Statistics is the science of collecting, analyzing, and making inferences from data. Statistics is particularly a useful branch of mathematics that is not only studied theoretically by advanced mathematicians but the one that is used by researchers in many fields to organize, analyze, and summarize data.
Statistical methods and analyses are often used to communicate research findings and to support hypotheses and give credibility to research methodology and conclusions.
Researchers and also consumers of research need to understand statistics so that they can be informed, evaluate the credibility and usefulness of information, and make appropriate decisions.
The word “statistics” is known to have originated from the Latin word “status,” meaning “state.”
For a long time, it was identified solely with the displays of data and charts about the economic, demographic, and political situations prevailing in a country.
Stretching well beyond the confines of data display, statistics now deals with collecting informative data, interpreting these data, and drawing conclusions about a phenomenon under study.
The scope of this subject naturally extends to all processes of acquiring knowledge that involves finding facts through the collection and examination of data.
Opinion polls, agricultural experiments, clinical studies of vaccines are just a few examples.
The principles and methodology of statistics are useful in answering such questions as:
- What kind and how much data need to be collected?
- How should we organize and interpret the data?
- How can we analyze data
- How can we make use of these data to conclude?
- Can we generalize the results so obtained?
Keeping the above questions in view, we present below a working definition of statistics:
Statistics is a subject that provides a body of principles and methodology for designing the methods of collecting, summarizing, analyzing, and interpreting data, drawing valid conclusions, and reaching a decision.
The use of statistics in any scientific investigation is indispensable. The detailed exposition of the subject in terms of its methods and importance can be found in many texts.
Our aim in this text is to make a brief overview of some statistical tools that will guide a researcher to statistically analyzing his/her data, interpreting and generalizing his/her results, and then assessing the extent of uncertainty underlying these generalizations.
Two broad classifications of the subject of statistics have been made in our endeavor to present statistical methods for analyzing and interpreting the results: descriptive statistics and inferential statistics.
We introduce the concepts of these two terms in turn.
The most common forms of descriptive statistics in use are measures of central tendency and variability of data.
Descriptive statistics are the tools that can enable us to describe a large volume of data in a summarized fashion, making it easy to comprehend.
When your findings are from a probability sample, summary descriptions, or statistics derived from this sample may be used to infer about the corresponding population parameters under certain assumptions about the distribution of the underlying population.
This falls under inferential statistics.
Statistical procedures that allow you to infer from what you found in a representative sample to the whole population are called inferential statistics.
Such statistics may be used to test hypotheses about the relationships that may exist within a population under study.
Put differently, and this is done by asking whether the patterns found in the sample data would differ from those in the population from which the sample data were drawn.