Standardized coefficient
Encyclopedia
In statistics
, standardized coefficients or beta coefficients are the estimates resulting from an analysis carried out on variables
that have been standardized so that their variance
s are 1. Therefore, standardized coefficients refer to how many standard deviations a dependent variable will change, per standard deviation increase in the predictor variable. Standardization of the coefficient is usually done to answer the question of which of the independent variable
s have a greater effect on the dependent variable in a multiple regression analysis, when the variables are measured in different units of measurement
(for example, income
measured in dollar
s and family size measured in number
of individual
s).
Some statistical software packages like PSPP
, SPSS
and SYSTAT
label the standardized regression coefficients as "Beta
" while the unstandarized coefficients are labeled "B". Others, like DAP
/SAS
label them "Standardized Coefficient". Sometimes the unstandardized variables are also labeled as "B" or "b".
A regression
carried out on original (unstandardized) variables produces unstandardized coefficients. A regression carried out on standardized variables produces standardized coefficients. Both standardized and unstandardized coefficients are also possible to estimate from the original variables.
Before solving a multiple regression equation, all variables (independent and dependent) can be standardized. Each variable can be standardized by subtracting its mean
from each of its values and then dividing these new values by the standard deviation
of the variable. Standardizing all variables in a multiple regression yields standardized regression coefficients that show the change in the dependent variable measured in standard deviation
s.
Advantages: Standard coefficients' advocates note that the coefficients ignore the independent variable's scale of units, which makes comparisons easy.
Disadvantages: Critics voice concerns that such a standardization can be misleading; a change of one standard deviation in one variable has no reason to be equivalent to a similar change in another predictor.
Some variables are easy to affect externally, e.g., the amount of time spent on an action. Weight or cholesterol level are more difficult, and some, like height or age, are impossible to affect externally.
Statistics
Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....
, standardized coefficients or beta coefficients are the estimates resulting from an analysis carried out on variables
Variable (mathematics)
In mathematics, a variable is a value that may change within the scope of a given problem or set of operations. In contrast, a constant is a value that remains unchanged, though often unknown or undetermined. The concepts of constants and variables are fundamental to many areas of mathematics and...
that have been standardized so that their variance
Variance
In probability theory and statistics, the variance is a measure of how far a set of numbers is spread out. It is one of several descriptors of a probability distribution, describing how far the numbers lie from the mean . In particular, the variance is one of the moments of a distribution...
s are 1. Therefore, standardized coefficients refer to how many standard deviations a dependent variable will change, per standard deviation increase in the predictor variable. Standardization of the coefficient is usually done to answer the question of which of the independent variable
Independent variable
The terms "dependent variable" and "independent variable" are used in similar but subtly different ways in mathematics and statistics as part of the standard terminology in those subjects...
s have a greater effect on the dependent variable in a multiple regression analysis, when the variables are measured in different units of measurement
Units of measurement
A unit of measurement is a definite magnitude of a physical quantity, defined and adopted by convention and/or by law, that is used as a standard for measurement of the same physical quantity. Any other value of the physical quantity can be expressed as a simple multiple of the unit of...
(for example, income
Income
Income is the consumption and savings opportunity gained by an entity within a specified time frame, which is generally expressed in monetary terms. However, for households and individuals, "income is the sum of all the wages, salaries, profits, interests payments, rents and other forms of earnings...
measured in dollar
Dollar
The dollar is the name of the official currency of many countries, including Australia, Belize, Canada, Ecuador, El Salvador, Hong Kong, New Zealand, Singapore, Taiwan, and the United States.-Etymology:...
s and family size measured in number
Number
A number is a mathematical object used to count and measure. In mathematics, the definition of number has been extended over the years to include such numbers as zero, negative numbers, rational numbers, irrational numbers, and complex numbers....
of individual
Individual
An individual is a person or any specific object or thing in a collection. Individuality is the state or quality of being an individual; a person separate from other persons and possessing his or her own needs, goals, and desires. Being self expressive...
s).
Some statistical software packages like PSPP
PSPP
PSPP is a free software application for analysis of sampled data. It has a graphical user interface and conventional command line interface. It is written in C, uses GNU Scientific Library for its mathematical routines, and plotutils for generating graphs....
, SPSS
SPSS
SPSS is a computer program used for survey authoring and deployment , data mining , text analytics, statistical analysis, and collaboration and deployment ....
and SYSTAT
SYSTAT
SYSTAT is a statistics and statistical graphics software package, developed by Leland Wilkinson in the late 1970s, who was at the time an assistant professor of psychology at the University of Illinois at Chicago...
label the standardized regression coefficients as "Beta
Beta coefficient
In finance, the Beta of a stock or portfolio is a number describing the relation of its returns with those of the financial market as a whole.An asset has a Beta of zero if its returns change independently of changes in the market's returns...
" while the unstandarized coefficients are labeled "B". Others, like DAP
DAP (software)
Dap is a statistics and graphics program, that performs data management, analysis, and graphical visualization tasks which are commonly required in statistical consulting practice....
/SAS
SAS System
SAS is an integrated system of software products provided by SAS Institute Inc. that enables programmers to perform:* retrieval, management, and mining* report writing and graphics* statistical analysis...
label them "Standardized Coefficient". Sometimes the unstandardized variables are also labeled as "B" or "b".
A regression
Regression analysis
In statistics, regression analysis includes many techniques for modeling and analyzing several variables, when the focus is on the relationship between a dependent variable and one or more independent variables...
carried out on original (unstandardized) variables produces unstandardized coefficients. A regression carried out on standardized variables produces standardized coefficients. Both standardized and unstandardized coefficients are also possible to estimate from the original variables.
Before solving a multiple regression equation, all variables (independent and dependent) can be standardized. Each variable can be standardized by subtracting its mean
Mean
In statistics, mean has two related meanings:* the arithmetic mean .* the expected value of a random variable, which is also called the population mean....
from each of its values and then dividing these new values by the standard deviation
Standard deviation
Standard deviation is a widely used measure of variability or diversity used in statistics and probability theory. It shows how much variation or "dispersion" there is from the average...
of the variable. Standardizing all variables in a multiple regression yields standardized regression coefficients that show the change in the dependent variable measured in standard deviation
Standard deviation
Standard deviation is a widely used measure of variability or diversity used in statistics and probability theory. It shows how much variation or "dispersion" there is from the average...
s.
Advantages: Standard coefficients' advocates note that the coefficients ignore the independent variable's scale of units, which makes comparisons easy.
Disadvantages: Critics voice concerns that such a standardization can be misleading; a change of one standard deviation in one variable has no reason to be equivalent to a similar change in another predictor.
Some variables are easy to affect externally, e.g., the amount of time spent on an action. Weight or cholesterol level are more difficult, and some, like height or age, are impossible to affect externally.
External links
- Glossary of social science terms
- Which Predictors Are More Important? - why standardized coefficients are used