Explain the Scales of Measurements

Why we need the scale of measurements?

Observation and measurement are the fundamentals of empirical research. One basic technique for studying any phenomenon involves carefully observing it as it occurs. Such observation is not the kind of informal inquiry that all of us practice from childhood on; rather, in scientific research, it is observation accompanied by careful, accurate measurements (Baron & Kalsher 2001). Uniform and replicable measurement scales make observation objective and comparable with those of other investigators both contemporaries and those of subsequent generations. However full of insight an investigator’s “considerings” might be, if they are not supported by observations objectively recorded in quantitative terms, they are unlikely to form a basis for the considerings of successive generations of investigators (MacMahon & Trichopoulos, 1996).

Same lacunae has been pointed out by Greenwood (1935), in Hippocrates’ paper titled On Airs, Waters, and Places, which states: “Whoever wishes to investigate medicine properly should proceed thus: in the first place to consider the seasons of the year, and what effects each of them produces. Then the winds, the hot and the cold, especially such as are common to all countries, and then such as are peculiar to each locality…one should consider most attentively the waters which the inhabitants use, whether they be marshy and soft, or hard and running from elevated and rocky situations, and then if saltish and unfit for cooking; and the ground, whether it be naked and deficient in water, or wooded and well watered, and whether it lies in a hollow, confined situation, or is elevated and cold; and one should consider the mode in which the inhabitants live, and what are their pursuits, whether they are fond of drinking and eating to excess, and given to indolence, or are fond of exercise and labor.”

In light of such clear instructions from this influential teacher, it is remarkable that virtually nothing was discovered about the cause-effect relationships of unhealthy environments during the subsequent 2000 years. Greenwood (1935), attributes this to the fact that the operative word in Hippocrates’ statement is consider, not count or measure.

Counting and Measurement

One of the first “counters” of health events was John Graunt. In 1662, John Graunt published his Natural and Political Observations Made upon the Bills of Mortality (Graunt 1662, re-published 1939). He is widely regarded as a founder of the science of biostatistics. In using quantitative methods, he led the way to epidemiology. Since the methods he used saw no further development for almost 200 years, Graunt might be more appropriately regarded as forerunner, rather than a founder of epidemiology.

The roots of today’s epidemiology are more clearly detectable in the work of William Farr, a physician who was given responsibility for medical statistics in the office of the Registrar General for England and Wales in 1839. The annual reports of the Registrar General during the subsequent 40 years established a tradition of the careful application of vital data to problems of public health. In considering the population at risk, the need to take into account differences in characteristics of compared groups, the biases involved in the selection of persons exposed to a suspected cause, and the ways of measuring risk, Farr identified some of the major concerns of researchers today [MacMahon & Trichopoulos 1996].

Types of measurement scale (Abramson & Abramson 1999)

As part of the process of clarifying each of the variables to be studied, its scale of measurement should be specified. The scale of measurement may be categorical (consisting of two or more mutually exclusive categories) or metric (noncategorical: interval and ratio scales).

Types of Scale of Measurements

Nominal :

A categorical scale consists of mutually exclusive categories (classes). If these do not fall into a natural order, the scale is nominal. Numbers may be used to identify the categories, but these are ‘code numbers’ with no quantitative significance. Examples are:

(a)        Marital status: single, married, widowed, divorced.

(b)        Religion: Hindu, Muslim, Buddhist, Christian, Sikh, others.

(c)        Types of Anemia: (i) iron deficiency, (ii) other deficiency anemia, (iii) hereditary hemolytic anemia, (iv) acquired hemolytic anemia, (v) aplastic anemia, (vi) other anemias.

If the categories fall into what is regarded as a natural order, the scale is ordinal. The scale shows ranks, or positions on a ladder; each class shows the same situational relationship to the class that follows it. If numbers are used, they indicate the positions of the categories in the series. Examples are:

(a) Social Class: I, II, III, IV

(b) Years of education: 0, 1 – 5, 6 – 9, 10 – 12, > 12.

(c)Limitations of activity: 0, none; 1, limited activity but not home-bound; 2, home-bound but not bed-bound; 3, bed-bound.

(d)Severity of disease: mild, moderate, severe.

(e)Pain score: 0, no pain; 1, mild pain; 2, moderate pain; 3, severe pain; 4, unbearable pain.

An ordinal scale of measurement is ‘stronger’ than a nominal one, in the sense that it provides more information. When there is a choice, use of an ordinal scale is preferable.


With ordinal scales, the order of the values is what’s important and significant, but the differences between each one is not really known.  Take a look at the example below.  In each case, we know that a #4 is better than a #3 or #2, but we don’t know–and cannot quantify–how much better it is.  For example, is the difference between “OK” and “Unhappy” the same as the difference between “Very Happy” and “Happy?”  We can’t say.Ordinal scales are typically measures of non-numeric concepts like satisfaction, happiness, discomfort, etc.“Ordinal” is easy to remember because is sounds like “order” and that’s the key to remember with “ordinal scales”–it is the order that matters, but that’s all you really get from these.

