Basic Statistics and Data Analysis

Lecture notes, MCQS of Statistics

Data Collection Methods

There are many methods to collect data, but these methods can be classified in four main methods (sources) of collecting data to use in statistical inference. These are (i) Survey Method (ii) Simulation (iii) Controlled Experiments (iv) Observational Study.

Survey Method

A very popular and widely used method is the survey, where people with special training go out and record observations of, the number of vehicles, traveling along a road, the acres of fields that farmers are using to grow a particular food crop; the number of house-holds that own more than one motor vehicle, the number of passenger using Metro transport and so on. Here the person making the study has no direct control over generating the data that can be recorded, although the recording methods need care and control.

Simulation

In Simulation, a computer model for the operation of a (industrial)  system is setup in which an important measurement is a percentage purity of a (chemical) product. A very large number of realizations of the model can be run in order to look for any pattern in the results. Here the success of the approach depends on how well that measurement can be explained by the model and this has to be tested by carrying out at least a small amount of work on the actual system in operation.

Controlled Experiments

An experiment is possible when the background conditions can be controlled, at least to some extent. For example, we may be interested in choosing the best type of a grass seed to use in sport field.

The first stage of work is to grow all the competing varieties of seed at the same place and make suitable records of their growth and development. The competing varieties should be grown in quite small units close together in the field as in the figure below

Controlled Experiment

 

This is the controlled experiment as it has certain constraints such as;

i) River on right side
ii) Shadow of trees on left side
iii) There are 3 different varieties (say, v1, v2, v3) and are distributed in 12 units.

In diagram below, much more control of local environmental conditions than there would have been of one variety had been replaced in strip in the shelter of the trees, another close by the river while third one is more exposed in center of the field;

Controlled experiment 2There are 3 experimental units. One is close to stream and other is to trees while third one is between them which is most beneficial than others. It is now our choice where to place any one of them at any of the side.

Observational Study

Like experiments, observational studies try to understand cause-and-effect relationships. However, unlike experiments, the researcher is not able to control (1) how subjects are assigned to groups and/or (2) which treatments each group receives.

 

Note that small units of land or plots are called experimental units or simply units.

There is no “right” side for a unit, it depends on the type of the crop, the work that is to be done on it and the measurements that are to be taken. Similarly, the measurements upon which inferences are eventually going to be based are to be taken as accurately as possible. The unit must therefore need not be so large as to make recording very tedious because that leads to errors and inaccuracy. On the other hand, if a unit is very small there is the danger that relatively minor physical errors in recording, can lead to a large percentage errors.

Experimenters and statisticians who collaborate with them, need to gain a good knowledge of their experimental material or units as a research program proceeds.

 

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The Author

Muhammad Imdadullah

Student and Instructor of Statistics and business mathematics. Currently Ph.D. Scholar (Statistics), Bahauddin Zakariya University Multan. Like Applied Statistics and Mathematics and Statistical Computing. Statistical and Mathematical software used are: SAS, STATA, GRETL, EVIEWS, R, SPSS, VBA in MS-Excel. Like to use type-setting LaTeX for composing Articles, thesis etc.

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