In experimental design, when the aim is to find an objective function or response as a function of variables, the real variables are converted to coded variables. For example, if the real variables of temperature are 30, 40, and 50 oC. The coded one can be obtained using the following equation: X=(T-Tcenter)/(Thigh-Tlow). So the coded temperatures are -0.5, 0, and 0.5.
I would not do that and there is a lot of posts on here advising against losing information by turning a continuous variables into categories.
It is not clear to me what "real variables" are. Anees Abdullah Khadom do you mean transforming continous variables into categorical ones, as proposed by Kelvyn Jones ?
Dear Rainer Duesing and Kelvyn Jones , Thank you for your answers. I'm sorry if my question was unclear. In my question, I mean the conversion of a real variable, such as temperature, to a coded one. For example, if the real variables of temperature are 30, 40, and 50 oC. The coded one can be obtained using the following equation: X=(T-Tcenter)/(Thigh-Tlow). So the coded temperatures are -0.5, 0, and 0.5.
In general, we use dimensionless variables to simplify the problem and generalize the results obtained.
Dear Yassmine Rghif
Thank you for your answer. In addition, I think this also equated the weight of each variable. For example, if we have data on temperature, pressure, and velocity (independent variables) as a function of reaction rate (dependent variable), a mathematical analysis can be used to correlate the variables by suggesting a mathematical model. If we deal with real variables (rate =f(T, P, V)), the weight of each independent variable is different from each other, and the comparison will not be accurate. While when using the coding variable (Rate=F(X1, X2< X3)), the effect of each variable is comparable and the statistical standard deviation between data is zero.
Dear Rainer Duesing
Thank you for your reply, as I mentioned for Yassmine Rghif the reason is to equated the weight of each variable. For example, if we have data on temperature, pressure, and velocity (independent variables) as a function of reaction rate (dependent variable), a mathematical analysis can be used to correlate the variables by suggesting a mathematical model. If we deal with real variables (rate =f(T, P, V)), the weight of each independent variable is different from each other, and the comparison will not be accurate. While when using the coding variable (Rate=F(X1, X2< X3)), the effect of each variable is comparable and the statistical standard deviation between data is zero.
Anees Abdullah Khadom You mean you want to standardize them in some way to make them comparable? In theory there is nothing wrong with this. What you seem to do is minmax normalisation (x-min(x))/(max(x)-min(x)). This can sometimes be helpfull (sometimes) such as machine learning.
In practice (mostly) this means you lose information and the only thing you could say is X1 > X2 or similair. The results beyond the study are completely meaningless (literally) because 0.6>0.2, but so what? Often the conlcusion is that 0.6 is more important than 0.2, because it is larger. But the only thing that adds meaning to the number is the "context", which is removed. Moreover, if max temparature = 200 and min = -10 then it becomes 1 and 0. But the same accounts for 30 and 5. You remove any measure of meaning degrees celcius. Boiling point, evaporation, freezing etc. are all ignored. Can you imagine the Ideal gas law, being uniteless? Hence, the meaning is in the "unit" or "context" an how it relates beyond a study. Losing two hairs on my head per day day is not so dramatic, but losing two limbs a day, I rather vote the first. Both the numbers were 2, but only the "unit" or "context" differed.
This form of "standardisation" or "normalization" is done because we want a dichotomy it is easy. So the only goals is: IF 1.) X1>X2=T or 2.) X1>X2=F. If 1.) X2 is more imprtant than X1. I too made such mistakes, but when I critizise and basically ban my own results to the "pseudo-sciences" (for mental effect) explaining why, nobody seems to care they want these standardized monsters.
Sorry for the harsh response, but now +100 years later in aquatic ecology/liminology I try to find out what the relation is i.e. a species (repsonse) and pollution (dependent) I cannot find a single regression coefficient and even worse is the absence of any online published data. Then what have we been doing for +100 years? So, now I ask any ecologist what is the "impact" on species number, nobody knows. So on what "meaning" are our environmental laws than based? I would simply avoid such a things althogheter as much as possible and If you do publish the data online.
Best,
Dear Wim Kaijser
thank you for these informative clarifications
Just like what Prof Annes has said. Coding the variables will help the computer to be able to analyse the interactive effects existing between the independent variables and the expected response.
There is no problem.
It is only a change of scale.
The significance (on the response) of the "factors" and their "interactions" is not affected by the linear transformation...
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