Understanding Statistics As A Language. Robert Andrews
in order to own and drive a car. The dynamic change in ownership of automobiles has changed all of that. The typical driver of today does not need to know details of the mechanics of automobiles in order to drive. All a driver needs to know is where to put in the gas and how to manipulate the controls.
A pilot in ground school learning to fly is taught to compute fuel usage, navigation, weight and balance data, and airspeed by means of a circular slide rule. When the student pilot steps into an airplane, most data management is preformed by a computer.
Ordinarily statistics had the same dichotomy between what was taught in the classroom and what was expected in actual use of statistics in a research project. Knowing how to compute a standard deviation or Chi square did not help when a researcher was confronted with a totally different problem such as converting questionnaire responses or quality control information into data for computer analysis. A researcher may have a brilliantly designed project that was approved by a committee, and be without sufficient logistical knowledge to bridge from questionnaire or production information to statistical analysis and presentation. The bridge from design to analysis is missing in research literature. The resulting gap has frustrated would-be students of statistics for generations. That gap is perceived as a lack of understanding of the mathematics of statistics, but it is really a gap in the language of statistics. Math is no longer a major issue. Just as an experienced pilot throws away the circular slide rule, the statistician lays aside the calculator, pen, and pencil and uses the computer.
The computer does the math; the researcher needs primarily to know the language of statistics. The language of statistics is not difficult. Statistical language can be broken down into three basic components: type of data, number of groups studied, number of measurements. When the data, groups, and measurements are known, the resulting statistical analysis is largely pre-determined, and the computer can easily work the statistical math. The key is understanding the language of data, groups, and measurements.
Behavior as a Statistic
Behavior can be expressed in statistical values, such as sums, means, proportions, differences, or ratios. The student of behavioral science must think about the behavior of people and animals in terms of statistical values. Understanding of behavior as a statistic must develop, not around isolated acts of an individual, but rather around the mean as an evaluation of a number of acts, whether from an individual or a group, or around the proportion of acts that are observed to be in a certain category or around the differences among individuals and the differences between groups.
Functions of Statistics
Statistical methods in behavioral and industrial sciences serve four related functions. The functions of summarizing, describing, generalizing and experimenting describe the acquisition and communication of new knowledge through research.
Summarizing
The first function of statistics is to summarize research data for communication. A researcher can communicate a mass of information best by first condensing and summarizing the information.
Definition: A summary is a condensation in which major points of the original account are retained and from which minor points are excluded. The loss of detailed information is regrettable but necessary if the main features of a large amount of data are communicated.
Summarization may involve arranging a set of numbers into a grouped frequency distribution table as an initial step in developing a graph. Central tendencies can then be easily visualized.
Definition: Summary statistics is a tool for collecting, condensing, and organizing numerical data.
Describing
A second function of statistics is description. Statistical descriptions include measures of central tendency, variability, correlation and regression, the normal distribution, standard scores, and graphing methods. Statistics in a text or table communicates with clarity the description of a set of numbers.
Generalizing
The third function of statistics is generalizing beyond the limits of a specific investigation to situations that have not been observed. Achieving the first two functions of summarizing and describing is a somewhat limited goal but one that is essential to the meaningfulness of the third function. If what has been observed cannot be expressed clearly and adequately, attributing to the unobserved certainly cannot be done with clarity and meaningfulness.
Results that remain particular usually garner little interest. Particular results that can be generalized, or more accurately, can be interpreted generally garner a great deal of interest. Arguing from the particular to the general is inductive inference. In the long history of arriving at generalized findings, the best solution available has been statistical inference.
Inferential statistics is a valuable body of theory and procedure for generalizing from particular data. Although inference from the particular to the general is subject to error, statistical inference is the best and the closest to an error-free procedure available. A statistical inference is essentially the act of making and communicating a decision about research results.
Definition: Inferential Statistics goes beyond description to draw conclusions or make predictions by interpreting the data. The two classes of inferential procedures are estimation and hypothesis testing. Frequently used inferential statistics are t statistics, F ratio, and chi-square.
Experimenting
Experimental design involves the manipulation of an independent variable in a study to determine the effect on a dependent variable, which is the variable of interest. The group to which the independent variable is assigned is known as the experimental group; the group in which no manipulation occurs is known as the control group. For example if the Fly-By-Night Pharmaceutical Company wanted to test the XYZ Elixir for stopping the hiccups, researchers would give the XYZ Elixir to one group of hiccuping people and a placebo to another group of hiccuping people. Stopping the hiccups would be the dependent variable, administering XYZ Elixir would be the independent variable, the group receiving the XYZ Elixir would be the experimental group, and the group receiving the placebo would be the control group. Testing for differences between the experimental group and the control group allows conclusions to be drawn about the effectiveness of the Elixir.
By contrast, survey research is retrospective – the effects of the independent variables on dependent variables are recorded after they have occurred. In this instance the Fly-By-Night Pharmaceutical Company might use a survey instrument to determine if people who used the Elixir reported different results in the treatment of their hiccups than people who did not use the Elixir.
Measurements
Numbers can be used in at least three different ways, depending on the level of measurement. When numbers are used in any fashion, data is created. Numbers may have identity, rank, and additivity. Series of numbers can be used (1) to categorize at the nominal level of measurement, (2) to rank or order at the ordinal level of measurement, and (3) to score at the interval level of measurement
Definition: Measurement is the assignment of numbers to observations.
Counting
The number of observations in a category is known as the frequency. A frequency distribution is a tabular display that displays how many individuals possess each value of a particular variable.
Percentages are used to compare groups of unequal size on an equitable basis. The common base for percentage is 100. Regardless of the number being compared in two or more categories, the base of comparison is 100 or more accurately 100% is the whole for each category.
Proportions have a base or total of 1.0. Proportions are always parts of something and can never exceed the total, which is 1.0. Proportions are frequently exchanged for probabilities.
Ratios describe rates and relationships and are fractions. The base, as with a proportion, is 1.0. Proportions are restricted to the relationship of a part to the total; ratios are helpful