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Fig. 4 International comparison of the distribution of proficiency levels on the PISA 2009 scale.
Figure 4 shows a comparison of our sample with students from two exemplary Anglophone countries, the UK and the US, in terms of the distribution of proficiency levels.
Our mismatch indicator is based on the minimum and maximum skill requirements by occupations, which are estimated as the minimum ((widehat {min}_{j})) and maximum ((widehat {max}_{j})) of the country-occupation distribution of proficiency for those workers who report neither feeling the need of training nor feeling to be able to do more demanding jobs.
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These priors on θ i allow for the possibility that blacks and whites, and people of different experience levels, census regions, and urban/rural status, have different distributions of proficiency.
In line with our discussion above, the prior on θ i is conditioned on race, age, census region, and urban/rural status, thereby allowing for the possibility that there are differences in distributions of proficiency for blacks and whites of different age groups, census regions, and urban/rural status.
Conditional distributions of proficiency are utilized to generate plausible values (multiple imputations) that are a representation of our finite knowledge concerning an individual's value on the latent trait scale, given the individual's pattern of correct and incorrect responses, as well as information on her background characteristics.
In a similar application [ 29] posterior distributions of proficiency measures were used in two nonparametric regression models (one with and one without group membership as a covariate) to compute posterior mean p values for the likelihood ratio based on the two models.
Table 6 Distribution of speakers' proficiency levels with regard to dialect and gender.
Additionally, the distribution of numeracy proficiency appears to be slightly more dispersed than that of literacy.
The adaptation involves mainly two things: adjusting the difficulty level of SASs (self-assessment statements) and investigating the distribution of learners' proficiency across the CEFR levels.
Table 4 Distribution of respondents based on proficiency in computer applications Proficiency No experience Limited Average Good Very good Use of computer 0 3 3 3 2 MS Excel 0 5 0 5 1 Eviews 7 2 0 2 0 SPSS 5 5 0 1 0 Stata 9 2 0 0 0 Source: Author's compilation based on diagnostic evaluation of potential trainees on policy analysis.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com