A scale with only two categories is a dichotomy (or binary scale). Many statistical procedures are applicable to dichotomies but not to scales with three or more categories (polychotomous). Numbers may be used as code numbers, or to indicate the presence or absence of an attribute (1 & 0) respectively.

Examples of dichotomous or binary scales are:

  • Agreement with a statement: agree, disagree.
  • Sex: 1, male; 2, female.
  • Presence of mental illness: 0, absent; 1, present.
  • Occurrence of headaches: 0, no; 1, yes.
Example of Ordinal Scales
Ordinal Scale Example

Interval and ratio scales(noncategorical, metric, or dimensional scales)

It use numbers that indicate the quantity of what is being measured. They have two features: firstly, equal differences in the attribute between any pairs of numbers in the scale mean equal differences in the attribute being measured, i.e. the difference between any two values reflects the magnitude of the difference in the attribute – the difference in temperature between 22 and 26º C is the same as that between 32 and 36° C; this makes the scale an interval scale. Secondly, in some of these scales, zero indicates absence of the attribute, as a consequence of which the ratio between any two values indicates the ratio between the amounts of the attribute for e.g. an income of Rs 1000 is twice as high as an income of Rs 500; this additional feature makes the scale a ratio scale. Most noncategorical scales have both these features; exceptional ones, like the Centigrade scale for temperature, are interval but not ratio scales – 0° C does not mean ‘absence of heat’, and 20° C is therefore not ‘twice as hot’ as 10° C. Examples of ratio scales are:

  • Weight: measured in kgs.
  • Height: measured in cm.
  • Blood pressure: measured in mm of Hg.

Interval or ratio scale provides more information than an ordinal one, and is to be preferred when there is a choice. Interval or ratio scale may be continuous or discrete. The scale is said to be continuous if an infinite number of values is possible along a continuum, e.g. when measuring or cholesterol level. It is discrete if only certain values along the scale are possible – a woman’s parity, for e.g. cannot be 3.44

example of interval scale
Interval Scale of Measurement

An interval or ratio scale may be ‘collapsed’ into broader categories by grouping values together, as under:

Income (in rupees); 500 – 999, 1000 – 1499, 1500 – 1999 and so on.If equal class intervals are used, as in the above example, the scale can still be treated as an interval one, taking the midpoints, ( 725, 1225, 1725, etc) as the values of the successive classes. However, it would be better to consider it an ordinal scale now, as the individual values may not be uniformly spread within the classes, and the intervals, between the average incomes of people in adjacent classes may hence not be equal. The scale is immediately degraded to an ordinal scale if an ‘open-ended’ category such as income > Rs 2000 is used. Also, if the class intervals vary, e.g. 500 – 999, 1000 – 2000, 2000 – 4000, etc, the scale is definitely an ordinal one.

Interval scales are numeric scales in which we know both the order and the exact differences between the values.  The classic example of an interval scale is Celsius temperature because the difference between each value is the same.  For example, the difference between 60 and 50 degrees is a measurable 10 degrees, as is the difference between 80 and 70 degrees.

Interval scales are nice because the realm of statistical analysis on these datasets opens up.  For example, central tendency can be measured by mode, median, or mean; standard deviation can also be calculated.

Like the others, you can remember the key points of an “interval scale” pretty easily. “Interval” itself means “space in between,” which is the important thing to remember–interval scales not only tell us about order, but also about the value between each item.

Here’s the problem with interval scales: they don’t have a “true zero.”  For example, there is no such thing as “no temperature,” at least not with celsius.  In the case of interval scales, zero doesn’t mean the absence of value, but is actually another number used on the scale, like 0 degrees celsius.  Negative numbers alsohave meaning.  Without a true zero, it is impossible to compute ratios.  With interval data, we can add and subtract, but cannot multiply or divide.


Confused?  Ok, consider this: 10 degrees C + 10 degrees C = 20 degrees C.  No problem there.  20 degrees C is not twice as hot as 10 degrees C, however, because there is no such thing as “no temperature” when it comes to the Celsius scale.  When converted to Fahrenheit, it’s clear: 10C=50F and 20C=68F, which is clearly not twice as hot.


Ratio scales are the ultimate nirvana when it comes to data measurement scales because they tell us about the order, they tell us the exact value between units, AND they also have an absolute zero–which allows for a wide range of both descriptive and inferential statistics to be applied.  At the risk of repeating myself, everything above about interval data applies to ratio scales, plus ratio scales have a clear definition of zero.  Good examples of ratio variables include height, weight, and duration.

Ratio scales provide a wealth of possibilities when it comes to statistical analysis. These variables can be meaningfully added, subtracted, multiplied, divided (ratios). Central tendency can be measured by mode, median, or mean; measures of dispersion, such as standard deviation and coefficient of variation can also be calculated from ratio scales.

