Ada
dua pendekatan yang bisa dipakai oleh peneliti dalam menguji efektifitas
perlakuan. Pertama menggunakan gain score, kadang disebut dengan change score,
atau differences score yang diuji melui analisis varians (ANOVA). Kedua,
merupakan pendekatan yang relatif lebih baru, yaitu menggunakan analisis
kovarians (ANCOVA) dengan menempatkan skor pre-test atau baseline sebagai
kovariat dan post-test sebagai variabel dependen. Pendekatan yang kedua yang
berbasis kovariat inilah yang kemudian memperluas fungsi pemodelan persamaan
struktural (SEM) dalam kancah penelitian eksperimental.
Berikut ini perbandingan antar kedua pendekatan tersebut. Saya lampirkan kutipan pendapat beberapa ahli agar membawa kita pada diskusi yang lebih komprehensif.
ANOVA LEBIH TEPAT DIKENAKAN KETIKA :
1) Perbedaan kondisi awal (pretest) antara kelompok perlakuan dan kontrol adalah signifikan.
“The analysis of gain scores is always appropriate, and that ANCOVA will bias results in non-equivalent groups or observational designs” (Fitzmaurice, Laird, & Ware, 2004)
2) Desain eksperimen memiliki lebih dari satu pretest (multiple baseline)
“ Equal change between repeated pretests of treated and control group suggests the use of ANOVA of change rather than ANCOVA” (van Breukelen, 2005).
ANCOVA LEBIH TEPAT DIKENAKAN KETIKA :
1) Menggunakan randomized design.
“ANCOVA assumes that there is no group difference at pretest. This assumption is warranted if treatment assignment is based on randomization or on the pretest” (van Breukelen, 2005)
2) Kondisi awal antara kelompok kontrol dan eksperimen adalah setara. Misalnya terapi depresi diberikan pada subjek dengan skor BDI sedang (19-25). Selain itu jika kondisi awal (pretest) antar kelompok adalah setara maka ANCOVA bisa diterapkan.
“ANCOVA addresses a conditional hypothesis. Thus, the question that ANCOVA answers may begin with an untenable assumption, that two participants have equivalent scores at baseline “ (Jamieson, 1999)
3) Banyak subjek yang bisa mencapai skor maksimal pengukuran (ceiling effect) sehingga varians skor mengalami penurunan.
“When post-test variance decreased (e.g., ceiling effect) difference scores lost power, while the power of regression based methods (analysis of covariance and partial correlations) and structural equation measures of change were unaffected “ (Cribbie & Jamieson, 2004)
.
BEBERAPA CATATAN :
1) ANCOVA dan ANOVA memfokuskan pada hal yang berbeda. ANCOVA memusatkan pada perbedaan efek perlakuan sedangkan ANOVA pada perubahan skor.
“ANCOVA tests the hypothesis of equivalence of adjusted means, assuming the groups were equivalent on the pretest.…ANOVA on difference scores tests the hypothesis of equivalence of means of differences, regardless of the pretest differences between groups”
“The analysis of gain scores answers a different research question than ANCOVA. The analysis of gains, for example, focuses on the improvements from pretest to posttest for whole groups. The gain score, however, tells us precisely how scores changed from pretest to posttest. (Smolkowski, 2010)
An ANCOVA, the alternative to gain scores, focuses on differences between the treatment groups at posttest while holding constant pretest differences. The ANCOVA, then, does not inform about the how the groups changed over time (Smolkowski, 2010).
2) Pada desain randomized, ANOVA dan ANCOVA akan memberikan hasil yang mirip, namun berbeda dalam hal ukuran efek dan powernya.
“ With the assumption of an equivalent comparison group, an analysis of gain scores should give similar results to an ANCOVA” (Maxwell & Delaney, 1990)
3) Penggunaan ANCOVA mensyaratkan pengukuran yang memiliki eror pengukuran rendah.
Eror pengukuran yang rendah ini artinya reliabilitas pengukuran yang dilakukan memuaskan.
“ It is critically important to use reliable measures and precisely measure variables consistently across subjects and over time, especially when using ANCOVA models” (Oakes & Feldman, 2001)
In the presence of measurement error, change-score models may be equally or even more powerful” (Fitzmaurice, Laird, & Ware, 2004)..
4) Untuk kasus skor yang banyak mengandung skor terendah atau tertinggi (floor dan ceiling) direkomendasikan menggunakan ANAKOVA akan tetapi berbasis SEM karena harus melibatkan konstrak laten.
