What is statistics?
The use of statistical methods is becoming increasingly important in all fields of everyday enterprise as well as to learn statistics. Indeed, it is almost impossible to name an activity that does not employ its own particular statistics as an aid to influencing human behaviour. But the usefulness of any statistical inquiry or market research depends entirely on the competence of those who attempt to interpret the results they obtain.
Since no commercial undertaking of the present day is willing to tolerate the doubtful judgments of mere amateurs applying ‘rules of thumb’, a greater than ever demand for individuals who are well-informed about the techniques and methods of statistics exists. A great deal of responsibility rests upon the shoulders of anyone acting in an advisory capacity related to the findings of a statistical inquiry. A responsibility that this article will enable him to assume with authority and confidence.
In order to study the subject of statistics and learn statistics intelligently. We should first understand what the term means today and know something of its origin.
As with most other words, the word ‘statistics’ has different meanings for different people. When most people hear the word, they think of tables of figures giving births, deaths, marriages, divorces, car accidents, and so on. This is indeed a vital and correct use of the term. In fact, the word ‘statistics’ was first applied to these affairs of the State, to data that government finds necessary for effective planning, ruling, and tax-collecting. Collectors and analysers of this information were once called ‘statists’, which shows much more clearly than the term ‘statistician’ the original preoccupation with the facts of the state.
Term statistics
Today, of course, the term ‘statistics’ is applied, in this first sense, to nearly any kind of factual information given in terms of number the so-called ‘facts and figures’. Radio and television announcers tell us that they will ‘have the statistics of the game in a few minutes’, and newspapers frequently publish articles about beauty contests giving the ‘statistics’ of the contestants.
The term Statistics’, however, has other meanings, and people who have not studied the subject are relatively unfamiliar with these other meanings. Statistics is a body of knowledge in the area of applied mathematics, with its own symbolism, terminology, content, theorems, and techniques. When people study the subject, statistics, they usually attempt to master some of these techniques.
The term ‘statistics’ has a second meaning for those who have been initiated into the mysteries of the subject ‘statistics’. In this second sense, researchers calculate ‘statistics’ as quantities from sample data; a single quantity derived this way is called a ‘statistic’. For example, the sample mean is a statistic, as are the sample median and sample mode. The sample variance is a statistic, and so is the sample range. The sample correlation coefficient is a statistic, and so on to learn statistics.
Meaning of learning statistics
We can summarize these meanings of the word ‘statistics“.
- The public meaning of facts and figures, graphs, and The word is plural when used in this sense.
- The subject itself, with a terminology, methodology, and body of knowledge of its The word is singular when used in this sense.
- Quantities calculated from sample data. The word is plural when used in this
In this article we will not use the word “statistics” at all in the first sense above. When we want to refer to ‘facts and figures’ we will use the term ‘observations’, or the term ‘data’. We will occasionally refer to a quantity that has been calculated from sample data as a ‘statistic’. In these cases, we will be using the singular of the word “statistics”, in the third sense above. Nearly always, when we use the word’statistics’ we will mean the subject itself the body of knowledge.
Understanding the methodology
The methodology of statistics is sufficiently misunderstood to give rise to a number of humorous comments about statistics and statisticians. For example: ‘A statistician is a person who draws a mathematically precise line from an unwarranted assumption to a foregone conclusion.’ This strikes out at two abuses of statistical techniques, although the abuse is not by professional statisticians. In order to apply most statistical techniques, certain assumptions must be made. The number and scope of the assumptions varying from situation to situation. Perhaps some persons do make assumptions that they know are not justified, and disguise their doubt to learn statistics.
And perhaps, also, some persons do have a conclusion already decided upon, and then choose their sample or ‘doctor’ their data in order to ‘prove’ their conclusion. Each of these abuses, when knowingly done, is dishonest.
One indictment of the techniques and methodology of statistics claims that “analysts often manipulate ambiguous data with dubious methods to solve a problem that remains undefined. There are three types of lies: lies, damned lies, and statistics. ” This quote, which Mark Twain likely attributed to a well-known remark criticizing how people use statistics, states, “He uses statistics as a drunk uses a street lamp—for support, rather than illumination.”
Importance of learning statistics
The application of statistical techniques is so widespread, and the influence of statistics on our lives and habits is so great, that the importance of statistics can hardly be overemphasized.
Our present agricultural abundance can be partially ascribed to the application of statistics to the design and analysis of agricultural experiments. This is an area in which statistical techniques were used relatively early. Some questions that the methods of statistics help to answer are:
- Which type of com gives the best yield?.
