Why do statistics exist

Probably the most common scale type is the ratio-scale. Observations of this type are on a scale that has a meaningful zero value but also have an equidistant measure i. For example, a 10 year-old girl is twice as old as a 5 year-old girl. Since you can measure zero years, time is a ratio-scale variable. Money is another common ratio-scale quantitative measure. Observations that you count are usually ratio-scale e.

A more general quantitative measure is the interval scale. Interval scales also have an equidistant measure.

However, the doubling principle breaks down in this scale. Quantitative Data : The graph shows a display of quantitative data. Statistics deals with all aspects of the collection, organization, analysis, interpretation, and presentation of data. It includes the planning of data collection in terms of the design of surveys and experiments.

Statistics can be used to improve data quality by developing specific experimental designs and survey samples. Statistics also provides tools for prediction and forecasting. Statistics is applicable to a wide variety of academic disciplines, including natural and social sciences as well as government and business.

Statistical methods can summarize or describe a collection of data. This is called descriptive statistics. This is particularly useful in communicating the results of experiments and research. Statistical models can also be used to draw statistical inferences about the process or population under study—a practice called inferential statistics. Inference is a vital element of scientific advancement, since it provides a way to draw conclusions from data that are subject to random variation.

Conclusions are tested in order to prove the propositions being investigated further, as part of the scientific method. Descriptive statistics and analysis of the new data tend to provide more information as to the truth of the proposition. Summary statistics : In descriptive statistics, summary statistics are used to summarize a set of observations, in order to communicate the largest amount as simply as possible.

It consists of five experiments, each made of 20 consecutive runs. When applying statistics to a scientific, industrial, or societal problems, it is necessary to begin with a population or process to be studied. A population can also be composed of observations of a process at various times, with the data from each observation serving as a different member of the overall group.

For practical reasons, a chosen subset of the population called a sample is studied—as opposed to compiling data about the entire group an operation called census. Once a sample that is representative of the population is determined, data is collected for the sample members in an observational or experimental setting. This data can then be subjected to statistical analysis, serving two related purposes: description and inference.

Descriptive statistics summarize the population data by describing what was observed in the sample numerically or graphically. Numerical descriptors include mean and standard deviation for continuous data types like heights or weights , while frequency and percentage are more useful in terms of describing categorical data like race. Inferential statistics uses patterns in the sample data to draw inferences about the population represented, accounting for randomness. Inference can extend to forecasting, prediction and estimation of unobserved values either in or associated with the population being studied.

It can include extrapolation and interpolation of time series or spatial data and can also include data mining. Statistical analysis of a data set often reveals that two variables of the population under consideration tend to vary together, as if they were connected. For example, a study of annual income that also looks at age of death might find that poor people tend to have shorter lives than affluent people.

The two variables are said to be correlated; however, they may or may not be the cause of one another. The correlation could be caused by a third, previously unconsidered phenomenon, called a confounding variable.

For this reason, there is no way to immediately infer the existence of a causal relationship between the two variables. To use a sample as a guide to an entire population, it is important that it truly represent the overall population.

Representative sampling assures that inferences and conclusions can safely extend from the sample to the population as a whole. A major problem lies in determining the extent that the sample chosen is actually representative. Statistics offers methods to estimate and correct for any random trending within the sample and data collection procedures.

There are also methods of experimental design for experiments that can lessen these issues at the outset of a study, strengthening its capability to discern truths about the population. Randomness is studied using the mathematical discipline of probability theory. The use of any statistical method is valid when the system or population under consideration satisfies the assumptions of the method. In applying statistics to a scientific, industrial, or societal problem, it is necessary to begin with a population or process to be studied.

Recall that the field of Statistics involves using samples to make inferences about populations and describing how variables relate to each other. The concept of correlation is particularly noteworthy for the potential confusion it can cause. Statistical analysis of a data set often reveals that two variables properties of the population under consideration tend to vary together, as if they were connected. The correlation phenomena could be caused by a third, previously unconsidered phenomenon, called a confounding variable.

