Appunti Statistica per la sperimentazione e le previsioni in ambito tecnologico (Parte 1)

GENERAL CONCEPT

Statistical data:

- Observational data: no dataset planned in advance, and the source is unknown. The

research do not manipulate any variables, they just observe what’s happening.

- Experimental data: are totally different kind of data. Analysis of variance can be very

useful when you start studying a set of data.

RSM: Resource Surface Methodology.

Variable: variable could be categorical (qualitative) or quantified (continued or discrete).

Difference between variable and factor:

- Variable (2° step DoE, statistical modeling): they can be quantitative or qualitative

and can assume all the values contained in X.

- Factors (1° step DoE, planning of the experiment): they represent SoVs, they can be

quantitative or categorical and they can assume a specific set of values called levels, which

define the X. A factor could be quantitative or qualitative.

SoVs= Sources of variation, to indicate the variables that can influence the results of an

experiment.

If one factor is categorical:

a) RV is estimated for each level of F

b) Replace it with a quantitative factor, where each set of value identifies a level 1

estimation of RV.

Interaction: measure how the effect of a factor on the RV, depends/ is affected by changing

the level of another one. If it’s null or negligible, it means that the effect of a factor on the RV is

the some across different levels of another factor.

2 Fs: we may define AB as the average difference between the effect of B at the high level of

A and the effect of B at the low level of A.

Effect: effect is different from variable. Direct (or indirect) impact of a factor on the RV, is

measured through a coefficient. It can be:

- Fixed: variables whose values are known and fixed, because we control them.

- Random: variables whose values are not known in advance, they’re not fixed. They

cannot be controlled a priori (eg. Xz method).

Source of variability: a fraction of the RV variability captured by a factor.

Statistical model: it describes the relationship (expressed by the model parameters) between

variables (independent) and the response variable (dependent), with the goal of making

inference. You don’t fit all the data point, but you try to minimize residuals.

REGRESSION MODEL

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