Statistical assumption

With the difference of the Dated mining, the statistical methods traditional require to set an assumption in a way preliminary to any work. This article presents this concept of assumption and gives some examples of them.

General assumption

The assumption is an anticipated explanation, a provisional assertion which describes or explains a phenomenon. It is a prediction consisting in connecting a variable and a behavior. It will be always expressed in the form “such variable has such effect on such behavior”. This prediction can be born either from the observation, or of data previously collected, or of a theory which it will try to validate. It will be expressed then in the following form: “if such theory is right in such situation it will occur such phenomenon”. A good assumption is a precise prediction which can be operational and in a simple way. An assumption cannot predict a consequence and its opposite. An irrefutable prediction could not be a scientific assumption. With Popper, it should be recalled that the refutability is the quality of all scientific assumption. The statistical transcription of the assumption is often to lay out so that one test to refute what one thinks false (H0). Example: if it is believed that two populations are different on a certain parameter (the average), the null assumption will be H0: the two averages are equal. The null assumption will be tested in a statistical way in order to decide if it is rejected (refutation).

Operational assumption

The operational assumption specifies the general assumption. It is presented in the form of a concrete example of application of the general assumption. The same diagram shows but by specifying the variables and the behaviors which will be studied in the experiment. The operational assumption thus consists in predicting the effect of the factors (variable independent) handled (S) in the experiment on the indicators (variable dependant) of the behavior studied by the researcher. The principal quality of a general assumption is of being able to be operationnalized. Too vague or too general assumptions will not be able obviously to generate operational assumptions. Only the assumptions having concrete implications being able to be the object of observations could be retained. To reinforce operational assumptions, decisions should be made. These decisions amount giving a concrete form with force of the assumption. It is said that it is about opérationnaliser the theoretical elements. For that it is necessary to introduce the VI, the VD and a prediction.

Ex. :  the projection in age influences the mnemic performances. O The people of more than 50 years have less good performances with a test of free recall (memorizing of 10 words) that people of less than 50. O The people being located in the age group 50-70 years have less good performances with a task of recall of space information (to place benchmarks on a chart) that people being located in the age group 20-40 years.

 the French cars are less expensive than the German cars O The Citroen are less expensive than BMW O Peugeot are less expensive than Mercedes

Statistical assumption

Independent variable

The independent variable is contextual with statistical modeling. In a general way it is a variable or explanatory factor. Example, if we try to explain the size of people according to their age, we will say that the age is the independent variable for this analysis.

Dependant variable

In the same way that for an independent variable, the concept of dependant variable is relating to the statistical model used. The dependant variable is the variable which one seeks to explain using independent variables.

Parasitic variable

The goal of the experimenter is to prove without ambiguity of the effect from such VI on such dependant variable. With this intention, it would be a question of having groups of equivalent subjects in all points except the differences induced by the methods of the independent variable. In other words, it would be necessary to handle an independent variable and to control all the others. The independent variables to control or variable parasites (VP) are very numerous and often unknown factors. Thus one tries to control the parasitic variables of which the researcher knows or supposes the effect on the dependant variable. The frequently controlled parasitic variables are: them characteristic of the subjects: the sex, the age, religious, political or cultural affiliation. - Variable “experimenter”: when several experimenters collect data, when the subject makes several tasks or more generally belongs to several experimental groups. E.g.: if I am interested in the performances in various tests of memory, it is important to preserve the same order of passage for all the subjects.

How to eliminate the effects of the parasitic variables? The controlled parasitic variables are called variables controls. However, all the parasitic variables cannot be controlled. One can, for example, to maintain his effect constant on the variable dependant i.e. by considering that only one on his methods.

Ex. : if the sex has an effect on the mnemic performance with space tests, to take only homogeneous groups, either only of the men, or only of the women.

Category: Statistics

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