correlation and its types

Definition

Degree and type of relationship between any two or more quantities (variables) in which they vary together over a period; for example, variation in the level of expenditure or savings with variation in the level of income. A positive correlation exists where the high values of one variable are associated with the high values of the other variable(s). A 'negative correlation' means association of high values of one with the low values of the other(s). Correlation can vary from +1 to -1. Values close to +1 indicate a high-degree of positive correlation, and values close to -1 indicate a high degree of negative correlation. Values close to zero indicate poor correlation of either kind, and 0 indicates no correlation at all. While correlation is useful in discovering possible connections between variables, it does not prove or disprove any cause-and-effect (causal) relationships between them. See also regression

Positive Correlation

Positive correlation occurs when an increase in one variable increases the value in another.

The line corresponding to the scatter plot is an increasing line.

Negative Correlation

Negative correlation occurs when an increase in one variable decreases the value of another.

The line corresponding to the scatter plot is a decreasing line.

No Correlation

No correlation occurs when there is no linear dependency between the variables.

Perfect Correlation

Perfect correlation occurs when there is a funcional dependency between the variables.

In this case all the points are in a straight line.

Strong Correlation

A correlation is stronger the closer the points are located to one another on the line.

Weak Correlation

A correlation is weaker the farther apart the points are located to one another on the line.

Comments

Runs Test for Detecting Non-randomness

Runs Test for Detecting Non-randomness Purpose: Detect Non-Randomness The runs test ( Bradley, 1968 ) can be used to decide if a data set is from a random process. A run is defined as a series of increasing values or a series of decreasing values. The number of increasing, or decreasing, values is the length of the run. In a random data set, the probability that the ( I +1)th value is larger or smaller than the I th value follows a binomial distribution , which forms the basis of the runs test. Typical Analysis and Test Statistics The first step in the runs test is to count the number of runs in the data sequence. There are several ways to define runs in the literature, however, in all cases the formulation must produce a dichotomous sequence of values. For example, a series of 20 coin tosses might produce the f...

The most femiliar statisticians

Gertrude Cox : Gertrude Mary Cox (of Experimental Statistics at North Carolina State University. She was later appointed director of both the Institute of Statistics of 1900 - 1978) was an influential American statistician and founder of the department the Consolidated University of North Carolina and the Statistics Research Division of North Carolina State University. Her most important and influential research dealt with experimental design; she wrote an important book on the subject with W. G. Cochran. In 1949 Cox became the first female elected into the International Statistical Institute and in 1956 she was president of the American Statistical Association. From 1931 to 1933 Cox undertook graduate studies in statistics at the University of California at Berkeley , then returned to Iowa State College as assistant in the Statistical Laboratory. Here she worked on the design of experiments . In 1939 she was appointed assistant professor of statisti...

Lognormal distribution

Lognormal Distribution Probability Density Function A variable X is lognormally distributed if Y = LN(X) is normally distributed with "LN" denoting the natural logarithm. The general formula for the probability density function of the lognormal distribution is where is the shape parameter , is the location parameter and m is the scale parameter . The case where = 0 and m = 1 is called the standard lognormal distribution . The case where equals zero is called the 2-parameter lognormal distribution. The equation for the standard lognormal distribution is Since the general form of probability functions can be expressed in terms of the standard distribution , all subsequent formulas in this section are given for the standard form of the function. The following is the plot of the lognormal probability density function for four values of . There are several commo...

Statistical Gallery

Search This Blog