**Stat 490 Group project**

In experimental design, designing an experiment is as important as analyzing the results. Through the semester we have learned 4 ways to design an experiment

- Design an experiment that is BIBD.
- Design an experiment that is an optimal design.

For these two types of designs you need to use R language to help you unless for simple cases. Even for the same input, you may end up different designs if you rerun the code. For example, the runs in the same treatment group may end up with different blocks. Or you may end up with different subset of the total runs that is still optimal.

**Design a blocked experiment with confounding structure.****Design a fractional experiment with aliases structure.**

For these two types of designs you can use either R or Excel to help you design the experiment. With the same confounding structure, same aliases structure, you will end up with the same design.

In this group project, you are asked to design 4 experiments and analyze the results. There is an excel file called “group_response.csv” on canvas, with two variables and in it. These will be the response variables for your analysis below.

**Experiment 1**

- Design a BIBD that has 6 treatment groups and 10 blocks. What is the number of runs in each treatment group? What is the number of runs in each block? What is the value of ?
- If the response variable is (sorted by treatment and block), analyze the results. Is there a significant main effect at treatment group? Is there a significant block effect?
- Analyze the residual to check whether there are any potential concerns about the validity of the assumptions.

**Experiment 2**

- Suppose that factor A has 3 levels, factor B and C each has 2 levels. Assuming you only have budget to have 30 runs, design a D-optimal experiment with these 3 factors such that a model with all first order term and second order term for A can be estimated, and there are 3 replicates in each treatment combination.
- If the response variable again is (sorted by treatment A, B, C), analyze the results. Is there a significant main effect at factor A, B or C?
- Have appropriate interaction plots and explain whether the interaction is significant or not. Develop the final regression model and have relevant contour plot from your final model.
- Analyze the residual to check whether there are any potential concerns about the validity of the assumptions.

**Experiment 3**

- Design a blocked experiment. Choose two three order or higher order interactions to be confounded with the blocks. To choose the confounded interaction terms, use the names from every member’s name. Pick one distinct letter (A-E) from each person’s name and form the interaction.
- If the response variable is (sorted by the order from the output from conf.design() function, that is the order of Blocks, E, D, C, B, A), analyze the results. Identify the significant factors and develop your model.
- Be careful that when you run Yates analysis the data should be in standard order, while the output from conf.design() function is not in standard order.

- Is there a significant block effect?
- Write down the complete confounding structure. Confirm the confounding structure using SS.
- Analyze the residual to check whether there are any potential concerns about the validity of the assumptions. Analyze dispersion effect if there is any.

**Experiment 4**

- Design a To choose the generators for the design, use the names from every member’s name. Pick one distinct letter (A-G) from each person’s name and form the generator.
- If the response variable again is , analyze the results. Identify the potential significant factors and develop your model.
- Use the same order as your data in experiment 3, that is you can just add two more factors to your experiment 3 data using the generators you have
- Be careful that conf.design() function is based on 0/1 coding, while defining relation is based on -1/1 coding.

- Write down the aliases structure for the main effects and two order interactions (ignore higher order interactions) and confirm the resolution of the design.
- Analyze the residual to check whether there are any potential concerns about the validity of the assumptions. Analyze dispersion effect if there is any.