Statistics: Theory and Analysis

Statistics: Theory and Analysis

Probability Theory

The probability of event A is a mathematical evaluation of the possibility of occurrence of this event as a result of experience. The probability of event A is the ratio of the number of outcomes favorable to event A to the total number of mutually exclusive outcomes of an experiment, forming a complete group of events.

The outcome is favorable for event A, if the appearance of a result of this outcome entails the occurrence of event A. It is obvious that the probability of certain events is unity, and the probability of the impossible - is zero. Thus, the probability of any event is a positive number between zero and one (Strauss & Corbin, 1998).

For instance, in the box there are 10 balls. 3 of them are red, 2 - green, others white. Find the probability that the ball will be taken out at random with red, green or white. The appearance of red, green and white balls form a complete group of events. We denote the emergence of the Red Ball as Event A, the appearance of green B and, the appearance of white is the event C. Since, there are 5 white balls; the probability of appearance of white balls is highest.

The classical definition of probability does not apply to tests with an infinite number of outcomes. To overcome this drawback we introduce the notion of geometric probability, i.e. the probability that a point in which - either a segment or part of the plane (space).

Independent and Dependent Events

It is an object, process or feature that is present, or supposedly present in the phenomenon that a scientist wants to study. The objects, features and processes are called event to the extent that the modification causes a change in another object, process or property. The main events which are often referred to research can be independent, dependent, as well as, intermediate, behavioral, observable or unobservable.

In the experimental verification, the researcher attempts to artificially reproduce the phenomena that occur spontaneously in reality and want to understand, when you have a hypothesis that establishes a causal link between a course object, process or characteristic (called cause) and the process object or feature that requires an explanation (the effect), experimentally manipulating the first to see if the effect that the hypothesis described. The event manipulated by the experimenter called the independent event. The affected event is called the dependent event (Altman, 1991).

The terms dependent and independent event is usually used in experimental studies, which have to manipulate some events. In this sense, the "independent" event is defined as the independence of the reaction, the properties of the objects and purposes of the experiment, etc. Some events are assumed to be "dependent" on the actions of the object of the experiment or the experimental conditions. These events may implicitly contain some information about the behavior or response of the object during the experiment. Independent events are the events whose values can be controlled, and the dependent ...