The essential skill of critical thinking will go a long way in helping one to develop statistical literacy. Experts and advocates often use numerical claims to bolster their arguments, and statistical literacy is a necessary skill to help one decide what experts mean and which advocates to believe.

This is important because statistics can be made to produce misrepresentations of data that may seem valid. The aim of statistical literacy is to improve the public understanding of numbers and figures. For example, results of opinion polling are often cited by news organizations, but the quality of such polls varies considerably.

Some understanding of the statistical technique of sampling is necessary in order to be able to correctly interpret polling results. Sample sizes may be too small to draw meaningful conclusions, and samples may be biased. The wording of a poll question may introduce a bias, and thus can even be used intentionally to produce a biased result.

Good polls use unbiased techniques, with much time and effort being spent in the design of the questions and polling strategy. Statistical literacy is necessary to understand what makes a poll trustworthy and to properly weigh the value of poll results and conclusions. Critical thinking is a way of deciding whether a claim is always true, sometimes true, partly true, or false.

The list of core critical thinking skills includes observation, interpretation, analysis, inference, evaluation, explanation, and meta-cognition. There is a reasonable level of consensus that an individual or group engaged in strong critical thinking gives due consideration to establish:. Critical Thinking : Critical thinking is an inherent part of data analysis and statistical literacy. Experimental design is the design of studies where variation, which may or may not be under full control of the experimenter, is present.

Outline the methodology for designing experiments in terms of comparison, randomization, replication, blocking, orthogonality, and factorial experiments. In general usage, design of experiments or experimental design is the design of any information-gathering exercises where variation is present, whether under the full control of the experimenter or not. Formal planned experimentation is often used in evaluating physical objects, chemical formulations, structures, components, and materials.

Design of experiments is thus a discipline that has very broad application across all the natural and social sciences and engineering.

A methodology for designing experiments was proposed by Ronald A. These methods have been broadly adapted in the physical and social sciences. Old-fashioned scale : A scale is emblematic of the methodology of experimental design which includes comparison, replication, and factorial considerations.

It is best that a process be in reasonable statistical control prior to conducting designed experiments. When this is not possible, proper blocking, replication, and randomization allow for the careful conduct of designed experiments. To control for nuisance variables, researchers institute control checks as additional measures.

Investigators should ensure that uncontrolled influences e. One of the most important requirements of experimental research designs is the necessity of eliminating the effects of spurious, intervening, and antecedent variables. In most designs, only one of these causes is manipulated at a time.

An unbiased random selection of individuals is important so that in the long run, the sample represents the population. Explain how simple random sampling leads to every object having the same possibility of being chosen. Sampling is concerned with the selection of a subset of individuals from within a statistical population to estimate characteristics of the whole population.

Two advantages of sampling are that the cost is lower and data collection is faster than measuring the entire population. Each observation measures one or more properties such as weight, location, color of observable bodies distinguished as independent objects or individuals.

In survey sampling, weights can be applied to the data to adjust for the sample design, particularly stratified sampling blocking. Results from probability theory and statistical theory are employed to guide practice.

In business and medical research, sampling is widely used for gathering information about a population. A simple random sample is a subset of individuals chosen from a larger set a population. A simple random sample is an unbiased surveying technique. Pioneering English demographers such as William Petty and John Graunt adapted mathematical techniques to estimate population changes, for which they were hired by Oliver Cromwell and Charles II. These path-breaking individuals were neither pure scholars nor government officials, but hovered somewhere between the two.

They were enthusiastic amateurs who offered a new way of thinking about populations that privileged aggregates and objective facts. Thanks to their mathematical prowess, they believed they could calculate what would otherwise require a vast census to discover. Only centralised nation states had the capacity to collect data across large populations in a standardised fashion and only states had any need for such data in the first place.

