Dear Andreas

In my opinion your experiment design is not a 2W-ANOVA. Your experiment design is a 1W-ANOVA with 1+3+3+9=16 treatments. A 2W-ANOVA would be a factorial N1xN2 with N1=(A,B) and N2=(1,2,3,4,5,6). For your experiment you can perform a 1W-ANOVA for the 16 treatments and then Tukey multiple comparison test for study which pair of treatment present significant difference.

Miguel Angel García-Alvarado

Thank you for your quick respons.

1WA with Tukey's (and Kruskal-Wallis with Dunn's for ceratin non-parametric outcomes) are already done and that was my first approach to as to handle the dataset.

My supervisors suggested to try a 2WA appraoch as to investigate if and how the two indiviudal components differ from the effects exerted by the combination of the two.

I might missunderstand what you mean so just to clearify. Structuring the data as below (example) and running the R-command "summary(aov(outcome1 ~[A]*[B]))" not a viable option even though I get to know the effect of the components and interaction between [A] and [B] on outcome.

Tretment [A] [B] outcome 1

Cont 0 0 1

A1 1 0 2

B4 0 4 1

A1B4 1 4 5

Regards // Andreas

Dear Andreas Nils Mauritz Eriksson

I think, you can get answer to your question through the following that explained 2-way ANOVA and when you can split data

https://statistics.laerd.com/spss-tutorials/two-way-anova-using-spss-statistics.php

Two-way ANOVA in SPSS Statistics

Introduction

The two-way ANOVA compares the mean differences between groups that have been split on two independent variables (called factors). The primary purpose of a two-way ANOVA is to understand if there is an interaction between the two independent variables on the dependent variable. For example, you could use a two-way ANOVA to understand whether there is an interaction between gender and educational level on test anxiety amongst university students, where gender (males/females) and education level (undergraduate/postgraduate) are your independent variables, and test anxiety is your dependent variable. Alternately, you may want to determine whether there is an interaction between physical activity level and gender on blood cholesterol concentration in children, where physical activity (low/moderate/high) and gender (male/female) are your independent variables, and cholesterol concentration is your dependent variable.

The interaction term in a two-way ANOVA informs you whether the effect of one of your independent variables on the dependent variable is the same for all values of your other independent variable (and vice versa). For example, is the effect of gender (male/female) on test anxiety influenced by educational level (undergraduate/postgraduate)? Additionally, if a statistically significant interaction is found, you need to determine whether there are any "simple main effects", and if there are, what these effects are (we discuss this later in our guide).

Note: If you have three independent variables rather than two, you need a three-way ANOVA. Alternatively, if you have a continuous covariate, you need a two-way ANCOVA.

In this "quick start" guide, we show you how to carry out a two-way ANOVA using SPSS Statistics, as well as interpret and report the results from this test. However, before we introduce you to this procedure, you need to understand the different assumptions that your data must meet in order for a two-way ANOVA to give you a valid result. We discuss these assumptions next.

SPSS Statistics

Assumptions

When you choose to analyse your data using a two-way ANOVA, part of the process involves checking to make sure that the data you want to analyse can actually be analysed using a two-way ANOVA. You need to do this because it is only appropriate to use a two-way ANOVA if your data "passes" six assumptions that are required for a two-way ANOVA to give you a valid result. In practice, checking for these six assumptions means that you have a few more procedures to run through in SPSS Statistics when performing your analysis, as well as spend a little bit more time thinking about your data, but it is not a difficult task.

Before we introduce you to these six assumptions, do not be surprised if, when analysing your own data using SPSS Statistics, one or more of these assumptions is violated (i.e., is not met). This is not uncommon when working with real-world data rather than textbook examples, which often only show you how to carry out a two-way ANOVA when everything goes well! However, don’t worry. Even when your data fails certain assumptions, there is often a solution to overcome this. First, let’s take a look at these six assumptions:

o Assumption #1: Your dependent variable should be measured at the continuous level (i.e., they are interval or ratio variables). Examples of continuous variables include revision time (measured in hours), intelligence (measured using IQ score), exam performance (measured from 0 to 100), weight (measured in kg), and so forth. You can learn more about interval and ratio variables in our article: Types of Variable.

o Assumption #2: Your two independent variables should each consist of two or more categorical, independent groups. Example independent variables that meet this criterion include gender (2 groups: male or female), ethnicity (3 groups: Caucasian, African American and Hispanic), profession (5 groups: surgeon, doctor, nurse, dentist, therapist), and so forth.

o Assumption #3: You should have independence of observations, which means that there is no relationship between the observations in each group or between the groups themselves. For example, there must be different participants in each group with no participant being in more than one group. This is more of a study design issue than something you would test for, but it is an important assumption of the two-way ANOVA. If your study fails this assumption, you will need to use another statistical test instead of the two-way ANOVA (e.g., a repeated measures design). If you are unsure whether your study meets this assumption, you can use our Statistical Test Selector, which is part of our enhanced guides.

In the section, Test Procedure in SPSS Statistics, we illustrate the SPSS Statistics procedure to perform a two-way ANOVA assuming that no assumptions have been violated. First, we set out the example we use to explain the two-way ANOVA procedure in SPSS Statistics.

Dear Andreas

If your supervisor suggested to you perform a 2W-ANOVA, you must perform another set of experiments in a completely random 2X3 factorial design (or may be 2X6 design).The 6 treatments (T) of your 2x3 design must be

A B

1 T1 T2

2 T3 T4

3 T5 T6

The only way to consider control is by expressing the responses of each treatment as the difference with respect to control. Otherwise you cannot perform a 2W-ANOVA.

If you require the 6 concentrations your 12 treatments (T) for a 2X6 design are,

A B

1 T1 T2

2 T3 T4

3 T5 T6

4 T7 T8

5 T9 T10

6 T11 T12