Specifically, for subjects with equal actual change, an easy test (a ceiling effect test) … (or) … a difficult test (a floor effect test) …. These problems with raw-score differences are eliminated by using modern approaches such as structural equation modeling (Dimitrov & Rumrill, 2003)
Berikut ini perbandingan antar kedua pendekatan tersebut. Saya lampirkan kutipan pendapat beberapa ahli agar membawa kita pada diskusi yang lebih komprehensif.
ANOVA LEBIH TEPAT DIKENAKAN KETIKA :
1) Perbedaan kondisi awal (pretest) antara kelompok perlakuan dan kontrol adalah signifikan.
“The analysis of gain scores is always appropriate, and that ANCOVA will bias results in non-equivalent groups or observational designs” (Fitzmaurice, Laird, & Ware, 2004)
2) Desain eksperimen memiliki lebih dari satu pretest (multiple baseline)
“ Equal change between repeated pretests of treated and control group suggests the use of ANOVA of change rather than ANCOVA” (van Breukelen, 2005).
ANCOVA LEBIH TEPAT DIKENAKAN KETIKA :
1) Menggunakan randomized design.
“ANCOVA assumes that there is no group difference at pretest. This assumption is warranted if treatment assignment is based on randomization or on the pretest” (van Breukelen, 2005)
2) Kondisi awal antara kelompok kontrol dan eksperimen adalah setara. Misalnya terapi depresi diberikan pada subjek dengan skor BDI sedang (19-25). Selain itu jika kondisi awal (pretest) antar kelompok adalah setara maka ANCOVA bisa diterapkan.
“ANCOVA addresses a conditional hypothesis. Thus, the question that ANCOVA answers may begin with an untenable assumption, that two participants have equivalent scores at baseline “ (Jamieson, 1999)
3) Banyak subjek yang bisa mencapai skor maksimal pengukuran (ceiling effect) sehingga varians skor mengalami penurunan.
“When post-test variance decreased (e.g., ceiling effect) difference scores lost power, while the power of regression based methods (analysis of covariance and partial correlations) and structural equation measures of change were unaffected “ (Cribbie & Jamieson, 2004)
.
BEBERAPA CATATAN :
1) ANCOVA dan ANOVA memfokuskan pada hal yang berbeda. ANCOVA memusatkan pada perbedaan efek perlakuan sedangkan ANOVA pada perubahan skor.
“ANCOVA tests the hypothesis of equivalence of adjusted means, assuming the groups were equivalent on the pretest.…ANOVA on difference scores tests the hypothesis of equivalence of means of differences, regardless of the pretest differences between groups”
“The analysis of gain scores answers a different research question than ANCOVA. The analysis of gains, for example, focuses on the improvements from pretest to posttest for whole groups. The gain score, however, tells us precisely how scores changed from pretest to posttest. (Smolkowski, 2010)
An ANCOVA, the alternative to gain scores, focuses on differences between the treatment groups at posttest while holding constant pretest differences. The ANCOVA, then, does not inform about the how the groups changed over time (Smolkowski, 2010).
2) Pada desain randomized, ANOVA dan ANCOVA akan memberikan hasil yang mirip, namun berbeda dalam hal ukuran efek dan powernya.
“ With the assumption of an equivalent comparison group, an analysis of gain scores should give similar results to an ANCOVA” (Maxwell & Delaney, 1990)
3) Penggunaan ANCOVA mensyaratkan pengukuran yang memiliki eror pengukuran rendah.
Eror pengukuran yang rendah ini artinya reliabilitas pengukuran yang dilakukan memuaskan.
“ It is critically important to use reliable measures and precisely measure variables consistently across subjects and over time, especially when using ANCOVA models” (Oakes & Feldman, 2001)
In the presence of measurement error, change-score models may be equally or even more powerful” (Fitzmaurice, Laird, & Ware, 2004)..
4) Untuk kasus skor yang banyak mengandung skor terendah atau tertinggi (floor dan ceiling) direkomendasikan menggunakan ANAKOVA akan tetapi berbasis SEM karena harus melibatkan konstrak laten.
Specifically, for subjects with equal actual change, an easy test (a ceiling effect test) … (or) … a difficult test (a floor effect test) …. These problems with raw-score differences are eliminated by using modern approaches such as structural equation modeling (Dimitrov & Rumrill, 2003)
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