Éfék ukuran

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Éfék ukuran ngajelaskeun sabaraha gede hubungan antara dua variabel. Informasi ieu penting dina panalungtikan ilmiah. Efek size bisa dipake henteu ngan sakadar keur ngayahokeun naha panalungtikan aya efekna tapi oge ukuran masing-masing efek. Efek ukuran oge ngabantu dina situasi praktis, upamana keur nyieun kaputusan.

Contona, lamun mahluk jomantara turun ka dunya, sabaraha lila waktu nu diperlukeun keur ngayakinkeun yen, sacara rata-rata, lalaki leuwih jangkung ti awewe ? Jawabanna pakait jeung efek ukuran dina beda jangkung antara awewe jeung lalaki. Lamun efek ukuranna gede, gampang keur nangtukeun yen lalaki leuwih jangkung. Lamun beda ukuranna leutik, mangka perlu waktu (sarta sampel nu leuwih loba) keur mastikeun yen lalaki, sacara rata-rata, leuwih jangkung tinimbang awewe.

Konsep efek ukuran mucunghul oge dina basa sapopoe. Upamana, program keur ngurangan beurat awak nu ngabalukarkeun leungitna beurat 30 pon. Dina hal ieu, 30 pon nunjukkeun efek ukuran. Conto sejenna yen program ngajar nu dipiharep bakal ningkatkeun hiji niley mata pangajaran. Naek ieu tingkatan disebut oge efek ukuran tina program.

Dina statistik inferensial, efek ukuran nyaeta ukuran bedana kayakinan statistik. Efek ukuran, nu digambarkeun ku N jeung nilai kritis alpa nangtukeun power dina tes hipotesa statistik. Dina meta-analysis, efek ukuran ilahar dipake salaku ukuran nu bisa ngitung bedana panalungtikan sarta dikombinasikeun keur sakabeh kasus analisa.

Tipe efek ukuran[édit | sunting sumber]

Korelasi Pearson r[édit | sunting sumber]

Korelasi Pearson's r salah sahiji metoda nu panglobana dipake keur nangtukeun efek ukuran. Bisa dipaké waktu data mayeng atawa biner, sabab kitu Pearson r nyaéta bisa disebutkeun ukuran éfék anu pang serbaguna. Ieu téh ukuran éfék penting mimiti nu diwangun dina statistika, sarta diwanohkeun ku Karl Pearson. Pearson's r bisa beda-beda gedena ti -1,00 nepi ka 1,00, kalawan -1,00 némbongkeun hubungan négatif anu sampurna, 1.00 némbongkeun hubungan positif anu sampurna, sarta enol anu henteu némbongkeun hubungan dua variabel.

Hal séjénna mindeng dipake keur ngukur hubungan dua variabel nyaéta kuadrat atawa r, mindeng disebut "r-kuadrat" atawa koefisien katangtuan, nyaéta ukuran bagian varian dibagi sarua ku dua variabel sarta beda-beda ti enol nepi ka 1,00.

Cohen's d[édit | sunting sumber]

Cohen's d nyaéta pendekatan ukuran éfék nu luyu pikeun digunakeun di konteks uji-t. d dihartikeun salaku béda antara dua mean dibagi ku simpangan baku keur dua mean eta. Mangka,

d = {\mathrm{mean}_1 - \mathrm{mean}_2 \over \sqrt{(\mathrm{SD}_1^2 + \mathrm{SD}_2^2) /2 \ }}
numana meani jeung SDi nyaeta mean jeung simpangan baku keur grup i, keur i = 1, 2.

Unggal panaliti nyarankeun cara nu beda keur ngagambarkeun hasil tina efek ukuran, tapi nu loba dipake nyaeta ti Cohen (1992) numana 0.2 nembongkeun efek nu leutik, 0.5 sedeng sarta 0.8 nu gede.

Sabab kitu, dina conto nalungtik jangkung mahluk jomantara lalaki jeung awewe, data (ti 1000 lalaki jeung 1000 awewe ti sampel nu dianggap ngawakilan di Inggris) bisa:

  • Lalaki: Jangkung rata-rata = 1754 mm; simpangan baku = 70.00 mm
  • Awewe: Jangkung rata-rata = 1620 mm; simpangan baku = 64.90 mm

Efek ukuran (make Cohen's d) bakal sarua jeung 1.99. Niley ieu kacida gedena sarta mahluk jomantara taya masalah dina nangtukeun beda jangkung ieu.

Salah sahiji cara keur ngurangan kasalahan nyaeta ku cara migunakeun simpangan baku, nu mana dina sababaraha kasus nembongkeun hasil leuwih hade (upamana dina kasus uji coba terapi). Cara sejenna nyaeta lobana sampel sarta sampel nu teu sarua teu dipake dina waktu keur ngitung - dumasar kana hasil panalungtikan Hedges.

Hedges' ĝ[édit | sunting sumber]

Hedges and Olkin (1985) noted that one could adjust effect size estimates by taking into account the sample size. The problem with Cohen's d is that the outcome is heavily influenced by the denominator in the equation. If one standard deviation is larger than the other then the denominator is weighted in that direction and the effect size is more conservative. However, surely it makes more sense to put stock in the larger sample size? Hedges' ĝ incorporates sample size by both computing a denominator which looks at the sample sizes of the respective standard deviations and also makes an adjustment to the overall effect size based on this sample size. The formula for Hedges' ĝ (as used by software such as the Effect Size Generator) is

\hat{g} = \frac{\bar{x}_1 - \bar{x}_2}{\sqrt{\frac{(n_1 - 1) SD_1^2 + (n_2 - 1) SD_2^2}{(N_\mathrm{total} - 2)}}} \times \bigg(1-\frac{3}{4(n_1+n_2)-9}\bigg).

Cohen's f^{2}[édit | sunting sumber]

Cohen's f^{2} is the appropriate effect size measure to use in the context of an F-test for multiple correlation or multiple regression. The f^{2} effect size measure for multiple regression is defined as:

f^{2} = {R^{2} \over 1 - R^{2}}
where R^{2} is the squared multiple correlation.

The f^{2} effect size measure for hierarchical multiple regression is defined as:

f^{2} = {(R^{2}_{AB} - R^{2}_A) \over 1 - R^{2}_{AB}}
where R^{2}_A is the variance accounted for by a set of one or more independent variables A, and R^{2}_{AB} is the combined variance accounted for by A and another set of one or more independent variables B.

By convention, f^{2} effect sizes of 0.02, 0.15, and 0.35 are considered small, medium, and large, respectively (Cohen, 1988).

Odds ratio[édit | sunting sumber]

The odds ratio is another useful effect size. It is appropriate when both variables are binary. For example, consider a study on spelling. In a control group, two students pass the class for every one who fails, so the odds of passing are two to one (or more briefly 2/1 = 2). In the treatment group, six students pass for every one who fails, so the odds of passing are six to one (or 6/1 = 6). The effect size can be computed by noting that the odds of passing in the treatment group are three times higher than in the control group (because 6 divided by 2 is 3). Therefore, the odds ratio is 3. However, odds ratio statistics are on a different scale to Cohen's d. So, this '3' is not comparable to a Cohen's d of '3'.

Tempo oge[édit | sunting sumber]

Rujukan[édit | sunting sumber]

Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Hillsdale, NJ: Erlbaum

Cohen, J. (1992). A power primer. Psychological Bulletin, 112 (1), 155-159.

Lipsey, M.W., & Wilson, D.B. (2001). Practical meta-analysis. Sage: Thousand Oaks, CA.

Tumbu kaluar[édit | sunting sumber]

Software

Further Explanations