Topik 8 Pengujian Hipotesis (Hypothesis Testing) oleh: Yusman Syaukat Departemen Ekonomi Sumberdaya dan Lingkungan Fakultas Ekonomi dan Manajemen Institut Pertanian Bogor

Variabel dan Atribut Variabel merupakan ide sentral dari penelitian kuantitatif. Variabel memiliki nilai/intensitas/jumlah yang bervariasi Penelitian kuantitatif selalu menggunakan variabel dan hubungan antar variabel Atribut: nilai/kategori dari suatu variabel. Terkadang variabel dan atribut membingungkan. Misal: status perkawinan= (kawin, tidak kawin, cerai, janda). Namun, “lama perkawinan” atau “kedalaman komitmen dalam perkawinan” juga merupakan variabel

Jenis Variabel Variabel (causal relationship variables): Independent Variable: variabel penyebab, variabel yang mempengaruhi variabel lainnya Dependent Variable: variabel yang dipengaruhi oleh variabel lain Terkadang dikenal variabel yang ketiga – intervening variable. Intervening variable berada diantara independent dan dependent variables dan menunjukkan hubungan atau mekanisme diantara keduanya Teori sederhana (Simple theory) memiliki satu dependent dan independent variables, sementara Complex theory memeiliki lebih dari 2 variabel tersebut

Hipotesis & Sebab-akibat Hipotesis merupakan suatu proposisi (proposition) yang akan diuji atau suatu pernyataan tentatif (tentative statements) dari suatu hubungan antar dua variabel. Hipotesis merupakan dugaan (guess) terhadap bagaimana dunia sosial bekerja Hipotesis memiliki peran yang sangat penting di dalam penelitian ilmiah Peneliti melakukan pengujian hipotesis untuk menjawab pertanyaan-pertanyaan penelitian (research questions) atau untuk mencari dukungan empiris terhadap suatu teori Peneliti menghindari kata terbukti (proved) ketika melakukan pengujian hipotesis, karena knowledge is tentative, and creating knowledge is an ongoing process

Lima Karakteristik Hipotesis Memiliki paling tidak dua variabel Menyatakan suatu hubungan sebab-akibat antar variabel –variabel tersebut Menyatakan suatu prediksi atau output masadepan yang diharapkan (expected future outcome) Secara logika, suatu hipotesis memiliki keterkaitan dengan suatu research question dan suatu teori Falsiafiable: dapat diuji melawan empirical evidence (kejadian empiris) dan hasilnya dapat betul atau salah (true or false)

Pengujian Hipotesis Peneliti merupakan orang-orang yang skeptis. Adanya dukungan terhadap suatu hipotesis tidak serta merta menyebabkan mereka menerima hipotesis tersebut. Peneliti menggunakan prinsip replikasi (replication principle): suatu hipotesis perlu diuji beberapa kali secara konsisten. Aspek lainnya, sebelum dapat dinyatakan diterima, hipotesis tersebut harus sesuai dengan suatu teori tertentu yang terkait dengannya

Negative Evidence Peneliti menggunakan hipotesis untuk menguji arah (test the direction) dan kekuatan suatu hubungan (strength of a relationship) antar variabel Peneliti menggunakan negative evidence ketika mengevaluasi suatu hipotesis (Karl Popper’s idea of falsification) Negative evidence is more significant because the hypothesis becomes “tarnished” (ternoda) or “soiled” (kotor) if the evidence fails to support it Negative evidence shows that the predictions are wrong

Cara Pengujian Hipotesis Dua cara pengujian hipotesis: langsung (straightforward) dan null hypothesis Peneliti lebih menyukai penggunaan null hypothesis. Mereka melihat empirical evidence untuk menolak atau menerima null hypothesis Peneliti membuat hipotesis untuk menduga suatu hubungan. Null hypothesis menyatakan lawan (opposite) dari hubungan tersebut, yakni: dengan menduga tidak adanya hubungan (no relationship) antar variabel Null hypothesis (H0) selalu diikuti dengan alternative hypothesis (H1)

5 Komponen Pengujian Hipotesis Null Hypothesis Alternate Hypothesis Test Statistic Rejection/Critical Region Conclusion

Statistical Hypotheses Test For example, say, we test the mean (m) of a population to see if an experiment has caused an increase or decrease in m. Null Hypothesis: “there is no difference between the procedures” and is denoted by H0: “there has been no increase or decrease in the mean”. Alternative Hypothesis: It is a hypothesis which states that “there is a difference between the procedures” and is denoted by HA.

