan over supply lele. Seorang business women melihat hal tersebut sebagai peluang untukmengembangkan industri baru dalam pengolahan ikan. Dua produk inovasinyadipercaya 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 akanlangsung memproduksi produk baru tersebut, sang wanita pengusaha memintakonsultan/peneliti untuk melakukan survai pasar. Penelitian lalu dilakukan di pusatperbelanjaan dengan mengambil 100 responden untuk mencicipi produk barutersebut dan produk yang telah ada di pasar, dengan double blind test. Empatproduk diujicobakan dengan terlebih dahulu masing-masing produk diberi kodetertentu. Responden lalu diminta mencoba produk tersebut dan setelah mencicipimasing-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?2. Bagaimana preferensi konsumen terhadap produk inovasi dari lele?

Kasus 6vSeorang mahasiswa ingin mengetahui apakah terdapat

perbedaan produksi per meter persegi dari lele lokal, lelesangkuriang, dan lele dumbo. Bagaimana desain penelitian yang harus dilakukan oleh mahasiswa untuk menjawab tujuanpenelitiannya dan analisis apa yang bisa digunakan?

vSeorang peneliti ingin mengetahui apakah pola pembinaan yang berbeda yang dilakukan terhadap pembudidaya ikanmenghasilkan produktivitas usaha yang berbeda atau tidak? Tigakelompok masyarakat yang telah dikategorikan sebagaikelompok pembudidaya ikan pemula, madya dan lanjut denganjumlah masing-masing 30 orang dikaji rata-rata produksi ikan per hektar? Alat analisis apa yang dapat digunakan oleh penelititersebut untuk menjawab tujuannya?

Kasus 7• Seorang peneliti ingin mengetahui

pengaruh harga, promosi, dankeragaman produk ikan terhadaptingkat kepuasan konsumen. – Pertanyaan?

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

• Bagaimana mengukur pengaruh secara individu ketigavariabel tersebut (harga, promosi, dan produk) terhadapvariabel kepuasan?

Tabulasi Respon MahasiswaKasus Paham Tidak Ragu

1

2

3

4

5

6

7

Materi Kuliah II

PendekatanPengolahan Data

Perikanan?• Perikanan adalah semua kegiatan yang

berhubungan dengan pengelolaan danpemanfaatan sumber daya ikan dan lingkungannya mulai dari praproduksi, produksi, pengolahan sampai denganpemasaran, yang dilaksanakan dalamsuatu sistem bisnis perikanan (UU No. 31/2004 tentang Perikanan).

Perikanan à aktivitasekonomi

• Produksi à Primary sector– Budidaya– Penangkapan– Ekstraksi bahan aktif

• Pengolahan à Produk à Secondary sector

• Distribusi & pemasaran à Tertiary sector

Kebutuhan data untuk pengelolaanperikanan

KebutuhanInformasi

Informasi Biologi

Informasi Teknis

Informasi habitat

Informasi Sosial

Informasi Ekonomi

Informasi Kelembagaan

Sumber: Widodo dan Suadi 2006

Aktor (pemangku kepentingan)• Nelayan, pembudidaya ikan• Pengolah dan industri pengolahan

hasil perikanan• Pedagang pengecer à eksportir• Regulator (pemerintah, legislator)• Peneliti• Pemangku kepentingan lainnya

Sistem Perikanan

Sumber: Charles 2001

Faktor eksternal

seperti perubahan iklim

Faktor eksternal seperti kebijakan pemerintah

Kebijakan danPerencanaan

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 sistemmempengaruhi keseluruhan sistem atausub-sistem?

• Fisheries system is connected

Pernyataan Penelitian

• Program minapolitan berpengaruhterhadap perilaku pembudidaya ikandalam mengelola usahanya

• Bagaimana mengukur pengaruh, apasaja yang akan dipengaruhi, data apasaja yang dibutuhkan, bagaimanamemperoleh data

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 dalampengertian 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

– Rancangan Percobaan à Experimental research

Tipe metode pengumpulandata 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 between theory and practice. Research is cyclical process.

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 samplingStratified random samplingCluster samplingSampling purposive

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

Statistik

ProsesstatistikInput data Output data

Penutup

Materi Kuliah III

Tipe AnalisisData

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

Penyajian Data: Tabulasi dan grafik

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

Prosedur analisis data

Prosedur analisis data

Prosedur analisis data

Pengambilan Keputusan

Tipe Analysis Data

• Asosiasi/korelasi

Statistik Parametrik dan Non Parametrik

Descriptifàuji normalitas & varians

Komparasi

Summary Table of Statistical TestsLevel of

MeasurementSample Characteristics Correlation

1 Sample

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

Independent Dependent Independent Dependent

Categorical or Nominal

Χ2 or bi-

nomial

Χ2 Macnarmar’s Χ2

Χ2 Cochran’s Q

Rank or Ordinal

Mann Whitney U

Wilcoxin Matched

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

(Plonskey, 2001)

Analisis Data TipeKategori – Analisis

NonParametrik

Materi Kuliah IV

Non-parametricAnalysis Procedures

Type of Analysis Type of dataSimilarity to the

Parametric Analysis’s 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-measuresANOVA

Spearman’s rank Association between 2 variables Pearson’s correlation

Testing for Normality• H0: The distribution of the data is

normal.• Ha: The distribution of the data is not

normal.