Over the second half of the 18th century, European states began to collect more statistics of the sort that would appear familiar to us today. Casting an eye over national populations, states became focused upon a range of quantities: births, deaths, baptisms, marriages, harvests, imports, exports, price fluctuations. Things that would previously have been registered locally and variously at parish level became aggregated at a national level.

New techniques were developed to represent these indicators, which exploited both the vertical and horizontal dimensions of the page, laying out data in matrices and tables, just as merchants had done with the development of standardised book-keeping techniques in the late 15th century. Organising numbers into rows and columns offered a powerful new way of displaying the attributes of a given society. Large, complex issues could now be surveyed simply by scanning the data laid out geometrically across a single page.

These innovations carried extraordinary potential for governments. By simplifying diverse populations down to specific indicators, and displaying them in suitable tables, governments could circumvent the need to acquire broader detailed local and historical insight.

Of course, viewed from a different perspective, this blindness to local cultural variability is precisely what makes statistics vulgar and potentially offensive. Regardless of whether a given nation had any common cultural identity, statisticians would assume some standard uniformity or, some might argue, impose that uniformity upon it.

Not every aspect of a given population can be captured by statistics. There is always an implicit choice in what is included and what is excluded, and this choice can become a political issue in its own right. The fact that GDP only captures the value of paid work, thereby excluding the work traditionally done by women in the domestic sphere, has made it a target of feminist critique since the s.

In France, it has been illegal to collect census data on ethnicity since , on the basis that such data could be used for racist political purposes. This has the side-effect of making systemic racism in the labour market much harder to quantify.

Despite these criticisms, the aspiration to depict a society in its entirety, and to do so in an objective fashion, has meant that various progressive ideals have been attached to statistics. The image of statistics as a dispassionate science of society is only one part of the story. S ince the high-point of the Enlightenment in the late 18th century, liberals and republicans have invested great hope that national measurement frameworks could produce a more rational politics, organised around demonstrable improvements in social and economic life.

Equally, they promise to reveal what historical path the nation is on: what kind of progress is occurring? How rapidly? For Enlightenment liberals, who saw nations as moving in a single historical direction, this question was crucial.

The potential of statistics to reveal the state of the nation was seized in post-revolutionary France. The Jacobin state set about imposing a whole new framework of national measurement and national data collection.

Uniformity of data collection, overseen by a centralised cadre of highly educated experts, was an integral part of the ideal of a centrally governed republic, which sought to establish a unified, egalitarian society. From the Enlightenment onwards, statistics played an increasingly important role in the public sphere, informing debate in the media, providing social movements with evidence they could use.

Over time, the production and analysis of such data became less dominated by the state. Academic social scientists began to analyse data for their own purposes, often entirely unconnected to government policy goals. To recognise how statistics have been entangled in notions of national progress, consider the case of GDP. This is fiendishly difficult to get right, and efforts to calculate this figure began, like so many mathematical techniques, as a matter of marginal, somewhat nerdish interest during the s.

It was only elevated to a matter of national political urgency by the second world war, when governments needed to know whether the national population was producing enough to keep up the war effort. Whether GDP is rising or falling is now virtually a proxy for whether society is moving forwards or backwards. Or take the example of opinion polling, an early instance of statistical innovation occurring in the private sector.

During the s, statisticians developed methods for identifying a representative sample of survey respondents, so as to glean the attitudes of the public as a whole.

This breakthrough, which was first seized upon by market researchers, soon led to the birth of the opinion polling. Nowadays, the flaws of polling are endlessly picked apart.

But this is partly due to the tremendous hopes that have been invested in polling since its origins. It is only to the extent that we believe in mass democracy that we are so fascinated or concerned by what the public thinks.

But for the most part it is thanks to statistics, and not to democratic institutions as such, that we can know what the public thinks about specific issues. As indicators of health, prosperity, equality, opinion and quality of life have come to tell us who we are collectively and whether things are getting better or worse, politicians have leaned heavily on statistics to buttress their authority.

