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Most accurate test for three independent variable, three dependent variable experiment.

wantmorestipend

Hello, I am a first time poster with novice experience with JMP.

I am currently extracting a specific phytochemical from algae with three different variables: coagulant agent (two different types), level of original plant matter concentration (three interval w/v%), and level of enzyme addition (none, 1mL and 2mL), which makes total 18 different combinations of treatment. Each combination is done triplicate. The response variables are: crude yield %, extract purity %, and true yield %. I have tried to teach myself statistic for a bit, and this is what I have come up with :

1. Perform total 9 ANOVA to see if individual independent factor has significant effect on each response variable with Tukey's HSD on each ANOVA. (well, for coagulant it would be t-test)

2. Perform three way MANOVA to see if there are significant interaction between the independent variables.

Does this look like a good plan? I want to be as conservative in my hypothesis rejection as necessary.

Accepted answers

Mark_Bailey

No, do not separate the data into groups and test within each group. Do not use MANOVA because this is not a repeated measures design. Use linear regression model with cross terms for the potential interaction effects.

Select Analyze > Fit Model
Select the 3 response data columns and click Y
Select the 3 factor data columns and click Macros > Factorial to Degree (2)
Click Run

All comments

Mark_Bailey

Select Analyze > Fit Model
Select the 3 response data columns and click Y
Select the 3 factor data columns and click Macros > Factorial to Degree (2)
Click Run

P_Bartell

Too add a bit to @Mark_Bailey 's advice (which I agree with) I recommend plotting your responses vs. factors using the Fit Y by X platform. You'll want to look for outliers, nonsense values, does the response values make sense from a domain expertise or first principles approach? Response values that are problematic in any of these areas can make modeling more difficult for your intended problem solving purpose.

wantmorestipend

Thank you but why factorial to degree instead of full factorial?

statman

Sorry, I can't be of more help, but I'm not sure I understand how you got the data? If I understand correctly, you did indeed do a full factorial 3^2x2^1 and you may certainly start your model building by using Macro>Full Factorial, but what I don't quite understand is the word "triplicate". Are these randomized replicates? Or are they multiple data points for each treatment combination acquired without any change to the treatment combinations (which means they might be repeats???). Please define an experimental unit for me. This must be established before I can recommend an analysis flow.

How confident are you in the measurement systems? Are they adequate? (e.g., Resolution, Precision, Stability, etc.). You might start with looking at the correlation of the Y's first (and check for multivariate outliers).

If triplicate means the experimental units are randomized replicates, were there any specific noise strategies employed (e.g., blocking)? Essentially is there anything we need to know about how and why you took samples as you did?

wantmorestipend

I just run each combination of experiment three times..? so i guess it's repeat.

As for measuring, all I did was to measure grams of extract with an electronic scale and measure purity with our own machine, which we calibrate often.

Mark_Bailey

Just because your data support the estimation of higher order terms, doesn't mean that you must estimate them. Terms of order greater than 2 are rare, so I prefer to save the degrees of freedom for more powerful tests of the lower order terms. The lack of fit test will suggest a problem of non-random variance in the response errors, and the examination of the residuals, which estimate the statistical errors assuming the model is correct, will provide clues about a problem.