Completely Randomized Design (CRD) With Two Path ANOVA Test

Completely Randomized Design (CRD) With Two Path ANOVA Test

Iskandar Muda Purwaamijaya¹, Rina Marina M², Muhammad Rafi Sabila Rahman (2001576)³

Civil Engineering Study Program

Faculty of Technology and Vocational Education Indonesian education university

2021

ABSTRACT

This article discusses the Complete Random Design (CRD) using the anova test (two way anova). The research method used is a qualitative method, which emphasizes the elaboration of interpretation without relying on numerical measurements. CRD is the simplest design among the standard experimental design. The advantages of using RAL include: easy design and implementation; data analysis relatively easy; flexible in terms of the number of treatments; there are suitable nonparametric analysis alternatives. RAL also has several shortcomings namely: the level of precision of the experiment may not be satisfactory unless the unit is homogeneous; only suitable for a number treatments that are not too much; the repetition of the experiment may be inconsistent (weak) if the experimental unit is not homogeneous. ANOVA is actually a more general form of t test that is suitable for use with three or more groups (it can also be used with two groups). The purpose and testing of this two way anova is to determine whether there is an influence of the various criteria tested on the desired result.

Keyword: Complate Random Design, Anova, Two way anova preliminary

In analyzing data for more than two populations, it is not recommended to use the t- test because there are weaknesses that can increase the value of (level of significance), meaning that will increase the chances of getting an erroneous result. Problems like this can solved with Anova. ANOVA or analysis of variance is a test that can be used to analyze the differences between more than two independent groups. The purpose is to compare more than two averages and is useful for testing abilities generalization means that the sample data is considered to represent the population (Riduwan, 2010). In ANOVA is not the mean but the variance. Anova too allows to be able to see the influence of the independent variable and the control variable, both separately or together, the dependent variable in other words can be see if there is an interaction between the independent variable and the control variable so that the

dependent variable pe the results will be different if the results of the control variables are different.

If there are different treatments for two groups of students at two times, different, then the difference occurs (it is hoped that because of the different treatment) different). But it does not rule out the presence or absence of that differencedue to sampling error. If the significance level is a = 0.05, then error due to taking the wrong sample is 5 out of 100. For example, in the case of actually the treatment did not show a statistically significant difference perbedaan at the significance level of 0.05, for 100 events there could be errors (state otherwise) a maximum of 5 pieces. The error of the maximum number of 5 pieces is errors caused by incorrect sample selection.

The concept underlying the ANOVA is the total variance of these values (scores). can be stacked on two sources, the first is the variance caused by there is treatment. The second is the inter-group variance, namely the error variance. In other words, anava is used to see if the difference between two means is or more it's bigger than what might arise from just a selection error sample (Rosenblad, 2009).

For example, if you want to know whether there are differences in the learning interests of elementary, middle and high scho and SMA to science textbooks, then the type of ANOVA that is done using One-way ANOVA, because only one independent variable is considered, namely the level of schooling only (elementary, middle, high school). But if you want to see the level of difference in understanding of interest in learning, female students, the type of ANOVA becomes a two-way ANOVA because the independent variable There will be two kinds of work, namely the level of schooling and gender (Rosenblad, 2009).

Method

This research is a type of library research which using books and other literature as data sources. Literature study is a study used to collect information and data with the help of various sources of material in the library such as documents, books, magazines, articles or journals, and others (Hamdi & Bahruddin, 2015). Sources of data in this study consists of primary sources taken from articles or research results, and OPTIKA: Journal of Physics Education Vol. 4(1), June 2020 56 secondary sources taken from books book. The data collection technique used in this research is by collect articles and books on simple experimental designs, namely Completely Randomized Design (CRD) with two-way ANOVA test. Based on the data that obtained from literature sources, then analyzed by content analysis techniques (content analysis). analysis) related to RAL with a two-way ANOVA test.

Results and Discussion

According to Harsojuwono, the characteristics that need to be known when using RAL i.e. diversity or variation is only caused by the treatment being tried and treatment it is the level of one particular factor. While the characteristics of ANOVA are: that the analysis

model is overparametered, so it must be made a limit for the parameters (Ispriyanti, 2007).

