Revision as of 21:44, 17 October 2018

Modelling the Design

In order to create a successful brick, we needed to try out different combinations of growth medium and preparation of the bricks to gain the best compressive strength. An important factor when designing experiments is to decide what to test and which combinations are needed. Figuring this out without any help is pretty much impossible, which is why we approach it by modelling the experimental design. By doing this we can reduce the number of experiments significantly.

Two experimental designs were successfully created and carried out utilizing the optimal design approach for the compressive strength experiments. The designs were a replicated design with 17 trials, with four replicates, and an unreplicated full factorial design with 64 trials.

The data obtained in these experiments, lead to the creation of multiple statistical models. The aim of the models are to link the factors of burning time, burning temperature, substrate, incubation time, mixing ratio and density to compressive strength. The models enable us to predict the optimal processing of the fungal bricks, ensuring that the best possible compressive strength can be achieved.

To identify the best models, the following steps are carried out:

Explorative and a descriptive analysis of the data. This was done at first to identify if any immediate trends can be discovered, which have to be taken into account in the modelling process.
The actual modelling process, where different types of models are fitted and considered based on the explorative analysis.
Modelling selection process, where the models are compared to determine which model describes the data best, with regards to parameter choice, likelihood and so on.
Post hoc analysis to quantify uncertainties of the parameters, prediction uncertainty and contrast comparison.

With these four steps the optimal statistical model can be identified by linking compression strength to the previously mentioned parameters.

Explorative and descriptive analysis of the data

Summary stats

The unreplicated pilot experiment consisted of the load response variable and X factors. These can be seen from the table below:

Level	Substrate	Burning time	Burning temperature	Incubation time
1	s1: (jasmin rice)	-1 (12 hours)	-1 ($75^{\circ}$ )	-1 (1 week)
2	s2: (jasmin rice + saw dust)	1 (16 hours)	1,($100 ^{\circ}$ )	1 (1.5 week)
3	s3: (coffee)	-	-	-
5	s5 (blended rice + saw dust)	-	-	-
6	s6 (coffe + saw dust)	-	-	-
7	s7 blended rice	-	-	-

Table 1: - Something

The replicated experiment consisted of 5 factors, 1 random effect and 1 response variable. These are listed in the table below.

level	substrate	burning time	burning temperature	incubation time	mixing ratio
1	s1 (jasmin rice)	-1 (12 hours)	-1 (75)	-1 (1 week)	mix1 1:0 (rice:saw dust)
2	s2 (blended rice)	1 (16 hours)	1 (100)	1 (1.5 week)	mix2 50:50(rice:saw dust)
3	coffee	-	-	-	mix3 75:25(rice:saw dust)

Table 1: - Something.

Correlation matrix

To check the actual orthogonality of our data, provided by our design, a factor correlation matrix was calculated.

	s1	s2	burn time	burn temp.	incubation time
s1	1.00	-1.00	0.22	0.22	0.07
s2	-1.00	1.00	0.22	0.22	-0.07
burn time	-0.22	0.22	1.00	0.27	-0.03
burn temp.	-0.22	0.22	0.27	1.00	-0.03
incubation time	0.07	-0.07	-0.03	0.03	1.00

Table 1: - From the correlation matrix it is seen that outside each factor level, very little confounding is present. Thus the actual design fulfills the purpose of little confounding between each factor.

Boxplots

To get an idea of which different levels of the fixed effects might have an influence on the material compressive strength, a set of box plots for the main effects was created to identify if any immediate visual difference would occur. This is shown in fig below (lav link til fig under) These are shown below.

Fig. 1: - Thies

From the boxplots it is seen that there is seemingly little difference between the burning times nor is there any difference between any of the mixing ratios. The factors which may differ are the burning temperatures, incubation times and substrates. To see if there actually is a significant difference see the post hoc analysis (link til post hoc).

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