Statistics is a scientific discipline that deal with random phenomena using data. As random phenomena (variables), we consider those that result from either a manmade action or a natural phenomenon. Therefore, the examples of: the weights of students in a class, the level of production in an economics sector, the birth rate, the level of rainfall, the number of people who are served in a queue, etc all these are examples of random variables. Statistics, has an important role in the applied branch of many scientific disciplines. So, through collecting data and present quantitative analysis Statistics can help in taking important decisions in natural and social sciences. Branches of Statistics include: Biostatistics, Econometrics, Geostatistics, Psychometrics etc. The objective of our Statistics courses is for the students to understand and analyse random phenomena through sampling (data collection) and basic Statistical analysis. In Statistics II (STAO 131), our objective is to link sample inference for a random phenomenon with population inference for the same phenomenon. To do so, we associate descriptive statistical results for a random phenomenon in a sample with inference results in population.

Thus, we start with sampling and how this influences basic statistical results. Next, we derive the sampling distributions of basic statistical measures, such as the mean estimator, the variance estimator etc. Through the use of theoretical destribution, we derive the Central Limit Theorem law for large number of observations. At this point, we manage to generalise results for random variables of different characteristics using the so-called Normal theoretical distribution. Next, point estimation inference is analysed, where three different types are examined: the least square estimation, the maximum likelihood estimation, and the method of moments. So far, inference about random variables has been based on specific statistical estimators; the point estimators. Next, inference concerning these statistical measures will be generalised for those measures in population. Thus, we derive the Confidence Intervals which represent ranges of values for statistical measures in population. Also, we see how one can set and test statistical hypotheses on various statistical measures in population. Finally, we see how two random phenomena can be associated with the help of basic statistical measures and linear regression. Here, linear regression analysis is associated with basic statistical inference and diagnostic testing.

Τελευταία τροποποίηση: Δευτέρα, 14 Οκτωβρίου 2013, 11:13 AM