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## Experimental and observational studies and Levels of measurement

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Experimental and observational studies
A common goal for a statistical research project is to investigate causality, and in particular to draw a conclusion on the effect of changes in the values of predictors or independent variables on response or dependent variables. There are two major types of causal statistical studies, experimental studies and observational studies. In both types of studies, the effect of differences of an independent variable (or variables) on the behavior of the dependent variable are observed. The difference between the two types is in how the study is actually conducted. Each can be very effective.

An experimental study involves taking measurements of the system under study, manipulating the system, and then taking additional measurements using the same procedure to determine if the manipulation may have modified the values of the measurements. In contrast, an observational study does not involve experimental manipulation. Instead data are gathered and correlations between predictors and the response are investigated.

An example of an experimental study is the famous Hawthorne studies which attempted to test changes to the working environment at the Hawthorne plant of the Western Electric Company. The researchers were interested in whether increased illumination would increase the productivity of the assembly line workers. The researchers first measured productivity in the plant then modified the illumination in an area of the plant to see if changes in illumination would affect productivity. As it turns out, productivity improved under all the experimental conditions (see Hawthorne effect). However, the study is today heavily criticized for errors in experimental procedures, specifically the lack of a control group and blindedness.

An example of an observational study is a study which explores the correlation between smoking and lung cancer. This type of study typically uses a survey to collect observations about the area of interest and then perform statistical analysis. In this case, the researchers would collect observations of both smokers and non-smokers, perhaps through a case-control study, and then look at the number of cases of lung cancer in each group.

The basic steps for an experiment are to:

plan the research including determining information sources, research subject selection, and ethical considerations for the proposed research and method,
design the experiment concentrating on the system model and the interaction of independent and dependent variables,
summarize a collection of observations to feature their commonality by suppressing details (descriptive statistics),
reach consensus about what the observations tell us about the world we observe (statistical inference),
document and present the results of the study.

Observational study
In statistics, the goal of an observational study is to draw inferences about the possible effect of a treatment on subjects, where the assignment of subjects into a treated group versus a control group is outside the control of the investigator. This is in contrast with controlled experiments, such as randomized controlled trials, where each subject is randomly assigned to a treated group or a control group before the start of the treatment.

The assignment of treatments may be beyond the control of the investigator for a variety of reasons:

A randomized experiment would violate ethical standards. Suppose one wanted to investigate the abortion–breast cancer hypothesis, which postulates a causal link between induced abortion and the incidence of breast cancer. In a hypothetical controlled experiment, one would start with a large subject pool of pregnant women and divide them randomly into a treatment group (receiving induced abortions) and a control group (bearing children), and then conduct regular cancer screenings for women from both groups. Needless to say, such an experiment would run counter to common ethical principles. (It would also suffer from various confounds and sources of bias, e.g., it would be impossible to conduct it as a blind experiment.) The published studies investigating the abortion–breast cancer hypothesis generally start with a group of women who already have received abortions. Membership in this “treated” group is not controlled by the investigator: the group is formed after the “treatment” has been assigned.
The investigator may simply lack the requisite influence. Suppose a scientist wants to study the public health effects of a community-wide ban on smoking in public indoor areas. In a controlled experiment, the investigator would randomly pick a set of communities to be in the treatment group. However, it is typically up to each community and/or its legislature to enact a smoking ban. The investigator can be expected to lack the political power to cause precisely those communities in the randomly selected treatment group to pass a smoking ban. In an observational study, she would typically start with a treatment group consisting of those communities where a smoking ban is already in effect.
A randomized experiment may be impractical. Suppose a researcher wants to study the suspected link between a certain medication and a very rare group of symptoms arising as a side effect. Setting aside any ethical considerations, a randomized experiment would be impractical because of the rarity of the effect. There may not be a subject pool large enough for the symptoms to be observed in at least one treated subject. An observational study would typically start with a group of symptomatic subjects and work backwards to find those who were given the medication and later developed the symptoms. Thus a subset of the treated group was determined based on the presence of symptoms, instead of by random assignment.
In all of those cases, if a randomized experiment cannot be carried out, the alternative line of investigation suffers from the problem that the decision which subjects receive the treatment and which subjects do not is not entirely random and thus is a potential source of bias. A major challenge in conducting observational studies is to draw inferences that are acceptably free from influences by overt biases, as well as to assess the influence of potential hidden biases.

In observational studies, investigators may use propensity score matching (PSM) in order to reduce overt biases.

In 2007, several prominent medical researchers issued the Strengthening the Reporting of Observational Studies in Epidemiology (STROBE) statement, in which they called for observational studies to conform to 22 criteria that would make their conclusions easier to understand and generalize.

Levels of measurement
There are four types of measurements or measurement scales used in statistics. The four types or levels of measurement (nominal, ordinal, interval, and ratio) have different degrees of usefulness in statistical research. Ratio measurements, where both a zero value and distances between different measurements are defined, provide the greatest flexibility in statistical methods that can be used for analyzing the data. Interval measurements have meaningful distances between measurements but no meaningful zero value (such as IQ measurements or temperature measurements in Fahrenheit). Ordinal measurements have imprecise differences between consecutive values but a meaningful order to those values. Nominal measurements have no meaningful rank order among values.

