at which ratio

USAGE SUMMARY

The phrase "at which ratio" is correct and usable in written English.
It can be used when discussing proportions, comparisons, or relationships between quantities in a mathematical or analytical context. Example: "The study aimed to determine the effectiveness of the treatment at which ratio the patients showed improvement."

✓ Grammatically correct

Science

Human-verified examples from authoritative sources

Exact Expressions

2 human-written examples

This density contrast is assumed to represent the low-density material as a mixture of 50% melt with some gas and 50% solid crystals, at which ratio the rheology shifts from viscous to rigid (Marsh 1996).

Earth, Planets and Space

Titer reported corresponds to last dilution at which ratio of response ≥two should be two words.

Annals of Clinical and Translational Neurology

Human-verified similar examples from authoritative sources

Similar Expressions

58 human-written examples

Figure 1 shows the ratio profiles of all 19 covariates together with their corresponding ratio profile scores; the horizontal line in each profile plot is the critical line at which the ratio is equal to 1.

BMC Medical Informatics and Decision Making

They were then about two weeks old, but still well below the age at which the ratio discrimination system seemed to kick in for untrained guppies.

BBC

This concentration difference that is clearly visible already at 10 years of exposure grows with the radius and the increase of depth at which the ratio is evaluated.

International Journal of Concrete Structures and Materials

There were times at which the ratio of mixed layer to depth of the euphotic zone was generally greater than what has been suggested for phytoplankton to produce net primary production.

International Aquatic Research

The optimal calibration volume (defined as the injected volume at which ΔPaw/ΔPes ratio was closer to 1) was identified for each PEEP group (VCLPEEP for lowPEEP, VCMPEEP for mediumPEEP, VCHPEEP for highPEEP).

Intensive Care Medicine Experimental

Cold threshold temperatures were calculated as the temperature at which fluorescence ratio increased by 0.5% upon cooling.

Plosone

In this way, all alignment methods and similarity measures were assessed on an equal basis, no matter at which alignment ratio cutoff point.

Plosone

Arrival judgment position was manipulated by varying the position of the red mark across the upper half of the stimulus, providing multiple points at which the ratio of CCW and CW arrival could be assessed.

Plosone

Interestingly, the rate at which the ratio of Shank1/synaptophysin apposition shifted after Aβ treatment was slower than that observed for Homer1b/synaptophysin, with the first significant change occurring after 6 h (94.2±4.5% of control, p<0.05) and a further reduction after 24 h (84.9±3.2% of control, p<0.05) of Aβ application (Fig. 3D).

Plosone

Expert writing Tips

Best practice

When using "at which ratio", ensure the context clearly establishes what two quantities are being compared and why their relationship is significant.

Common error

Avoid using "at which ratio" without clearly defining the two quantities being compared. Vague references can confuse the reader and weaken your analysis.

Linguistic Context

The phrase "at which ratio" functions as a relative clause, modifying a noun or noun phrase by specifying a particular proportional relationship. This allows for precise definition of conditions or points where a specific ratio is significant, as evidenced by Ludwig examples.

Expression frequency: Rare

Frequent in

Science

100%

Less common in

News & Media

0%

Formal & Business

0%

Encyclopedias

0%

Ludwig's WRAP-UP

The phrase "at which ratio" serves as a relative clause, primarily functioning to define specific conditions based on proportional relationships, as shown by Ludwig. While grammatically correct, its usage is relatively rare and leans heavily towards formal and scientific contexts. Ludwig AI confirms the phrase is correct and usable. For broader applications, alternatives like "at what proportion" or "at what rate" may be suitable. When employing "at which ratio", clarity in defining the compared quantities is paramount to avoid ambiguity.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

at what proportion

Replaces "ratio" with "proportion", emphasizing the relative size of different parts.

at what rate

Substitutes "ratio" with "rate", focusing on the speed at which something occurs relative to something else.

at what level

Replaces "ratio" with "level", indicating a specific point on a scale or range of values.

under what conditions of proportionality

Expands the phrase to explicitly mention "proportionality", making the relationship more formal and detailed.

given what relative quantities

Rephrases to highlight the "relative quantities" involved, changing the focus to specific measurements.

at what comparative measure

Uses "comparative measure" instead of "ratio", suggesting a broader scope of comparison.

with what relative frequency

Focuses on the "frequency" of occurrence in relation to something else, rather than a direct proportional relationship.

depending on which quotient

Specifies "quotient" as the mathematical result of division, relevant when a numerical relationship is central.

according to which index

Emphasizes the use of an "index" as a reference point for comparison.

based on which relative magnitude

Highlights "relative magnitude", focusing on the size or extent of something in comparison.

FAQs

How can I use "at which ratio" in a sentence?

Use "at which ratio" to specify a particular proportion or relationship between two quantities. For example: "The experiment determined the temperature "at which ratio" the reaction rate was optimal".

What are some alternatives to "at which ratio"?

Alternatives include "at what proportion", "at what rate", or "at what level", depending on the specific meaning you want to convey.

Is it better to use "at which ratio" or "at what ratio"?

Both "at which ratio" and "at what ratio" are grammatically correct, but "at what ratio" is generally more common in contemporary English. The choice often depends on personal preference and the specific context.

When is "at which ratio" most appropriate?

"At which ratio" is particularly useful in technical or scientific contexts where precise quantification and comparison are essential, such as describing experimental results or defining thresholds in a process.