- Which feed mixture should chickens be fed so that they will gain the most weight?.
- What kind of mixture of grass seeds gives the most tons of hay per are?.
All of these questions, and hundreds of others, have a direct effect on all of us through the local supermarket.
The methodology of statistics is also used constantly in medical and pharma- ceutical research. The effectiveness of new drugs is determined by experiments, first on animals, and then on humans. New developments in medical research and new drugs affect most of us.
Use of statistics in Government sector
Statistics is used by the Government as well. Economic data are studied and affect the policies of the government in the areas of taxation, funds spent for public works (such as roads, bridges, etc.), public assistance funds, and so on. Statistics on unemployment affect efforts to lower the unemployment rate. Statistical methods are used to evaluate the performance of every sort of military equipment, from bullets used in pistols to huge missiles. Probability theory and statistics (especially a rather new area known as statistical decision theory) are used as an aid in making extremely important decisions at the highest levels.
Use of statistics in private sector
In private industry the uses of statistics are nearly as important and their effects nearly as widespread as they are in government use. Statistical tech- niques are used to control the quality of products being produced and to evaluate new products before they are marketed. Statistics are used in market- ing, in decisions to expand business, in the analysis of the effectiveness of advertising, and so on. Insurance companies make use of statistics in establish- ing their rates at a realistic level.
The list could go on and on. Statistics is used in geology, biology, psychology, and sociology. In any area in which decisions must be made on the basis of incomplete information. Statistics is used in educational testing, in safety engineering. Meteorology, the science of weather prediction, is using statistics now. Therefore, it is important to learn statistics.
On the lighter side, statistical studies have been made of the effect of the full moon on trout fishing; of which of two kinds of water glasses are better for use in restaurants; and of the optimum strategies for games of skill and chance such as bridge.
There can be little doubt, then, of the effect of statistics and statistical techniques on each of us. The results of statistical studies are seen, but perhaps not realized, in our wage packets, our national security, our insurance premiums, our satisfaction with products of many kinds, and our health.
Learn statistics by types of statistics
-
Descriptive statistics
You should know the types of it before learning statistics. In addition to a brief consideration of the basic elements of probability, there are two kinds of statistics.
- We are concerned primarily with the description of data.
- We treat the pictorial description of data.
- We treat the numerical description of data. The natural name for this kind of statistics is descriptive statistics.
Classification of data
The drawing of histograms that correspond to the frequency distributions that result after the data are classified. The representation of data by other sorts of graphs, such as line graphs, bar graphs, and pictograms. The computation of sample means, medians, or modes. The computation of variances, mean absolute deviations, and range. All these activities deal with descriptive statistics. The statistical work via learn statistics done back in the nineteenth century and the early part of this century was largely descriptive statistics.
-
Inferential statistics
The second important kind of statistics is known as inferential statistics. Statistics has been described as the science of making decisions in the face of uncertainty; that is, making the best decision on the basis of incomplete information. In order to make a decision about a population, a sample of that population is selected from it. The selection is usually by a random process. Although there are various kinds of sampling, the kind that we will be assuming throughout this book is known as random sampling.
As the name implies, this type of sampling involves some sort of process that the experimenter is not in control of choosing the members of the sample. There are various mathematical definitions of random sampling, but we will consider it as a sample for which each member of the population has an equal chance of being selected, and for which the selection of any one member does not affect the selection of any
On the basis of the random sample, we infer things about the population. This inferring about populations on the basis of samples is known as statistical inference. In other words, statistical inference is the use of a sample to reach conclusions about the populations from which those samples have been drawn.
Examples
Let us mention several examples of statistical inference. A medical research worker wants to determine whether a new drug is superior to the old one. One hundred patients in a large hospital are divided at random into two groups. One group is given the old drug and the other group is given the new drug. Various medical data are obtained for each patient on the day the administration of the drug began, and the same things measured ten days later. By analysing the data for each group, and by comparing the data, a conclusion may be reached about the relative effectiveness of the two.
What is a hypothesis?
A hypothesis, known as the null hypothesis, is proposed about a population. A random sample is obtained from the population, and a numerical quantity, known as a statistic, is calculated from the sample data. The null hypothesis is accepted or rejected, depending upon the value of the statistic. An alternative hypothesis is formulated at the time as the null hypothesis, and rejection of the null hypothesis means automatic acceptance of the alternative hypothesis. Thus, the testing of a statistical hypothesis is an illustration of statistical inference, because a decision is made about a population by means of a sample. All this is possible by learning statistics or to learn statistics.