Example of Ratio Scales

  1. Height of person
  2. Weight of person
  3. Pulse per min
  4. Volume in units


General Information:

Visual analogue scale (VAS)

A frequently used tool in measuring a diverse range of subjective phenomenon (rather frequent in psychological research), is the 0 – 100 visual analogue scale [Revill et al 1976]. This may be used to measure pain, anxiety, patient satisfaction, etc. Because there are infinite possible values that can occur throughout the range 0 – 100, describing a continuum of for e.g. pain intensity, most researchers treat the resulting data as continuous [ Mantha S et al 1993, Dexter and Chestnut 1995]. However, if there is doubt about the sample distribution, then the data should

be considered ordinal. VAS should also be treated as ordinal scale when small number of observations are being analyzed [sample size < 30].

A Visual Analogue Scale (VAS) is a measurement instrument that tries to measure a characteristic or attitude that is believed to range across a continuum of values and cannot easily be directly measured.[1] It is often used in epidemiologic and clinical research to measure the intensity or frequency of various symptoms.[2] 

For example, the amount of pain that a patient feels ranges across a continuum from none to an extreme amount of pain.[1] From the patient’s perspective, this spectrum appears continuous ± their pain does not take discrete jumps, as a categorization of none, mild, moderate and severe would suggest. It was to capture this idea of an underlying continuum that the VAS was devised

A common problem in anesthesia is to assess the effect of some intervention on levels of pain. For example, one may want to know whether patients who have a wound infiltrated with local anesthetic have less pain postoperatively. Visual analog scale (VAS) measurements are frequently used for pain assessment. Subjects mark the position along a 10-cm line, which denotes the severity of their pain. The distance from the marked point to the bottom of the scale is used as a measure of pain. For guidance, the phrases “no pain” and “worst imaginable pain” are placed at the bottom and top of the line, respectively.

The choice of a statistical test to analyze VAS data is controversial. [1] Procedures based on the rank order of data (nonparametric procedures) have an advantage. They do not incorrectly suggest that a difference exists among groups more often than specified by the nominal false-positive or type 1 error rate, regardless of whether the statistical distribution of VAS measurements is normal or not. Scott and Huskisson [2] have recommended that nonparametric methods be used to analyze VAS measurements. Procedures that assume that the VAS measurements follow a normal distribution (parametric procedures) also have an advantage. If the distribution of the data were normal, the tests would have the highest power (i.e., ability) to detect differences among groups. However, even if the distribution were not normal, parametric tests usually give false-positive rates that are close to the nominal value. [3] Therefore, Philip [4] recommended that parametric statistics be used to analyze VAS data. A recent literature review of papers that analyzed VAS measurements showed that 54% of the studies used a nonparametric test (Mann-Whitney or Kruskal-Wallis), and 34% used a parametric test (t test or analysis of variance [ANOVA]). [1] It appears no consensus has emerged in the scientific literature.

VAS can be presented in a number of ways, including:

  • scales with a middle point,graduations or numbers (numerical rating scales),
  • meter-shaped scales (curvilinear analogue scales),
  • “box-scales” consisting of circles equidistant from each other (one of which the subject has to mark), and
  • scales with descriptive terms at intervals along a line (graphic rating scales or Likert scales)

The most simple VAS is a straight horizontal line of fixed length, usually 100 mm. The ends are defined as the extreme limits of the parameter to be measured (symptom,pain,health) orientated from the left (worst) to the right (best). In some studies,horizontal scales are orientated from right to left ,and many investigators use vertical VAS.

Scoring and Interpretation

Using a ruler, the score is determined by mea-suring the distance (mm) on the 10-cm line between the “no pain” anchor and the patient’s mark, providing a range of scores from 0–100. A higher score indicates greater pain intensity. Based on the distribution of pain VAS scores in post- surgical patients (knee replacement, hyster-ectomy, or laparoscopic myomectomy) who described their postoperative pain intensity as none, mild, moderate, or severe, the following cut points on the pain VAS have been recommended: no pain (0–4 mm), mild pain(5-44 mm), moderate pain (45–74 mm), and severe pain (75–100 mm) (11). Normative values are not available. The scale has to be shown to the patient otherwise it is an auditory scale not a visual one.

Sadface vas.jpg
Perceptioons Of VAS Scale

Merits and Demerits Vas Scale

  • The VAS is widely used due to its simplicity and adaptability to a broad range of populations and set-tings.
  • VAS is more sensitive to small changes than are simple descriptive ordinal scales in which symptoms are rated,for example, as mild or slight,moderate,or severe to agonizing.
  • These scales are of most value when looking at change within individuals
  • The VAS takes < 1 minute to complete
  • No training is required other than the ability to use a ruler to measure distance to determine a score
  • Minimal translation difficul-ties have led to an unknown number of cross-cultural adaptations
  • However, assessment is clearly highly subjective
  • Are of less value for comparing across a group of individuals at one time point.
  • It could be argued that a VAS is trying to produce interval/ratio data out of subjective values that are at best ordinal.
  • The VAS is administered as a paper and pencil measure. As a result, it cannot be admin-istered verbally or by phone.
  • Caution is required when photo-copying the scale as this may change the length of the 10-cm line and also, the same alignment of scale should be used consistently within the same

Decisions regarding scale of measurements

This has to be undertaken in the planning stage of the study as these effects the mode of data collection and designing of study instruments. Moreover, choice of scales will also dictate the choice of statistical procedures. As a rule of thumb, interval or ratio scales facilitate most robust statistical tests (parametric tests such as t-test, ANOVA), categorical scales the least rigorous (chi- square), with ordinal scale in between the two (non-parametric tests such as Kruskal Wallis and Mann-Whitney). Choice of measurement scale also has a bearing on the sample size. If outcome of interest is measured on the interval or ratio scale a smaller sample size may suffice than if measured in categorical scale.

