The standard error of moving average smoothed equipercentile equating

A very important aspect of virtually any kind of systematic investigation is to be able to identify whether two entities are different, and, almost equivalently, whether they are the same. We need to be sure that measurements made at different time in different places by different experimenters are equivalent. To do this in the social sciences, the procedure of equating is necessary to be able to compare measurements made using different instruments. Small sample sizes can lead to apparent jaggedness in the formulae for equating two quantities, and some kind of smoothing procedure is frequently necessary when dealing with relatively small samples. A large-sample formula is developed for the standard error of moving average smoothed equipercentile equating on a single sample. An example is given of the application in equating two versions of a reading test, and the results are verified using a bootstrap procedure. The large sample formula gives a result that is close to the bootstrap procedure, except at very sparse frequencies.     

When is a Compositional Effect not a Compositional Effect?

The question of compositional effects (that is, the effect of collective properties of a pupil body on the individual members), or Aggregated Group-Level Effects (AGLEs) as the author prefers to call them, has been the subject of considerable controversy. Some authors, e.g. Rutter et al. [Fifteen thousand hours: Secondary Schools and Their Effects on Children. London: Open Books.], Willms [Oxford Review of Education 11(1): 33–41; (1986). American Sociological Review, 51, 224–241.], Bondi [British Educational Research Journal, 17(3), 203-218.], have claimed to find such effects, while on the other hand Mortimore et al. [School Matters: the Junior Years. Wells: Open Books.] and Thomas and Mortimore [Oxford Review of Education 16(2): 137–158.] did not. Others, for example Hauser [1970], have implied that many apparent AGLEs may be spurious, while Gray et al. [Review of Research in Education, 8, 158–193.] have suggested that at least in certain circumstances such apparent effects may arise as a result of inadequate allowance for pre-existing differences. A possible statistical mechanism for this is outlined in the work of Burstein [In R. Dreeben, & J. A. Thomas (Eds.), The Analysis of Educational Productivity. Volume 1: Issues in Microanalysis, Cambridge, MASS: Ballinger, pp. 119–190] on the effect of aggregating the data when a variable is omitted from the model used. This paper suggests another way in which spurious AGLEs can arise. It shows mathematically that even if there are no omitted variables, measurement error in an explanatory variable could give rise to apparent, but spurious, AGLEs, when analysed using a multilevel modelling procedure. Using simulation methods, it investigates what the practical effects of this are likely to be, and shows that statistically significant spurious effects occur systematically under fairly standard conditions.     

Augmenting the use of the Rasch model under time constraints

This paper proposes a method for estimating national standardizations of partially speeded tests composed of items from a previously standardized item bank. The model combines two submodels, one for whether the examinee reaches the item, and the second for whether she is successful if she does reach it. The former model is comparable to that for survival analysis using item position in test as a quasi-time parameter (Hutchison 1988). The latter is a straightforward Rasch Model. Combining the two submodels allows for the possibility that ability and drop-out were correlated. The model proposed here is superior that of Bolt et al. (2002), which divides the population into a speeded and a non-speeded group, in that it allows for a range of speededness effects. The model is tested using three UK national standardizations on one outcome and comparing the actual and predicted distributions. It is suggested that the observed discrepancies may be due to differences in the samples drawn, and that in some circumstances the model may actually produce a better estimate than an actual standardization exercise.     

Event history and survival analysis in the social sciences II. Advanced applications and recent developments

A previous paper (Hutchison, 1988) in this journal has provided an introduction to the basic concepts of survival and event history analysis, originally developed in medical research, econometrics and engineering, and argued the case for their wider application in the social sciences. This paper introduces some further complications that the researcher is likely to meet, and offers some guidelines for handling problems that arise in applying such methods to the highly complex social situations involved.     

The Effect of Measurement Errors on Apparent Group Level Effects in Educational Progress

Aggregated group-level effects (AGLEs) are widely considered to be an extremelyimportant aspect of learning. However some authors have implied that many apparentfindings of such effects are spurious and arise because of omission or inadequatemeasurement of pre-existing differences. This study considers a further trap, inwhich the appropriate variables are included, but are measured with error.It shows allowing for measurement error does in fact impact on apparent AGLEs,and that the effects of allowing for measurement error, while apparently inconsistent,can largely be explained as increasing the apparent effect of a variable, and decreasingthe apparent effects of other correlated variables.     

Reliability of Assessment of Reading Ability in Three Countries

Over the last few decades, there have been a number ofnational and international programmes to assessperformance in key subjects. For example theInternational Association for Evaluation ofEducational Attainment (IEA), International Assessmentof Educational Progress (IAEP), and the ThirdInternational Mathematics and Science Survey (TIMSS)programs have aimed to compare performance betweenparticipating countries.Such exercises have different requirements from thosetests, such as public examinations, which aim toassess the attainment of individuals. National andinternational assessments aim to cover a very widerange of materials, and often use the technique ofmultiple matrix sampling to do so.The investigation is based on generalizability-typeanalyses of three national data sets at two ages, andlooks not only at the variance components arising fromsampling of schools, and of pupils within them, butalso at the variation between different assessmentinstruments, and between items within assessmentinstruments. If interpreted with care, such resultscan be of value in the design of future studies. Thispaper concentrates largely on the precision ofestimates of overall means, but analyses of the typedescribed could also be used to compare theperformance of subpopulations.     

Building a 3-D model of a flood basalt: an example from the Etendeka, NW Namibia

Flood basalts represent large outpourings of lavas which often cover, and interact with, sedimentary basins. For this reason areas with significant flood basalt cover are often targets for hydrocarbon exploration. Problems exist, however, when trying to image sediments and structures in offshore regions covered by basalts. Here we present preliminary 3-D models of the Etendeka flood basalt province from NW Namibia, which can act as an aid in understanding the internal and external architecture of the flood basalt cover. Satellite images, digital elevation models, measured geological logs, sections and maps, are used to create the geological model. Models are presented in 2 parts; 1) models created using topography with images such as Land Sat and geological maps draped over them, and 2) a 3-D model of key lava and sediment surfaces in the basin as defined by measured geological sections. Initial results show a palaeo-volcanic feature early in the flood basalt history which is onlapped by later Iavas. The modelling also allows a simple correction for post emplacement subsidence by assuming an original sub horizontal position for the first basin wide silicic flow unit.