ANOVA is part of the statistical method that belongs to the comparative analysis of more than two averages (Riduwan, 2010). There are several types of ANOVA, among others: one- way ANOVA, two-way ANOVA without interaction, and two-way ANOVA with interaction.

1 Completely Randomized Design (CRD)

Completely Randomized Design (CRD) is the most simple among standard experimental designs (Hinkelmann, 2012). This pattern is known as complete randomization or randomization with nothing restrictions. Completely Randomized Design (CRD) is seen as more useful in laboratory experiments or in experiments on some type of experimental material certain characteristics that have relatively homogeneous properties. RAL is a design with single factor. This factor consists of at least two levels. Each level is called with treatment. Completely Randomized Design (CRD) is also known as randomized design perfect because in addition to the treatment, all influential variables can be controlled (Sarmanu, 2017). In the RAL experiment, each treatment at least repeated twice (Cortina & Nouri, 2012).

According to Adji S. in (Murdiyanto, 1999) the experimental unit used in the experiment is required homogeneous. Placement of treatment into the experimental unit is done randomly complete means that each trial unit has an equal chance of obtaining treatment.

Generally these experiments are carried out in a laboratory with an experimental unit unit which is not large enough and the number of treatments is limited. Advantage using RAL include: (1) easy design and implementation; (2)data analysis is relatively easy; (3) flexible in terms of the number of treatments; (4) there are suitable alternative nonparametric analysis. Besides Random Design Complete (RAL) also has several shortcomings, namely: (1) the level of precision the experiment may be unsatisfactory unless the experimental unit is completely homogeneous; (2) only suitable for a small number of treatments; (3) repetition The experiment may be inconsistent (weak) if the experimental unit is not completely homogeneous, especially if the number of replicates is relatively small

2 Analysis of Variance (ANOVA)

ANOVA is a test that can be used to analyze more differences of 2 independent population groups. This ANOVA technique was developed by Ronald A.

Fisher, using the F distribution (Bakdash & Marusich, 2017; Judd et al., 2018). This technique is often used for research, especially in the design research that has implications for the decision to use new technology, new procedures or new policies Anova comes from agricultural research (agricultural research). But in the years The latter has been developed as a powerful tool in analyzing other scientific problems such as in business and economic problems. According to Mendenhall, the procedure of analysis of variance aims to analyze the variation of a response and to determine the share of this variation for each independent variable group. That means, the purpose of the analysis of variance is to place important independent variables in a study and to determine how they interact and influence each other.

When the researcher wants to know whether there is a significant difference between the means of more than two groups, researchers often use techniques that This is called analysis of variance (ANOVA). ANOVA is actually a more generalization of the appropriate t-test used with three or more groups (it is also can be used with two groups), (Gu, 2014). In short, good variety in within and between each group were statistically analyzed, yields what is known as an F value. As in the t-test, this F value then checked in the statistical table to see if it is significantly statistics. This is interpreted quite similarly to the value of t, that the greater the value of obtained from F, the more likely it is that there is significance statistics. When only two groups are compared, the F test is sufficient for determine whether significance has been achieved. If more than two groups compared, the F test is no longer significant. For that it is necessary to test using another procedure, namely Post Hoc analysis. ANOVA is also used when more than one independent variable is investigated as in a factorial design.

3 Two-Way Analysis of Variance

Two-way ANOVA was used to test the comparison hypothesis of more than two samples and each sample consists of two or more types together (Harmon et al., 2016; Nugroho, 2017). The two-way ANOVA model in which there is only one observation each scope is often interpreted as randomized block design, because there is a special type in the use of this model. The basic concept of two-way ANOVA is generally no difference between hypothesis testing anova one path or two paths (Ismail, 2018), the difference is in the number of variables independent, in one-way ANOVA there is only one independent variable, while In two-way ANOVA there are two or more independent variables (Hamdi & Bahruddin, 2015). In ANOVA, the joining of groups is called blocks, and because individual or single events are determined randomly based on identification of block membership, its shape is associated with randomized blocks design. Two-way ANOVA is an ANOVA test based on observations two criteria, each criterion in the ANOVA test has a level.