During planning it is often helpful to construct skeleton or dummy tables, i.e. tables without figures, or containing fictional figures respectively, incorporating variables under consideration. If there are categories, they should be specified in the column or row headings. At this stage it is not essential to decide exactly how the finer categories will be ‘collapsed’ into broader categories for the purpose of analysis. It is often desirable to defer such decisions, since they may be difficult to make without knowing the actual distribution of the values. If doubt exists about the way a variable will be treated in the analysis, care should be taken to collect data in such a way as to leave the options open.

Criteria of a satisfactory scale [Abramson & Abramson 1999].

A satisfactory scale of measurement is one that meets the following seven requirements.

1.Appropriate (keeping in view the conceptual definition of the variable and the study question)

2.Practicable (to the methods that will be used in data collection, e.g. record study may limit the choice of scales as data is pre-recorded)

3.Sufficiently powerful (to satisfy the objectives of the study. If there is a choice, on ordinal scale is preferred over a categorical one, and interval scale over ordinal)

4.Clearly defined components (operational definitions should be formulated not only for the variables but also for the categories)

5.Sufficient categories (the compression of data into too few categories may lead to loss of essential information)

6.Comprehensive (the scale should be collectively exhaustive providing niche for the

classification of every subject)

7.Mutually exclusive (each item of information should fit into only one place along the scale)

That’s it!  I hope this explanation is clear and that you know understand the four types of data measurement scales: nominal, ordinal, interval, and ratio!  

  1. Abramson J H & Abramson Z H (1999). Scales of measurement. In: Survey Methods in Community Medicine. 5th ed. Churchill Livingstone. Edinburgh. 141 – 150.
  2. Baron R A & Kalsher M J (2001). Research Methods in Psychology. In: Psychology. 5th ed. Allyn & Bacon. Boston. 24 – 33.
  3. Dexter F & Chestnut D H (1995). Analysis of statistical tests to compare visual analogue scale data measurements among groups. Anesthesiology; 82: 896 – 902.
  4. Graunt J (1662, republished 1939). Natural and political observations made upon the bills of mortality. London. John Martin. James Allestry, and Thomas Dicas/Baltimore: The John Hopkins Press.
  5. Greenwood M (1935). Epidemics and crowd diseases. An introduction to the study of epidemiology. New York: MacMillan.
  6. MacMahon B & Trichopoulos D (1996) Epidemiology – Principles and Methods. Little Brown and Company. Boston; 1 – 18
  7. Mantha S, Thisted R, Foss J et al (1993). A proposal to use confidence intervals for visual analogue scale data for pain measurement to determine clinical significance. Anesth Analg; 77: 1041 – 1047
  8. Revill S I, Robinson J O, Rosen M et al (1976). The reliability of a linear analogue for evaluating pain. Anaesthesia; 31: 1191 – 1198
  9. Mantha S, Thisted R, Foss J, Ellis JE, Roizen MF: A proposal to use confidence intervals for visual analog scale data for pain measurement to determine clinical significance Anesth Analg 77:1041-1047, 1993.
  10. Scott J, Huskisson EC: Graphic representation of pain. Pain 2:175-184, 1976.
  11. Fleiss JL: The Design and Analysis of Clinical Experiments. New York, John Wiley and Sons, 1986, pp 62, 66, 76-77, 103, 369.
  12. Philip BK: Parametric statistics for evaluation of the visual analog scale (letter). Anesth Analg 71:710, 1990.
  13. Seymour RA, Simpson JM, Charlton JE, Phillips ME: An evaluation of length and end-phrase of visual analogue scales in dental pain. Pain 21:177-185, 1985.
  14. Chestnut DH, Vincent RD Jr, McGrath JM, Choi WW, Bates JN: Does early administration of epidural analgesia affect obstetric outcome in nulliparous women who are receiving intravenous oxytocin? ANESTHESIOLOGY 80:1193-1200, 1994.
  15. Chestnut DH, McGrath JM, Vincent RD Jr, Penning DH, Choi WW, Bates JN, McFarlane C: Does early administration of epidural analgesia affect obstetric outcome in nulliparous women who are in spontaneous labor? ANESTHESIOLOGY 80:1201-1208, 1994.
  16. Blalock HM: Social Statistics. Revised 2nd edition. New York, McGraw-Hill, 1979, pp 214, 286, 289.
  17. Law AM, Kelton WD: Simulation Modeling and Analysis. New York, McGraw-Hill, 1982, pp 176, 261.
  18. Dexter F: Analysis of statistical tests to compare doses of analgesics among groups. ANESTHESIOLOGY 81:610-615, 1994.
  19. Carroll RJ, Ruppert D: Transformation and Weighting in Regression, New York, Chapman and Hall, 1988, p 116.