Often, they lean too heavily, stretching evidence too far, interpreting data too loosely, to serve their cause. But that is an inevitable hazard of the prevalence of numbers in public life, and need not necessarily trigger the type of wholehearted rejections of expertise that we have witnessed recently.

On the other hand, statistics together with elected representatives performed an adequate job of supporting a credible public discourse for decades if not centuries. What changed? T he crisis of statistics is not quite as sudden as it might seem. For roughly years, the great achievement of statisticians has been to reduce the complexity and fluidity of national populations into manageable, comprehensible facts and figures. Yet in recent decades, the world has changed dramatically, thanks to the cultural politics that emerged in the s and the reshaping of the global economy that began soon after.

It is not clear that the statisticians have always kept pace with these changes. Traditional forms of statistical classification and definition are coming under strain from more fluid identities, attitudes and economic pathways.

Efforts to represent demographic, social and economic changes in terms of simple, well-recognised indicators are losing legitimacy. Consider the changing political and economic geography of nation states over the past 40 years. The statistics that dominate political debate are largely national in character: poverty levels, unemployment, GDP, net migration.

But the geography of capitalism has been pulling in somewhat different directions. Plainly globalisation has not rendered geography irrelevant. In many cases it has made the location of economic activity far more important, exacerbating the inequality between successful locations such as London or San Francisco and less successful locations such as north-east England or the US rust belt.

The key geographic units involved are no longer nation states. Rather, it is cities, regions or individual urban neighbourhoods that are rising and falling. The Enlightenment ideal of the nation as a single community, bound together by a common measurement framework, is harder and harder to sustain.

When macroeconomics is used to make a political argument, this implies that the losses in one part of the country are offset by gains somewhere else. Descriptive statistics help us understand the collective properties of the elements of a data sample and form the basis for testing hypotheses and making predictions using inferential statistics.

Inferential statistics are tools that statisticians use to draw conclusions about the characteristics of a population, drawn from the characteristics of a sample, and to decide how certain they can be of the reliability of those conclusions. Based on the sample size and distribution statisticians can calculate the probability that statistics, which measure the central tendency, variability, distribution, and relationships between characteristics within a data sample, provide an accurate picture of the corresponding parameters of the whole population from which the sample is drawn.

Inferential statistics are used to make generalizations about large groups, such as estimating average demand for a product by surveying a sample of consumers' buying habits or to attempt to predict future events, such as projecting the future return of a security or asset class based on returns in a sample period.

Regression analysis is a widely used technique of statistical inference used to determine the strength and nature of the relationship i. The output of a regression model is often analyzed for statistical significance , which refers to the claim that a result from findings generated by testing or experimentation is not likely to have occurred randomly or by chance but is likely to be attributable to a specific cause elucidated by the data.

Having statistical significance is important for academic disciplines or practitioners that rely heavily on analyzing data and research. Descriptive statistics are used to describe or summarize the characteristics of a sample or data set, such as a variable's mean, standard deviation, or frequency. Inferential statistics, in contrast, employs any number of techniques to relate variables in a data set to one another, for example using correlation or regression analysis.

These can then be used to estimate forecasts or infer causality. Statistics are used widely across an array of applications and professions. Any time data are collected and analyzed, statistics are being done.

This can range from government agencies to academic research to analyzing investments. Economists collect and look at all sorts of data, ranging from consumer spending to housing starts to inflation to GDP growth. In finance, analysts and investors collect data about companies, industries, sentiment, and market data on price and volume. Together, the use of inferential statistics in these fields is known as econometrics. Trading Basic Education. Financial Analysis. Advanced Technical Analysis Concepts.

Your Privacy Rights. To change or withdraw your consent choices for Investopedia. At any time, you can update your settings through the "EU Privacy" link at the bottom of any page. These choices will be signaled globally to our partners and will not affect browsing data.

We and our partners process data to: Actively scan device characteristics for identification. I Accept Show Purposes. Your Money. Personal Finance.