Two-way ANOVA used when the source of diversity that occurs is not only due to one factor (treatment) but other factors are also sources that must be considered (Siregar, 2017; Syofian Siregar, 2013). The purpose and test of this two-way ANOVA is to find out whether there is an effect and the various criteria tested on the results obtained desired (Ismail, 2018). Two-way ANOVA mathematical model with interactions between factors are:

x_ij=μ+R_i+C_j+

(

^Ri× C_j

)

^+eij

Description: :

x_ij : Measurement results

 : Average value of data R_i : Variance of first factor

C_j : Variance of second factor e_ij : Error

R_i× C_j : Relationship / interaction between Assumptions on the fixed model:

 : General average

i : Effect of the i level of factor A

j : Effect of j level of factor B ()ij : Effect of intepaction i and j

ijk : Component random error 1 Fixed model bidirectional Anova

The two-way ANOVA of the fixed model is a three-way difference hypothesis testing on average or more with two influencing factors and the interaction between the two factors removed. Using this technique we can compare several the average derived from several categories or groups for one variable treatment. The advantage of using this analytical technique is that it allows extend the analysis to situations where what is being measured is affected by two or more variables. Hypothesis Formulation:

a The main influence of factor A

H0: 1 = … = i = 0 (no influence of factor A)

H1: there is at least one i with i  0 (there is the influence of factor A) b The main influence of factor B

H0: 1 = … = i = 0 (no influence of factor B)

H1: there is at least one j with j  0 (there is the influence of factor B) c Effect of interaction of factor A with factor B

H0: ( )11 = ( )12 = …..= ( )ij = 0 (no interaction effect of factor A interaksi and factor B)

H1: at least there are pairs (i,j) with ( )ij  0 (there is an interaction effect factor A and factor B).

d Determine the level of significance :

For row : v1 = b – 1 and v2 = (k – 1)(b – 1) For column : v1 = k – 1 and v2 = (k – 1)(b – 1)

e Define test criteria

H0 is accepted if F0 ≤ F (v1;v2) H0 is rejected if F0 F (v1;v2) 2 Two-way Anova random model

Two-way ANOVA random model is a three-way difference hypothesis testing average or more with two factors that influence the interaction between the two factor.

Hypothesis Formulation:

a The main influence of factor A

H0 : ² = 0 (no influence of factor A)

H1 : there is at least one i i with ² 0(there is the influence of factor A)

b The main influence of factor B

H0 : ² = 0 (no influence of factor B)

H1 : there is at least one j with ²  0 (there is the influence of factor B) c Effect of interaction of factor A with factor B

H0 : ² = 0 (no interaction effect of factor A and factor B)

H1 : at least there are pairs (i, j) with ²  0 (no effect interaction of factor A and factor B).

d The real level ()and F table are determined by the degree of the numerator and denominator each:

For row : v1 = b – 1 and v2 = kb (n – 1) For column : v1 = k – 1 and v2 = kb (n-1)

For interaction: v1 = (k – 1) (b – 1) dan v2 = kb (n – 1) e Define test criteria :

1) For row

H0 is accepted if F0 ≤ F (v1;v2) H0 is rejected if F0  F (v1;v2) 2) Untuk kolom

H0 is accepted if F0 ≤ Fa (v1;v2) H0 is rejected if F0  F (v1;v2) 3) Untuk interaksi

H0 is accepted if F0 ≤ F (v1;v2) H0 is rejected if F0  F (v1;v2) 3 Anova two-way mixed model

Hypothesis Formulation:

a The main influence of factor A

H0 : 1 = … = i = 0 (no influence of factor A)

H1 : there is at least one i with i  0 (there is the influence of factor A) b The main influence of factor B

H0 : ² = 0 (no influence of factor B)

H1 : there is at least one j with ²  0 (there is the influence of factor B)

c Effect of interaction of factor A with factor B

H0 : ² = 0 (no interaction effect of factor A and factor B)

H1 : at least there are pairs (i, j) with ²  0 (effect interaction of factor A and factor B)

Sv Db JK KT Fhitung

Perlakuan (r – k) – 1 JKP JKP / (r – k) – 1 KTP / KTG

Baris r – 1 JKB JKB / (r – 1) KTB / KTG

Kolom k – 1 JKK JKK / (k – 1) KTK / KTG

Interaksi (r – 1) – (k – 1) JK (BK) JK (BK) / (r – 1) – (k – 1) KTI / KTG

Galat rk (n – 1) JKG JKG / { rk (n – 1)}

Total rkn - 1 JKT

Tabel 1 Formula for calculating the number of squares Test criteria: If F Count > F Table, then H0 rejected (significant):

Information:

FK : Correlation factor JKT : Sum of the total squares

JKP : The number of squares of treatment JKB : Sum of squares

JKK : Sum of the squares of the column r : Number of rows

k : Number of columns n : The number of repetitions ar : The amount of data

To perform the above calculations can be done with the help of the SPSS program.