Define the Statistics and illustrate the concept.

The subject of Statistics, as it seems, is not a new discipline but it is as old as the human society itself. Statistical methods and principles have found applications in many fields, business, the social sciences, engineering and the natural and physical sciences. In fact, modern age is the age of statistics. H.G. Well’s prediction that, “Statistical thinking will one day be as necessary for efficient citizenship as the ability to read and write”, has become valid in the context of today’s competitive business environment where many organizations find themselves data-rich but information-poor. Thus for decision-makers it is important to develop the ability to extract meaningful information from raw data to make better decisions. It is possible only through the careful analysis of data guided by statistical thinking.

Almost every aspect of natural phenomenon and human and other activity is now subjected to measurement and interpretation in terms of statistics. Through application of appropriate statistical methods, current performance may be measured, significant relationships may be studied, past experience may be analysed and probable future trends appraised. To acquire knowledge and to express it precisely statistical methods and statistics, have a vital role to play.

Meaning and Definition of Statistics

The word ‘statistics’ of English Language has either been derived from the Latin word ‘Status’ or Italian word ‘Statistics’ or German word ‘Statistics’. In each case it means, ‘an organized political state.’

Broadly speaking the word statistics means:

  1. Statistics or statistical data;
  2. Statistical methods or science of statistics;
  3. Statistics, plural of the word statistic.

The common man refers the word statistics as numerical data. In Kendall and Buckland Statistical Dictionary the word statistics is explained as:

The three meanings of the word ‘statistics’ are contained in the statement due to Tute. ‘You compute statistics by statistics from statistics’.

Definition of Statistics. Different authors have given different definitions of statistics. Some of the definitions of statistics describing it as quantitatively are:

“Statistics are the classified facts representing the conditions of the people in a state especially those facts which can be stated in number or in a table of numbers or in any tabular or classified arrangement”.

Another definition due to Bowley is:

“Statistics is a numerical statement of facts in any department of enquiry placed in relation to each other “.

These definitions are not clear and exhaustive. But the following definition given by Secrist is modern and convincing.

It is ‘a body of knowledge’; a branch of applied mathematics. It has its own symbols, techniques and theorems.

  1. “By Statistics we mean aggregate of facts affected to a marked extent by multiplicity of causes, numerically expressed, enumerated or estimated according to reasonable standards of accuracy, collected in a systematic manner for a pre-determined purpose and placed in relation to each other.”
  2. Statistics are an aggregate of facts:

The series of observations of temperature of patients over a period of, say, one week taken at regular intervals will constitute statistics. If you say the temperature is 102° F, at a particular time, this single isolated figure is not statistics. The collection of figures of height, weight, income etc., of a group of persons can be called ‘Statistics’.

  • Statistics are affected to a marked extent by multiplicity of causes:

In fact, only when the problem is complex we turn to statistics. In the above example, the rise and fall in the temperature of a patient are caused by many factors such as his diet, his constitution, the climate, the drugs etc. There are usually many factors which affect the figures of production of sale, price, import, export etc. of any commodity.

  • Statistics are numerically expressed:

The statements made in the numerical form are statistics. “A particular student has an excellent academic record” or Mr. X is an efficient administrator”, neither is a statistical statement. But “the student has scored 60% marks at B.Com., 65% at M.Com.”; or “Mr. X increased the production in his factory by 7% in the last but one year, 10% in the last year.” Both are statistical statements as they are expressed numerically.

  • Statistics are estimated according to reasonable standard of accuracy:

As statistics are numerical expressions, the figures can be obtained either by actual counting and measuring or by estimation. But in either case, complete accuracy is neither possible nor desirable. For example, when heights of students are measured it is sufficient to measure unto centimeters. The meaning of “reasonable standards of accuracy” should be taken in the context of the problem. For example, gold will have to be weighed in grams and even in milligrams.

  • Statistics are collected in systematic manner :

If the figures are collected by an untrained man without any method, the results will not be reliable. In the above example, the temperatures would be noted at regular intervals of, say, four hours, in centigrade by a trained nurse with a particular type of thermometer.

  • Statistics are collected for a pre-determined purpose:

In our daily life also our actions are usually guided by our purpose. For example, the purpose was to study and compare the effects of the drugs ‘A’ and ‘B’ on the patients suffering from fever. Data collected with no purpose often result in waste of money, time and energy.

  • Statistics are placed in relation to each other:

It is only by comparing the results of drugs ‘A’ and ‘B’ a conclusion as to which drug is more effective can be arrived at.

