Statistical Analysis on Results Obtained from a Model

[runningman19]

Homework Statement

We recently collected data on a reverse osmosis system for our unit ops lab. The report LERF (Laboratory Experiment Request Form) requests that we ascertain a value of A_w, the water permeability coefficient, for our membrane. We need to perform a T-Test on the data, however exactly how this is to be done is unclear to me.

Some more in depth information:
We ran a reverse osmosis system at two different pressures, and two different feed concentrations at each pressure. Data is given to provide some insight on exactly what we are trying to do:

Where P (psig) and Feed Conc (mg/L) are manipulated variables and the rest are measured "response" variables. From this data, we are calculating a value for the water permeability coefficient A_w via a model (given by Equation 1 in the Relevant Equations section).

My questions are these:
What is a T-Test and how is it performed in this situation? I understand that T-Tests are performed to determine statistical differences between averages, but which averages?

Is there any other statistical analysis I should be performing on this data?

Homework Equations

(1)

Where J_W,ΔP, ΔC_S and Ψ are all known, and A_W is being calculated. ΔC_S is Change in Conc [mg/L], ΔP is pressure drop (psi), which is simply P (psi) in the data given above as the permeate stream leaves at atmospheric, J_W is permeate flux [ft/min], and Ψ is a constant equal to 0.00864.

The Attempt at a Solution

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I feel as though the best way to approach this problem is to average the results of each of the measured "response" variables at their respective concentrations and pressures (in this case, we would have 4 averages as we have 3 trials for each concentration and pressure and 12 trials total), perform a T-Test on each of the calculated averages, and then calculate A_W if the averages are statistically significant.

As for other statistical tests, I feel that this may be sufficient but was told to consider an outlier analysis as well. I feel this is not necessary, and in addition I am not sure how to perform an outlier analysis.

 

[Stephen Tashi]

I understand that T-Tests are performed to determine statistical differences between averages, but which averages?

The mean value of ##J_W## in cases where ##P = 200## versus the mean value of ##J_W## in cases where ##P = 800##.

( The correct technical vocabulary is that a T-test can be done to test the hypothesis that two different normally distributed populations have the same population mean. The test employs the averages measured from two samples, one from each population. )

Of course, you can do a T-Test to compare other ways of dividing the population of cases - e.g. "low"##\triangle C_S## vs "high" ##\triangle C_S##. If the directions indicate you are to so a single T-Test, the division of cases into ##P = 200## versus ##P=800## is probably what the directions intend.

Is there any other statistical analysis I should be performing on this data?

If the directions say to perform an outlier test, they probably want an outlier test done on the set of all the calculated values of ##J_W##.

The types of statistical tests that can be done on data is immense. The proper (and seldom followed) procedure is that the statistical analysis of an experiment is planned before the experiment is conducted. For academic labs, you are faced with mind reading what the directions intend you to do.