Statistical Hypotheses Test (2) Table 1. Various types of H0 and HA Case Null Hypothesis H 0 Alternate Hypothesis H A 1 m1 = m2 m1 � m2 2 m1 < m2 m1 > m2 3

Test Statistic It is the random variable X whose value is tested to arrive at a decision. The Central Limit Theorem states that for large sample sizes (n > 30) drawn randomly from a population, the distribution of the means of those samples will approximate normality, even when the data in the parent population are not distributed normally. A Z-statistic is usually used for large sample sizes (n > 30), but often large samples are not easy to obtain, in which case the t-distribution can be used.

Test Statistic (2) The population standard deviation s is estimated by the sample standard deviation, s. The t curves are bell shaped and distributed around t=0. The exact shape on a given t-curve depends on the degrees of freedom. In case of performing multiple comparisons by one way Anova, the F-statistic is normally used. It is defined as the ratio of the mean square due to the variability between groups to the mean square due to the variability within groups. The critical value of F is read off from tables on the F-distribution knowing the Type-I error aand the degrees of freedom between & within the groups.

Hypotesis Test The Two Sided hypothesis test P(z)=1-a /2 The two sided hypothesis test of H0 gives the same result as a confidence interval. The One Sided Hypothesis test P(z)=1-a

Hypothesis Test General Formula for Test Statistic   Significance Level  The level of significance α is the probability of rejecting a true null hypothesis. P values The exact probability of getting a value as extreme or more extreme than that observed if the null hypothesis is true.

Hypothesis Test Type I error α The probability of rejecting a true null hypothesis. Type II error β The probability of not rejecting a false null hypothesis Power of the Test 1- β The probability of rejecting false null hypothesis. The power of a test tells us how likely we are to find a significant difference given that the alternative hypothesis is true (the true mean is different from the mean under the null hypothesis).

Conclusion If H0 is rejected, we conclude that HA is true. If H0 is not rejected, we conclude that H0 may be true.

Logical Error in Causal Explanation Tautology Teleology Ecological Fallacy Reductionism Spuriousness

Tautology Tautology is a form of circular reasoning in which someone appears to say something new but is really talking in circles and making a statement that is true by definition. Tautology can not be tested with empirical data Contoh: “Sally is conservative because she believes that there should be less regulation”  This looks like a causal statement, but it is not a causal explanation. The set of attitudes is a reason to label Sally as a conservative, but those attitudes cannot be the cause of Sally’s conservatism

Teleology A teleology is something directed by an ultimate purpose or goal (bisa dipengaruhi berbagai faktor, seperti ‘God’s plan’, spirit, dsb. Misal: The nuclear family is the dominant family form in Western industrial societies because it is functional for the survival of the society -> tidak dapat di-test

Ecological Fallacy The ecological fallacy arises from a mismatch of units of analysis Ecological fallacy occurs when a researcher gather data at a higher or an aggregated unit of analysis but wants to make a statement about a lower or disaggregated unit. Contoh: Kota A lebih lebih makmur dibandingkan dengan kota B, karena kota A lebih banyak orang kaya dan lebih banyak sepeda motor  kita tidak tahu bagaimana hubungan antara tingkat pendapatan dengan kepemilikan sepeda motor

Reductionism Reductionism (fallacy of non-equivalence) occurs when a researcher explains macro-level events but has evidence only about specific individuals. Contoh: Mengapa Perang Dunia I pecah? Ini terjadi karena seorang Serbia menembak mati seorang Pangeran Hungaria pada tahun 1912.

Spuriousness Spurious = false Spuriousness occurs when two variables are associated but are not casually related because there is actually an unseen third factor that the real cause Misal: Seorang pria 15 tahun lebih suka bermain sepakbola dari pada berbelanja pakaian di mall. Seorang pria 15 tahun lebih tinggi dari seorang perempuan yang berusia sama, dan si pria suka sepakbola.

Reference Newman, W Lawrence. 2000. Social Research Methods: Qualitative and Quantitative Approaches (4th edition). Allyn and Bacon, Boston.