I was wondering how should I do my statistical test with the following experiment:
Reaction components: A + B (when mixed, the reaction rate is recorded)
Variables: Temperature, pH, sunlight exposure and age of reagent A.
For each reactions, only one of which is changed while others are kept constant. And each of these reactions are repeated thrice (i.e. a triplicate). After all, the example is:
(4C + pH 3 + sunlight + 2 days old reagent A) x 3
(4C + pH 7 + sunlight + 2 days old reagent A) x 3
(25C + pH 3 +sunlight + 2 days old reagent A) x 3
... Likewise for the rest.
Objective: To find out whether such a variation caused a significant change in the reaction rate.
Thank you very much in advance!
Hi Mr.Ping,
Very interesting case and I would suggest you may use a t-test or 1-way ANOVA for the same. The null hypothesis to be used is ' Variation causes a significant change in reaction rate'. i.e H0 : mu1 = mu2. mu1 is the reaction rate before the experiment and mu2 is after. In case you wish to use ANOVA for checking on multiple means, you may use the null hypothesis : mu1 = mu2 = mu3 = ........... where 2,3,4, and so on will represent a particular change in the conditions of the reaction.
I see that you put down 4 factors that can change. I can actually see a 5th. If I was doing this experiment in my lab, I would use something called an optimal response surface. The Optimal Response Surface will test different combinations of your variables plus, you can add in a ratio of A to B. The Optimal Response Surface is far more powerful and requires fewer samples than a one change at a time approach you were proposing. Once you have this data, you will need to use ANOVA to analyze your data. If you go through and test all the combinations you have, you can use statistical software and use the Design of Experiment section to analyze your data.
Essentially, you will have a regression model where your model is:
Reaction Rate= F(Temp, pH, Sun, time)
Dear Ping,
For checking on multiple means in this experiment you need to test the significance of the difference between the effects of different levels for each of the three factors (Temperature, pH, sunlight exposure and age of reagent A) on the reaction rate. For this, you need to consider the three-way ANOVA. The null hypothesis to be used is: mu1i = mu2i = mu3i = ........... where i represent the factor number (i=1,2,3) and 1, 2,3,.. represents the levels within the factor i. Then mu will represent the average reaction rate of the level for each of the three factors.
Regards..
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