Variables conforming only to nominal or ordinal measurements are together sometimes called categorical variables, since they cannot reasonably be numerically measured, whereas ratio and interval measurements are grouped together as quantitative or continuous variables due to their numerical nature.

The level of measurement of a variable in mathematics and statistics is a classification that was proposed in order to describe the nature of information contained within numbers assigned to objects and, therefore, within the variable. The levels were proposed by Stanley Smith Stevens in his 1946 article On the theory of scales of measurement. According to Stevens’ theory of scales, different mathematical operations on variables are possible, depending on the level at which a variable is measured.

1 Classification levels
According to the classification scheme, in statistics the kinds of descriptive statistics and significance tests that are appropriate depend on the level of measurement of the variables concerned

Stevens proposed four levels of measurement, described below:

nominal (also categorical or discrete)
ordinal
interval
ratio
Interval and ratio variables are also grouped together as continuous variables.

In the paper in which Stevens introduced the classification Scheme, he also proposed the definition that is widely cited in texts in some version: “Measurement is the assignment of numbers to objects or events according to a rule”. This definition has received criticism on a number of grounds (e.g. Duncan, 1984; Michell, 1986, 1999). However, the scheme is widely used.

1.1 Nominal measurement
In this type of measurement, names are assigned to objects as labels. This assignment is performed by evaluating, by some procedure, the similarity of the to-be-measured instance to each of a set of named exemplars or category definitions. The name of the most similar named exemplar or definition in the set is the “value” assigned by nominal measurement to the given instance. If two instances have the same name associated with them, they belong to the same category, and that is the only significance that nominal measurements have. For practical data processing the names may be numerals, but in that case the numerical value of these numerals is irrelevant. The only comparisons that can be made between variable values are equality and inequality. There are no “less than” or “greater than” relations among the classifying names, nor operations such as addition or subtraction. “Nominal measurement” was first identified by psychologist Stanley Smith Stevens in the context of a child learning to categorize colors (red, blue and so on) by comparing the similarity of a perceived color to each of a set of named colors previously learned by intensives definition. Other examples include: geographical location in a country represented by that country’s international telephone access code, the marital status of a person, or the make or model of a car. The only kind of measure of central tendency is the mode. Statistical dispersion may be measured with a variation ratio, index of qualitative variation, or via information entropy, but no notion of standard deviation exists. Variables that are measured only nominally are also called categorical variables. In social research, variables measured at a nominal level include gender, race, religious affiliation, political party affiliation, college major, and birthplace.

1.2 Ordinal measurement
In this classification, the numbers assigned to objects represent the rank order (1st, 2nd, 3rd etc.) of the entities measured. The numbers are called ordinals. The variables are called ordinal variables or rank variables. Comparisons of greater and less can be made, in addition to equality and inequality. However, operations such as conventional addition and subtraction are still meaningless. Examples include the Mohs scale of mineral hardness; the results of a horse race, which say only which horses arrived first, second, third, etc. but no time intervals; and many measurements in psychology and other social sciences, for example attitudes like preference, conservatism or prejudice and social class. The central tendency of an originally measured variable can be represented by its mode or its median; the latter gives more information.

1.3 Interval measurement
The numbers assigned to objects have all the features of ordinal measurements, and in addition equal differences between measurements represent equivalent intervals. That is, differences between arbitrary pairs of measurements can be meaningfully compared. Operations such as addition and subtraction are therefore meaningful. The zero point on the scale is arbitrary; negative values can be used. Ratios between numbers on the scale are not meaningful, so operations such as multiplication and division cannot be carried out directly. But ratios of differences can be expressed; for example, one difference can be twice another. The central tendency of a variable measured at the interval level can be represented by its mode, its median, or its arithmetic mean; the mean gives the most information. Variables measured at the interval level are called interval variables, or sometimes scaled variables, though the latter usage is not obvious and is not recommended. Examples of interval measures are the year date in many calendars, and temperature in Celsius scale or Fahrenheit scale.

1.4 Ratio measurement
The numbers assigned to objects have all the features of interval measurement and also have meaningful ratios between arbitrary pairs of numbers. Operations such as multiplication and division are therefore meaningful. The zero value on a ratio scale is non-arbitrary. Variables measured at the ratio level are called ratio variables. Most physical quantities, such as mass, length or energy are measured on ratio scales; so is temperature measured in kelvins, that is, relative to absolute zero. The central tendency of a variable measured at the ratio level can be represented by its mode, its median, its arithmetic mean, or its geometric mean; as with an interval scale, however, the arithmetic mean gives the most useful information. Social variables of ratio measure include age, length of residence in a given place, number of organizations belonged to or number of church attendances in a particular time.

The interval and ratio measurement levels are sometimes collectively called “true measurement”, although it has been argued that this usage reflects a lack of understanding of the uses of ordinal measurement. Only ratio or interval scales can correctly be said to have units of measurement.

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Reference

http://en.wikipedia.org/wiki/Statistics

http://en.wikipedia.org/wiki/Observational_study

http://en.wikipedia.org/wiki/Levels_of_measurement