# Statistical Analysis on Results Obtained from a Model

• runningman19
In summary, The report LERF (Laboratory Experiment Request Form) requests that we determine the value of Aw, the water permeability coefficient, for our reverse osmosis membrane. To do this, we need to perform a T-Test on the data collected from running the reverse osmosis system at different pressures and feed concentrations. We can average the results of each measured variable at their respective concentrations and pressures and perform a T-Test on these averages to determine if they are statistically significant. Additionally, we may also consider performing an outlier test on the calculated values of JW.
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 Aw, 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 Aw 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 JW,ΔP, ΔCS and Ψ are all known, and AW is being calculated. ΔCS 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, JW 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 AW 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.

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runningman19 said:
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.

## 1. What is statistical analysis?

Statistical analysis is a collection of methods used to organize, interpret, and draw conclusions from data. It involves using mathematical models and techniques to analyze and make sense of large datasets.

## 2. How is statistical analysis used in modeling?

Statistical analysis is used in modeling to validate and evaluate the performance of a model. It helps to identify patterns, trends, and relationships in the data, which can then be used to make predictions and inform decision making.

## 3. What are the steps involved in statistical analysis on results obtained from a model?

The steps involved in statistical analysis on results obtained from a model typically include data cleaning and preparation, exploratory data analysis, hypothesis testing, model building and evaluation, and interpretation of results.

## 4. Why is statistical analysis important in modeling?

Statistical analysis is important in modeling because it provides a rigorous and systematic approach to analyzing data and evaluating the performance of a model. It helps to ensure that the model is accurate, reliable, and can be applied to real-world situations.

## 5. What are some common statistical methods used in modeling?

Some common statistical methods used in modeling include regression analysis, ANOVA, t-tests, chi-square tests, and cluster analysis. These methods can help to identify key variables, assess the significance of relationships, and make predictions based on the data.

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