4 Assumptions in Anova

a The experimental error has a homogeneous variance. Testable via variance data on all populations or groups/the same treatment

b Experimental error is independent

c Experimental error (observation) is normally distributed in each population or treatment/group.

Closing

It has been described about Completely Randomized Design (CRD) which is the simplest design among other designs. ANOVA is actually a more general form of t-test that is suitable for use with three or more groups (it can also be used with two groups). The concept underlying the ANOVA is the total variance of the values that can be stacked on two sources, the first is the variance caused by the treatment, the second is the inter-group variance, namely the error variance. In other words, ANOVA is used to see if the difference between two or more means is greater than that which might arise from simply a sample selection error.

Bibliography

Bakdash, J. Z., & Marusich, L. R. (2017). Repeated measures correlation. Frontiers in Psychology. https://doi.org/10.3389/fpsyg.2017.00456

Cortina, J., & Nouri, H. (2012). Effect Size for ANOVA Designs. In Effect Size for ANOVA Designs. https://doi.org/10.4135/9781412984010

Gu, C. (2014). Smoothing spline ANOVA models: R package gss. Journal of Statistical Software. https://doi.org/10.18637/jss.v058.i05

Hamdi, A. S., & Bahruddin, E. (2015). Metode Kuantitatif Aplikasi Dalam pendidikan. In Metode penelitian kuantitatif aplikasi dalam pendidikan.

Harmon, M., Skow, B., Simonson, P., Peck, J., Craig, R. T., Jackson, J. P., Simonson, P., Peck, J., Craig, R. T., Jackson, J. P., Pointon, D., Sugiyono, A., Thiel, C., Priyono, Sugiyono, S., Bentley, J. L., Van Fraassen, B. C., Creswell, John W. Edition, T., Hirschberg, W., … McCrae, R. R. (2016). Metode Penelitian Kuantitatif. In Philosophy of Science. https://doi.org/http://dx.doi.org/10.1007/978-1-4419-8580-4_5 Hinkelmann, K. (2012). Design and Analysis of Experiments. In Design and Analysis of

Experiments. https://doi.org/10.1002/9781118147634

Ismail, F. (2018). Statistika untuk penelitian pendidikan dan ilmu-ilmu sosial. OPTIKA:

Jurnal Pendidikan Fisika Vol. 4(1), Juni 2020 62 Prenadamedia Group.

Ispriyanti, D. (2007). Pendekatan Regresi Untuk Analisis Ragam Klasifikasi Dua-arah. Jurnal Matematika Undip.

Judd, C. M., McClelland, G. H., Ryan, C. S., Judd, C. M., McClelland, G. H., & Ryan, C. S.

(2018). Repeated-Measures ANOVA. In Data Analysis.

https://doi.org/10.4324/9781315744131-11

Murdiyanto, B. (1999). Rancangan Percobaan. Metodologi Penelitian Bidang Kedokteran.

Nugroho, S. (2017). Metode Kuantitatif. In UNIB Press.

Riduwan. (2010). Dasar Dasar Statistika. Pendidikan Dan Perilaku Kesehatan.

Rosenblad, A. (2009). Applied Multivariate Statistics for the Social Sciences, Fifth Edition by James P. Stevens. International Statistical Review. https://doi.org/10.1111/j.1751- 5823.2009.00095_13.x

Sarmanu. (2017). Dasar Metodologi Penelitian Kuantitatif Kualitatif dan Statistika. In Airlangga University Press.

Siregar, S. (2017). Statistika Parametik untuk Penelitian Kuantitatif Dilengkapi dengan Perhitungan Manual dan Aplikasi SPSS Versi 17. In Statistika Parametik untuk Penelitian Kuantitatif Dilengkapi dengan Perhitungan Manual dan Aplikasi SPSS Versi 17.

Syofian Siregar. (2013). Statistika parametrik untuk penelitian kuantitatif. In Bumi aksara