427:, weather datasets are acquired over many years of record and, as part of this, measurements at certain stations may cease occasionally while, at around the same time, measurements may start at nearby locations. There are then questions as to whether, if the records are combined to form a single longer set of records, those records can be considered homogeneous over time. An example of homogeneity testing of wind speed and direction data can be found in Romanić
415:, data-series across a number of sites composed of annual values of the within-year annual maximum river-flow are analysed. A common model is that the distributions of these values are the same for all sites apart from a simple scaling factor, so that the location and scale are linked in a simple way. There can then be questions of examining the homogeneity across sites of the distribution of the scaled values.
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Differences in the typical values across the dataset might initially be dealt with by constructing a regression model using certain explanatory variables to relate variations in the typical value to known quantities. There should then be a later stage of analysis to examine whether the errors in the
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The concept of homogeneity can be applied in many different ways and, for certain types of statistical analysis, it is used to look for further properties that might need to be treated as varying within a dataset once some initial types of non-homogeneity have been dealt with.
439:
Simple populations surveys may start from the idea that responses will be homogeneous across the whole of a population. Assessing the homogeneity of the population would involve looking to see whether the responses of certain identifiable
402:
The initial stages in the analysis of a time series may involve plotting values against time to examine homogeneity of the series in various ways: stability across time as opposed to a trend; stability of local fluctuations over time.
390:
predictions from the regression behave in the same way across the dataset. Thus the question becomes one of the homogeneity of the distribution of the residuals, as the explanatory variables change. See
42:, or several datasets. They relate to the validity of the often convenient assumption that the statistical properties of any one part of an overall dataset are the same as any other part. In
761:
Romanić D. Ćurić M- Jovičić I. Lompar M. 2015. Long-term trends of the ‘Koshava’ wind during the period 1949–2010. International
Journal of Climatology 35(2):288-302. DOI:10.1002/joc.3981.
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are also frequently used. “Skedasticity” comes from the
Ancient Greek word “skedánnymi”, meaning “to scatter”. Assuming a variable is homoscedastic when in reality it is heteroscedastic (
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estimator is still unbiased in the presence of heteroscedasticity, it is inefficient and inference based on the assumption of homoskedasticity is misleading. In that case,
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214:; this is also known as homogeneity of variance. The complementary notion is called heteroscedasticity, also known as heterogeneity of variance. The spellings
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differ from those of others. For example, car-owners may differ from non-car-owners, or there may be differences between different age-groups.
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675:
46:, which combines the data from several studies, homogeneity measures the differences or similarities between the several studies (see also
719:
Engle, Robert F. (July 1982). "Autoregressive
Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation".
694:; Trivedi, Pravin K. (1993). "Some Specification Tests for the Linear Regression Model". In Bollen, Kenneth A.; Long, J. Scott (eds.).
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White, Halbert (1980). "A heteroskedasticity-consistent covariance matrix estimator and a direct test for heteroskedasticity".
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Loevinger, J. (1948). The technic of homogeneous tests compared with some aspects of scale analysis and factor analysis.
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Krus, D.J., & Blackman, H.S. (1988).Test reliability and homogeneity from perspective of the ordinal test theory.
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A test for homogeneity, in the sense of exact equivalence of statistical distributions, can be based on an
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of data-values changes throughout a dataset. However, questions of homogeneity apply to all aspects of the
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Hall, M.J. (2003) The interpretation of non-homogeneous hydrometeorological time series a case study.
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331:(GLS) was frequently used in the past. Nowadays, standard practice in econometrics is to include
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Homogeneity can be studied to several degrees of complexity. For example, considerations of
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instead of using GLS, as GLS can exhibit strong bias in small samples if the actual
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in the presence of heteroscedasticity, which led to his formulation of the
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69:. Thus, a more detailed study would examine changes to the whole of the
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Plot with random data showing heteroscedasticity: The variance of the
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77:. In addition to these, questions of homogeneity apply also to the
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Plot with random data showing homoscedasticity: at each value of
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tests the simpler hypothesis that distributions have the same
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The existence of heteroscedasticity is a major concern in
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581:(Fifth ed.). Boston: McGraw-Hill Irwin. p. 400.
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Angrist, Joshua D.; Pischke, Jörn-Steffen (2009-12-31).
130:-values of the dots increases with increasing values of
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Mostly
Harmless Econometrics: An Empiricist's Companion
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McCulloch, J. Huston (1985). "On
Heteros*edasticity".
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350:of the errors, its presence is referred to as
373:autoregressive conditional heteroscedasticity
333:Heteroskedasticity-consistent standard errors
8:
613:. New York: John Wiley & Sons. pp.
645:. New York: McGraw-Hill. pp. 214–221.
38:, arise in describing the properties of a
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497:For the Greek etymology of the term, see
19:For broader coverage of this topic, see
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296:, and may result in overestimating the
96:Homoscedasticity and heteroscedasticity
323:all have the same variance. While the
114:-value of the dots has about the same
16:Descriptions of properties of datasets
7:
342:Because heteroscedasticity concerns
696:Testing Structural Equation Models
407:Combining information across sites
365:Nobel Memorial Prize for Economics
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792:Applied Measurement in Education,
698:. London: Sage. pp. 66–110.
317:statistical tests of significance
224:
156:
94:This section is an excerpt from
662:. Princeton University Press.
435:Homogeneity within populations
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419:Combining information sources
21:Homogeneity and heterogeneity
777:Meteorological Applications
292:and in biased estimates of
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375:(ARCH) modeling technique.
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786:10.1017/S1350482703005061
329:generalized least squares
63:statistical distributions
479:Reliability (statistics)
474:Consistency (statistics)
802:Psychological Bulletin,
325:ordinary least squares
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119:
668:10.1515/9781400829828
603:Goldberger, Arthur S.
363:was awarded the 2003
354:of the second order.
319:that assume that the
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71:marginal distribution
57:examine how much the
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315:, as it invalidates
313:analysis of variance
780:, 10, 61–67.
643:Econometric Methods
392:regression analysis
369:regression analysis
367:for his studies on
309:regression analysis
302:Pearson coefficient
300:as measured by the
79:joint distributions
48:Study heterogeneity
804:45, 507–529.
796:(Request reprint).
609:Econometric Theory
579:Basic Econometrics
462:location parameter
337:skedastic function
220:heteroskedasticity
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67:location parameter
34:and its opposite,
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454:E-statistic
425:meteorology
398:Time series
287:inefficient
89:Of variance
59:variability
32:homogeneity
812:Categories
509:(2): 483.
485:References
385:Regression
140:statistics
28:statistics
741:0012-9682
538:CiteSeerX
431:., 2015.
413:hydrology
641:(1972).
605:(1964).
577:(2009).
468:See also
380:Examples
311:and the
283:unbiased
212:variance
144:sequence
116:variance
75:skewness
749:1912773
615:238–243
560:1912934
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556:JSTOR
511:JSTOR
448:Tests
429:et al
737:ISSN
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672:ISBN
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356:The
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