  • Statistics as ‘Statistical Methods’: The best of the definitions which emphasizes this aspect is given by Croxton and Cowdon. It is as follows:

“Statistics may be defined as the collection, presentation, analysis and interpretation of numerical data.” This definition points out the following characteristics of Statistics as a branch of knowledge and its methods.

  1. Collection of data:

Collection of data is the first step of statistical methods. Since the whole base of statistics stands on the foundation of the collected data, maximum care should be taken at this stage. The results obtained can never be better than the data on which they are based.

  1. Presentation of data:

The data collected are in the form of figures spread irregularly or in the form of answers. These figures cannot tell us much unless they are properly arranged. The second stage in the statistical investigation is to classify the data and put them in the form of tables.

  1. Analysis of data:

It is necessary to analyse the data further in order to arrive at some definite results. The characteristic properties of the problem are revealed only when quantities like measures of central tendency, measures of variation, correlation etc; are calculated. These single figures tell us much about the problem.

Interpretation of data:

This is the last stage in the process and therefore, is perhaps the most difficult part, requiring a high degree of skill and experience. The results of the third stage are in the form of numbers and need to be transformed into statements. These interpretations are, to some extent, probable but could never be taken as absolutely certain. The probability of the results depends upon every stage from the beginning to the end.

Development of Statistics and Statistical Thinking

Statistics has different meanings to different people which depend largely on its use. For example,

  • For the census department, statistics consists of information about the birth rate per thousand and the sex ratio in different states
  • For a cricket fan, statistics refers to numerical information or data relating to the runs scored by a cricketer
  • For a share broker, statistics is the information on changes in share prices over a period of time
  • For an environmentalist, statistics refers to information on the quantity of pollution released into the atmosphere by all types of vehicles in different cities; and so on.

Moreover, with the developments in the statistical techniques during the last few decades, today, statistics is viewed not only as a mere device for collecting numerical data but as a means of sound techniques for their inferences from them. Accordingly, it is not merely a by-product of the administrative set up of the state but it embraces all sciences-social, physical and natural, and is finding numerous applications in various diversified fields. It is rather impossible to think of any sphere of human activity where statistics does not creep in. It will not be exaggeration to say that statistics has assumed unprecedented dimensions these days and statistical thinking is becoming more and more indispensable every day for an able citizenship. In fact to a very striking degree, the modern culture has become the statistical culture and the subject of statistics has acquired tremendous progress in the recent past so much so that an elementary knowledge of statistical methods has became a part of the general education in the curricula of many Universities all over the world.

The development of mathematics in relation to the probability theory and the advent of fast-speed computers have substantially changed the field of statistics in the last few decades. The use of computer softwares, such as SAS and SPSS has brought about a technological revolution.

An integral part of the managerial approach focuses on the quality of products manufactured or services provided by an organization. This approach requires the application of certain statistical methods and the statistical thinking. Statistical thinking may be defined as the thought process that focuses on ways to identify, control and reduce variations present in all phenomena. A better understanding of a phenomenon through statistical thinking and use of statistical methods for data analysis enhances opportunities for improvement in the quality of products or services.

The steps of statistical thinking necessary for increased understanding of an improvement in the process are as follows:

  • Specify the aim of the study;
  • Understand how the process works;
  • Assess the current process performance;
  • Identify strategies for improvement;
  • Test the effectiveness of the proposed strategy;
  • If successful, implement the strategy; if not then identify some other strategy.

Characteristics of Statistics

Following are the characteristics of statistics (According to Secrist):

  • Statistics are the aggregate of facts.
  • Statistics are numerically expressed.
  • Statistics should be collected in a statistic manner.
  • Statistics should be collected for a predetermined purpose.
  • Statistics are affected to a marked extent by multiplicity of causes and not by a single cause.
  • Statistics should be placed in relation to each other.
  • The reasonable standard of accuracy should be maintained in statistics.

Importance and Usefulness of Statistics

Statistics help in presenting large quantity of data in a simple and classified form.

  1. It gives the methods of comparison of data and it weighs and judges them in the right perspective.
  2. It simplifies unwieldy and complex data so as to make them understandable.
  3. It enlarges individual experience.
  4. It helps in finding the conditions of relationship between the variables.
  5. It provides guidance in the formation of business policies.
  6. It helps in establishing cause and effect relationships.
  7. It proves useful in a number of fields like Banks, Railways, Army etc., etc.

Is Statistics   Science or Art?

Statistics as a Science

Science is a body of systematized knowledge from which specific propositions are deducted in accordance with a few general principles. Although all sciences differ, the logical scientific methods are common to all the sciences. Using the approach of systematic doubt, scientific method is a process of discovering the truth in a systematized manner by logical considerations. There are in general four stages in a scientific inquiry: (i) Observation, (ii) hypothesis, (iii) prediction and (iv) verification. Since statistical methods are based on the some fundamental ideas and processes as other sciences, so statistics is said to be a science. But statistics is different from physics, chemistry etc.

