Statistics concepts and applications

Statistics: A Question Unanswered

Before there can exist any intelligent discussion with respect to the topic of statistics one must understand that a statistical process does not stand alone nor does it function without being a part of a much larger plan, namely, research investigation as a whole. Statistics and their accompanying processes are only one such part of the research plan and, as such, must be viewed in totality of purpose over single identification. Without a formidable research plan a statistical process is without merit and akin to discussing how many angles can be placed on the head of a pin. In general, and from a philosophical perspective, the research plans and statistical analysis, according to Ohlson (1998) " ... are not unlike an artist's canvas, as they strive to capture forever the intrinsic and observable subject placed before it" (10).

Research activities, whether clinical trial based, best practice directed, experimental or descriptive, must command and exhibit interest, enthusiasm, and passionate commitment. It is vital that the research investigator catch the essential quality of excitement of discovery that comes from research well done if expected results are to be gained. If this sole tenet cannot be achieved, then the difficulties and frustrations of the research performance, while never completely vanishing, will play a much lesser role. Achieving all necessary tenets in formatting a good research investigation the investigator must pay close attention to approach, need, purpose, measurement, data analysis, and summary conclusions. In order to accomplish this the research investigator must be ever vigilant with respect to the flow of a research report wherein statistics plays a crucial role. Although the focus of this paper is on statistics, a brief presentation must be made with respect to that which comes before the need for statistical analysis. Without this understanding and need statistics and statistical processes have no value, purpose, or use.

The first step in achieving purposeful use of statistics is the attainment of a desired research goal is to develop a scientific approach toward research investigative endeavors (Kerlinger, 1964). No research question can be answered through statistical analysis if first it is not stated in testable form. Second to accomplish meaningful research the investigator must be able to grasp the intimate and often difficult relations that exist between a research problem, and the design and methodology of its' solution. Herein lies the task placed before the investigator, namely to think relationally, structurally, and architectonically. Last, the research investigator must possess an ardent understanding of the value of the statistical process in achieving desired research goals. Foremost on the dais of statistical process understanding is an acceptance that there is a right way and a wrong way to utilize statistical methods in data analysis. When used wrongly the researcher will inevitably misguide the misguided and very likely accept research phenomenon that is in err; and reject one that is acceptable. At all times, therefore, the research investigator must clearly understand the solution to the problem and realize that statistics and statistical processes will according to Ohlson (1998) " ... deliver to you the answer to your question" (23). In order to deliver the answer the research question through statistics the investigator must follow the simple format presented below:

1. Clearly identify the investigative or research area.

2. Precisely and accurately state the research question.

3. State the research hypothesis (alternate and null) in testable form.

4. Systematically and carefully outline the limits of the investigation.

5. Correctly define all terms being investigated.

6. Identify all accountable and unaccountable error variables.

7. Select the most appropriate and best fit statistical process for data analysis.

8. Present rationale for statistical process selection.

9. Set the confidence level necessary for acceptance or rejection of the testable hypotheses.

10. Statistically analyze the testable data.

11. Report the investigative findings based upon testable hypotheses.

12. Provide an answer to the initial research question based upon the acceptance and/or rejection of the set hypotheses.

13. Outline and discuss inferences to future studies based upon answers provided to the research question.

14. Identify and structure guidelines for future or subsequent research endeavors.

Should this outline not be followed and there exists an ad hoc and loosely defined research procedure and incorrect statistical data analysis the research outcome will be worthless, serve no purpose, and fail to contribute to any scientific body of knowledge.

Statistics and Their Importance to Research Investigation. Although all research activities do not require the use of statistical data analysis when an investigator wants to report upon the differences, effects and/or relationships between and amongst groups or phenomena (i.e. variables) there must a concerted effort to measure the phenomenon with as much precision and accuracy as possible (Mendenhall & Ramey, 1973). This is, of course, accomplished through the use of statistics. Situations wherein statistical processes are not required are generally reserved for qualitative types of research such as historical, philosophical, and/or cultural trend studies.

One of man's greatest fears is that of the power of numbers. For most people numbers are nothing more than a hodgepodge of digits that are bewildering and often meaningless. As a result individuals often prefer to judge events, occurrences, phenomena, and situations from a traditionalist point-of-view wherein reason, conclusion, and inference are made on the basis of past acceptance rather than on a best practices policy. Justification for historical acceptance is usually based upon a fear of numbers and a lack of willingness to extract meaningful information from them. For those accepting of alternatives, statistical tools have been devised wherein it is possible to extract meaningful information from data and interpret whatever the data holds as its' secret (Freund, 1967). However, as test data often comes to the researcher investigator in unintelligible form, as test numbers by themselves are, the researcher must be knowledgeable enough to be able to choose the most reliable and efficient best-fit practice statistical procedure. If the appropriate procedure is not chosen the researcher will then wander through a labyrinth of unimportant data and embark upon an odyssey of failure (Ohlson 1998).

Before one enters the world of statistics one must put away all their fears and illusions about statistics. The stimuli that incite mathematical panic are largely illusory. Many of the formulas used by scientists in their statistical computations present an awesome, if not terrifying, appearance, but beneath the strange symbols lurks nothing more foreboding than the simple arithmetic we all mastered in school. The uses one will make of best practice statistics require no differential equations, no calculus, and no analytic geometry. The sometimes-horrifying mathematical manipulations that fill one with ghastly anxiety as they approach a lesson in statistics ultimately reveal themselves as addition, subtraction, multiplication, and division. By becoming familiar with the statistical techniques one might possibly develop a benevolent tolerance for the tedium and possibly even a reverent respect for the almost magical things statistics allows one to do with mere numbers.