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The phrase "a further test for" is correct and usable in written English.
It can be used when discussing an additional examination or evaluation intended to assess something more deeply or thoroughly.
Example: "The researchers conducted a further test for the effectiveness of the new drug on a larger sample size."
Alternatives: "an additional test for" or "a subsequent test for".
Exact(19)
The election in Belgrade of the apparently reasonable, legally minded Serb, Vojislav Kostunica, has spoiled that dream, and consequently, Kosovo has become a more explosive place, providing a further test for Western troops and diplomacy.
That will inevitably provide a further test for the complex structured products created in recent years, such as collateralised debt obligations (CDOS .Investors will be looking to see whether the subprime effect is repeated in corporate debt; in other words, whether the repackaging of loans and bonds has led to a lowering of credit standards.
As the pre and post scores would be explored separately, Cronbach's α values for single questionnaires were calculated from the complete sample as well as a further test for scale reliability.
As a further test for evidence of a contribution of NMD to the differences in the intron expression, observed between individuals, we identified a set of unprocessed pseudogenes, expressed above background (p<0.05) in at least 10 cell lines.
A Genetic Algorithm for Recombination Detection (GARD) [40] implemented in HyPhy [68] via the DataMonkey web interface [69] was applied to a concatenation of all families (restricted to the 18 common sequences) as a further test for shared phylogenetic signal, estimating substitution frequencies and a proportion of invariable sites from the data with 4 rate categories in a beta-gamma distribution.
We added a further test for the real data sets.
Similar(41)
A further test of partial occlusion for the proposed method was shown in Figure 14.
A further test is for exponential divergence and the calculation of Lyapunov exponents, which if positive indicates chaos.
A further test is scheduled for Jerez in Spain 23-255 Mahead, ahead of the first race of the 2012 season in Qatar on 8 April.
From 25 June, however, the law on protected disclosures is changing and a further test is being introduced for workers under the Enterprise and Regulatory Reform Act 2013.
The Titans said last night that McNair had a bruised sternum but no broken bones, and that he would remain at the hospital for a further test today.
More suggestions(16)
a further proof for
a further analysis for
a further criterion for
a further evaluation for
a new test for
a further trial for
a further requirement for
a supplementary test for
a further try for
a greater test for
a further difficulty for
a critical test for
a litmus test for
a further proposal for
a key test for
a further setback for
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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