Statistics as an Art

An art is an applied knowledge and creation of beauty of leading to perfection. If science is knowledge then art is action. Since the successful application of statistical methods depends to a considerable degree on the skill and special experience of the statistician and his knowledge of the field of application, statistics may be called an art of applying scientific methods similar to an artist who possesses and can apply the requisite skill, experience and patience for the creation of beauty leading to perfection.

Statistics is Both a Science and an Art

According to Toppett “It is both a science and an art. It is a science in that its methods are basically systematic and have general application, and an art in that their successful application depends to a considerable of the statistician and his knowledge of the field of application, e.g., Economics.”

Division of Statistics

The subject matter f the statistics may be classified into the following main divisions:

(a)          Theoretical Statistics

Mathematical theory which is the basis of the science of statistics is called theoretical statistics. The basis of theoretical statistics often called Theory of Probability and deals with the chance variation of the observations.

(b)          Statistical Methods

Statistical methods are the devices by which complex and numerical data are analysed in such a way that way become intelligible and lead to correct conclusions. The important statistical methods are:

  1. Collection of data,
  2. Classification of data,
  3.  Tabulation of data,
  4.  Presentation of data,
  5.  Analysis of data,
  6.  Interpretation of data,
  7.  Forecasting.

(c)           Applied Statistics

This division of the science of statistics deals with the application of rules and principles developed in theoretical statistics to specific problems in different disciplines. For example, Statistical Quality Control, Sample Survey, Design of Experiments, Analysis of Time-Series, Index Numbers etc. The two sub-divisions of applied statistics are as follows:

  1. Descriptive Applied Statistics. The branch of applied statistics which deals with the existing facts of historical importance that are of great interest is known as Descriptive Applied Statistics.
  2. Scientific Applied Statistics. The branch of applied statistics which deals with the establishment of definite laws, rules and doctrines is known as Scientific Applied Statistics subject matter of Applied Statistics.

(d) Business Statistics

A new branch of statistics called Business Statistics under Applied Statistics has been developed. This branch has been expending so rapidly due to the use of statistical methods in business. Every business passes through four phases: prosperity, decline, depression and recovery. Statistical methods are very helpful in forecasting about these phases.

Now-a-days various problems regarding business are studied, analysed and solved through statistical methods.

Importance and Scope of Statistics

The science of statistics is growing in importance every day. It is now being used in almost every field of human activity. Its application has become so wide that no branch of human knowledge from the graphic arts to astrophysics and from numerical composition to missile guidance escapes its approach. Statistics provides tools and techniques for research workers in analysis of problems in both natural and social sciences. There is hardly and field whether it be economics, commerce, industry, trade, biology, sociology, psychology medicine, physics, chemistry, education, astronomy meteorology, administration, insurance, banking or planning where statistical methods are not applicable. That is why it is said that, “Sciences without statistics bear no fruit, statistics without sciences has no root”. In the absence of statistics, most of our problems would have remained unsolved and our knowledge would have limited.

To be more specific we may discuss the application (or relationship) of statistics in (or with) various fields.

Statistics in State:

 Earlier statistics was used by the rulers to assess their military and economic strength. State Government collects information on the economic conditions of the people and resources available. Facts are necessary to plan the use of resources and to assess from time to time the achievement of the objective. All these require collection and analysis of statistics on a regular basis.

Statistics and Economics.

Statistical techniques have proved immensely useful in the solution of a variety of economic problems such as production, consumption, distribution of income and wealth, expenditure and poverty etc. Presently, statistics serves as the base for the mathematical approach to Economics. Some of the uses of statistics in economics are as follows:

  1. Measures of gross national product and input-output analysis have greatly advanced overall economic knowledge and opened up entirely new fields of study.
  2. Financial statistics are basis in the field of money and banking, short-term credit, consumer finance and public finance.
  3. Statistical studies of business cycles, long term growth and seasonal fluctuations serve to expand our knowledge of economic instability and to modify older theories.
  4. Studies of competition, oligopoly and monopoly require statistical comparison of market prices,
    cost and profits of individual firms.
  5. Statistical surveys of prices are essential in studying the theories of prices, pricing policy and price
    trends as well as their relationship to the general problem of inflation.
  6. Operational studies of public utilities require both statistical and legal tools of analysis.
  7. Analysis of population, land economics and economic geography are basically statistical in their approach.
  8. In solving various economic problems such as poverty, unemployment, disparities in the distribution of income and wealth, statistical data and statistical methods play a vital role.

Statistics and Physical Sciences:

 Currently, the physical sciences seem to be making increasing use of statistics, especially in astronomy, chemistry, engineering, geology, meteorology and certain branches of physics.

Statistics and Natural Sciences:

 Statistical techniques have proved to be extremely useful in the study of all natural sciences like astronomy, biology, medicine, meteorology, zoology, botany etc. For example, in diagnosing the correct disease the doctor has to rely heavily on actual data like temperature of the body, pulse rate, blood pressure. Similarly, in judging the efficiency of a particular drug for causing a certain disease experiments have to be conducted and success or failure would depend upon the number of people who are cured after using the drug. In fact, it is difficult to find any scientific activity where statistical data and statistical methods are not used.