• Kolmogorov-Smirnov and Shapiro-Wilktest 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

Testing for normal distribution

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

Page 197

Prosedur Analysis Nonparametric• Mann-Whitney U (perbandingan dua kelompok

independent): alternatif nonparametric dari uji t (duabeda rerata independen)

• Kruskal-Wallis (perbandingan dua atau lebih kelompokindependent): alternatif nonparametric dari uji Anovasatu arah

• Sign test or Wilcoxon test (perbandingan dua kelompokdengan pengukuran berulang atau data berpasangan): alternatif nonparametric dari uji t berpasasangan (duabeda rerata berpasangan)

• Friedman’s test (perbandingan dua kelompok atau lebihdengan pengukuran berulang atau data berpasangan): alternatif nonparametric dari Anova dua arah

• Spearman’s rank correlation (mengukur asosiasi antaradua variabel): alternatif analisis nonparametric untukPearson’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.

• Ordinal data (ranked data)

Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons. 17-53

Contoh Kasus

ServiceHealth Educational

Service20.10 26.1919.80 23.8822.36 25.5018.75 21.6421.90 24.8522.96 25.3020.75 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 compensation

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 Group18.75 1 H19.80 2 H20.10 3 H20.75 4 H21.64 5 E21.90 6 H22.36 7 H22.96 8 H23.45 9 E23.88 10 E24.12 11 E24.85 12 E25.30 13 E25.50 14 E26.19 15 E

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

17-55

Mann-Whitney U Test: Small Sample Example

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Contoh Kasus• Hipotesis

H0: Kedua populasi memiliki distribusi yang samaHa: Kedua populasi memiliki distribusi berbeda

– Kasus:Seorang peneliti ingin menguji apakah terdapatperbedaan antara tanaman yang diberi pupukmerk A dan pupuk merk B. Secara acak, 7 buahtanaman di beri pupuk A dan 6 buah tanamandiberi pupuk B dari awal penanaman.

Hasil/output è Menulis Hasil“Tinggi tanaman yang diberi kedua jenispupuk adalah sama atau memilikiditsribusi nilai tinggi yang sama”

“Distribusi nilai tinggi tanaman yang diberi pupuk A tidak berbeda secarasignifikan dengan pupuk B. Mann-Whitney U = 12.5, p = 0.23.”

2. Sign Test and WilcoxonSigned-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.

Contohkasus

Seseorang menguji apakah diet yang dilakukan 15 orang secara efektifdapat menurunkan berat dalam 1 bulan dengan melihat data beratsebelum dan sesudah melakukan diet

Menulis Hasil

“Uji Wilcoxon digunakan untuk melihat apakahdiet efektif/berhasil menurunkan berat badan.”

“Uji Wilcoxon menunjukkan diet berjalan efektif(berat badan turun) pada 10 dari 15 orang (p = 0.035).”

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 dilakukanuntuk mengetahui efek 4 jenisobat yang dipercaya dapatmenurunkan frekuensi‘mendengkur’ seseorang. Delapan pasien diberikan obatsecara acak selama 1 minggudengan penilaian:-frekuensi mendengkur per menitdihitung sebelum diberikan obat-frekuensi mendengkurdinyatakan menurun bila <100-frekuensi mendengkurdinyatakan meningkat bila >100

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 mendengkurseseorang. 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– H0: There are no differences in the

distributions of the groups.– Ha: There are differences in the

distributions of the groups.

ExampleFour 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?

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

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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 (Ri) Diet data with ranks

Weight WeightStart 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 33 65,98 67,7 77,89 1 2 34 107,27 102,72 91,33 3 2 15 66,58 69,45 72,87 1 2 36 120,46 119,96 114,26 3 2 17 62,01 66,09 68,01 1 2 38 71,87 73,62 55,43 2 3 19 83,01 75,81 71,63 3 2 1

10 76,62 67,66 68,6 3 1 219 20 21Ri

Always the 3scores are compared:

The smallestone gets 1,the next 2,

and the biggestone 3.

The Test statistic FrFrom the sum of ranks for each group, the

test statistic Fr is derived: k

Fr= 12/Nk (k+1) Σi=1 R2i - 3N(k+1)

= (12/(10x3)(3+1)) (192 + 202 + 212)) – (3x10)(3+1)=12/120 (361+400+441) – 120=0.1 (1202) – 120=120.2 - 120 = 0.2

Start Month 1 Month 219 20 21Ri

Sebuah percobaan dilakukanuntuk mengetahui efek 4 jenisobat yang dipercaya dapatmenurunkan frekuensi‘mendengkur’ seseorang. Delapan pasien diberikan obatsecara acak selama 1 minggudengan penilaian:-frekuensi mendengkur per menitdihitung sebelum diberikan obat-frekuensi mendengkurdinyatakan menurun bila <100-frekuensi mendengkurdinyatakan meningkat bila >100

Output“Friedman’s test digunakan karena normalitasdata tidak dapat diketahui dan sampeldata kecil.”

“Hasil χ2(3) = 22.5 and p < 0.001. MenunjukkanObat 2 yang paling efektif menurunkan frekuensimendengkur seseorang. Tidak ada perbedaansignifikan 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.– Could Data Be Transformed?

Hypotheses for Spearman’s Rho

– H0: There is no monotonic relationship between the two variables.

– Ha: There is a monotonic relationship between the two variables.

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.

Verify Results With a Graph

Hasil

“Korelasi Spearman’s rho digunakan untuk melihathubungan antara kehadiran dan nilai siswa”

“Nilai uji Spearman’s rho = –0.85, p < 0.001. Hal inimenjelaskan bahwa siswa yang jarang hadir memilikinilai yang rendah”

Analisis Korelasi Data TipeKategori

• 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.Hypothesis:

• 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 guidebook: With SPSS examples.