Éfék ukuran

**Éfék ukuran** ngajelaskeun sabaraha gedé hubungan antara dua variabel.  Informasi ieu penting dina panalungtikan ilmiah.  Efek size bisa dipaké henteu ngan sakadar keur ngayahokeun naha panalungtikan aya efekna tapi ogé ukuran masing-masing efek.  Efek ukuran ogé 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 béda jangkung antara awewe jeung lalaki. Lamun efek ukuranna gedé, gampang keur nangtukeun yén lalaki leuwih jangkung. Lamun béda ukuranna leutik, mangka perlu waktu (sarta sampel nu leuwih loba) keur mastikeun yén lalaki, sacara rata-rata, leuwih jangkung tinimbang awewe.

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

Dina statistik inferensial, efek ukuran nyaéta ukuran bédana kayakinan statistik.  Efek ukuran, nu digambarkeun ku N jeung nilai kritis alpa nangtukeun *power* dina tes hipotesa statistik.  Dina meta-analysis, efek ukuran ilahar dipaké salaku ukuran nu bisa ngitung bédana panalungtikan sarta dikombinasikeun keur sakabéh kasus analisa.

## Tipe efek ukuran 
### Korelasi Pearson *r* 
Korelasi Péarson's *r* salah sahiji métodeu  nu panglobana dipaké keur nangtukeun efek ukuran. Bisa dipaké waktu data mayeng atawa biner, sabab kitu Péarson *r* nyaéta bisa disebutkeun ukuran éfék anu pang serbaguna.
Ieu téh ukuran éfék penting mimiti nu diwangun dina statistika, sarta diwanohkeun ku Karl Péarson.
Péarson's *r* bisa béda-béda gedéna 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 dipaké 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 béda-béda ti enol nepi ka 1,00.

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

:d = {\mathrm{mean}_1 - \mathrm{mean}_2 \over \sqrt{(\mathrm{SD}_1^2 + \mathrm{SD}_2^2) /2 \ }}

:numana mean*i* jeung SD*i* nyaéta mean jeung simpangan baku keur grup *i*, keur *i* = 1, 2.

Unggal panalungtik nyarankeun cara nu béda keur ngagambarkeun hasil tina efek ukuran, tapi nu loba dipaké nyaéta ti Cohen (1992) nu mana 0.2 nembongkeun efek nu leutik, 0.5 sedeng sarta 0.8 nu gedé.

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&nbsp;mm; simpangan baku = 70.00&nbsp;mm
* **Awewe**: Jangkung rata-rata = 1620&nbsp;mm; simpangan baku = 64.90&nbsp;mm

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

Salah sahiji cara keur ngurangan kasalahan nyaéta ku cara ngagunakeun simpangan baku, nu mana dina sababaraha kasus nembongkeun hasil leuwih hadé (upamana dina kasus uji coba terapi). Cara séjénna nyaéta lobana sampel sarta sampel nu teu sarua teu dipaké dina waktu keur ngitung - dumasar kana hasil panalungtikan Hedges.

### Hedges' *ĝ* 
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 héavily 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} 
Cohen's f^{2} is the appropriate effect size méasure to use in the context of an F-test for multiple correlation or multiple regression. The f^{2} effect size méasure 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 méasure 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 
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 tréatment 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 tréatment 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
* Standard score
* Odds ratio

## Rujukan
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
**Software**
* Free Effect Size Generator Software - PC & Mac Software
* Free Odds Ratio Generator Software - PC Software
* Free GPower Software  - PC & Mac Software
*Free Effect Size Calculator for Multiple Regression - Web Based
*Free Effect Size Calculator for Hierarchical Multiple Regression - Web Based

**Further Explanations**
* Measuring Effect Size
* Effect size for two independent groups 
* Effect size for two dependent groups