Statistics in Social Sciences:

 Some specific areas of applications of statistics in social sciences are as follows:

  1. Regression and correlation analysis technique are used to study and isolate all those factors associated with each social phenomenon which bring out the changes in data with respect to time, place, and object.
  2. Sampling techniques and estimation theory are indispensable methods for conducting any social   survey pertaining to any strata of society, and drawing valid inferences.
  3. In sociology, statistical methods are used to study mortality rates, fertility trends, population growth, and other aspects of vital statistics.

Statistics and Computers:

Computers and information technology, in general, have had a fundamental effect on most business and service organizations. Computers help in processing and maintaining past records of operations involving payroll calculations, inventory management, railway/airline reservations etc. Use of computers hardware, however, presupposes that the user it’s able to interpret the computer outputs that are generated.

Limitations of Statistics

Although statistics is so much useful in the modern world and although it has grown enormously in recent years it is misunderstood by many. It is misunderstood by those who believe in the popular notion that by statistics you can prove anything. The reasons of this misunderstanding are as follows.

  1. It is not useful for individual case.
    1. It cannot study qualitative phenomenon.
    2. Its results are true only on an average.
    3. The statistical results are subject to bias.
    4. It can be misused. Statistical results may be misleading if quoted without context.
    5. Results may be misleading if quoted without context.

Misuse of Statistics

By misuse of statistics we mean the improper use of statistical tools by unscrupulous people with an improper statistical bend of mind and misinterpretation of data.

Misuse of statistics occurs when a statistical argument asserts a falsehood. In the period since statistics began to play a significant role in society, they have often been misused. In some cases, the misuse was accidental. In others, it was purposeful and for the gain of the perpetrator. When the statistical reason involved is false or misapplied, this constitutes a statistical fallacy.

The false statistics trap can be quite damaging to the quest for knowledge. For example, in medical science, correcting a falsehood way take decades and cost lives.

Misuses can be easy to fall into professional scientists, even mathematicians and professional statisticians; can be tooled by even some simple methods, even if they are careful to check everything. Scientists have been known to fool themselves with statistics due to lack of knowledge of probability theory and lack of standardization of their tests.

The misuse of statistics is the main cause to discredit this science and has led to the public distrust in statistics. The various ways in which statistics are often misused are:

  1. Inappropriate comparison of data.
  2. Deliberate manipulation of statistics by selfish persons to achieve their personal ends.
  3. Mathematical manipulations such as wrong use of percentages.
  4. Quoting figures without proper context.      
  5. Ignorance of limitations of statistics. Misuse of statistics can be avoided by:
    Use of sufficient and appropriate data.
  6. Use of statistics by experts.
  7. Logical use of statistical techniques.
  8. Keeping eternal vigilance.
  9. Keeping in mind the limitations of statistics.

In brief, to avoid misuse of statistics, the statistical data should be handled only by those who are aware of their use limitations and dangers and are free from prejudice. Utmost care and precautions should be taken for the interpretations of data in all manifestations.

Distrust of Statistics

Distrust of statistics is the lack of confidence in statistical methods and statements. The following are some derogatory remarks against statistics:

  1. Statistics can prove or disprove anything.
  2. Statistics is like clay of which one can make a God or Devil, one likes.
  3. Statistics are like bikinis. They reveal what is interesting and conceal what is vital.
  4. There are three kinds of lies—Lies, Damn Lies and Statistics.

Reasons for Distrust in Statistics

The causes of distrust in statistics are as follows:

  1. Defective data.
  2. Insufficient data.
  3. Non-comparable data.
  4. Innocence of the figures.
  5. Misinterpretation of Data.
  6. Inappropriate statistical methods.
  7. Absence of an objective lest.

Methods of Removing Distrust of Statistics

  1. Statistics should be used by a person who knows statistical techniques.
  2. There should be patience and self-restraint in the person who collects data and who use them.
  3. Statistical data should be obtained and analysed with independent conversation.
  4. Statistical limits should be kept in mind while interpreting the data.
  5. Precautions should be taken at each step.

The subject of Statistics, as it seems, is not a new discipline but it is as old as the human society itself. Statistical methods and principles have found applications in many fields, business, the social sciences, engineering and the natural and physical sciences. In fact, modern age is the age of statistics. H.G. Well’s prediction that, “Statistical thinking will one day be as necessary for efficient citizenship as the ability to read and write”, has become valid in the context of today’s competitive business environment where many organizations find themselves data-rich but information-poor. Thus for decision-makers it is important to develop the ability to extract meaningful information from raw data to make better decisions. It is possible only through the careful analysis of data guided by statistical thinking.

Almost every aspect of natural phenomenon and human and other activity is now subjected to measurement and interpretation in terms of statistics. Through application of appropriate statistical methods, current performance may be measured, significant relationships may be studied, past experience may be analysed and probable future trends appraised. To acquire knowledge and to express it precisely statistical methods and statistics, have a vital role to play.