the proportion by which

USAGE SUMMARY

The phrase "the proportion by which" is correct and usable in written English.
It can be used when discussing a specific ratio or fraction in relation to a particular quantity or context. Example: "The proportion by which the population has increased over the last decade is significant."

✓ Grammatically correct

Science

News & Media

Formal & Business

Human-verified examples from authoritative sources

Exact Expressions

13 human-written examples

This method also depends on the proportion by which a pixel is going to be observed as background.

EURASIP Journal on Advances in Signal Processing

Here the telling figure is "35%." That's the proportion by which the state budget has expanded since Gov. Arnold Schwarzenegger took office in 2003.

Forbes

In model (2.1) (0leqtheta<1) is the proportion by which the pest density is reduced by killing or trapping once the number of pests reaches (V_{L}), while τ is the constant number of natural enemies released at this time t.

Advances in Difference Equations

We model mosquito-stage transmission blocking vaccines by defining the efficacy to be the proportion by which the probability that a mosquito becomes infected from any one feed is reduced.

Plosone

The nearly constant drop in current amplitude observed at positive voltages for the protamine-induced transition from full opening to substate is unusual and it implies that the proportion by which the conductance is reduced (relative to the size of the full open channel) is less as the holding voltage increases.

Plosone

The correlation between input and output can be characterized by two parameters, namely the Magnitude (the proportion by which the system amplifies the input sine wave) and the phase shift (the degree by which the output sine wave is delayed comparing to the input).

Plosone

Human-verified similar examples from authoritative sources

Similar Expressions

46 human-written examples

By undertaking a detailed phylogenetic analysis, we were able to further separate the contribution by various African regions into 7-10 genetically diverse groups/regions and estimate the proportions by which these regions contributed to the admixed African and American populations.

Plosone

The results relating to possible shifts in the proportions by which single domains impact on the intention remain ambiguous in the present study.

BMC Medical Informatics and Decision Making

In the present study, we use the estimated abundances in order to estimate the proportions by which different protein classes contribute to mitotic chromosomes and to construct classifier I.

Cell

The proportions by which PCSs overlap with coding exons are even higher for imprinted genes compared to the rate for all protein-coding human genes (Wilcoxon test, p < 0.0001).

BMC Genomics

The mean proportion by which the mortality rate would have been reduced had all patients gained timely access to HIV care between 2003 and 2006 was found to be similar to the 43.0% observed between 1995, the year that preceded the introduction of antiretroviral therapy in Brazil, and 2006 (Figure 5).

Plosone

Expert writing Tips

Best practice

When using "the proportion by which", ensure that the context clearly indicates what is being measured and what it is being compared to. This helps to avoid ambiguity and ensures that the meaning is clear to the reader.

Common error

A common mistake is failing to clearly define the original value from which the proportion is calculated. Always specify what the change is relative to; otherwise, the statement can be misleading.

Linguistic Context

The phrase "the proportion by which" functions as a prepositional phrase introducing a relative clause. It quantifies the extent of change or difference. Ludwig examples illustrate its usage across scientific, news, and formal business contexts, supporting this analytical quantification.

Expression frequency: Common

Frequent in

Science

77%

News & Media

15%

Formal & Business

8%

Less common in

Encyclopedias

0%

Wiki

0%

Reference

0%

Ludwig's WRAP-UP

In summary, "the proportion by which" is a grammatically correct and commonly used phrase, as confirmed by Ludwig. It serves to quantify the degree of change between two quantities, finding frequent use in scientific, news, and formal business contexts. While semantically similar alternatives exist, such as "the rate at which" or "the extent to which", the phrase maintains its unique emphasis on proportional change. When using this phrase, clarity in defining the base value is crucial to avoid ambiguity. Ludwig examples reflect its versatility and precision in various domains.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

the rate at which

Changes the focus from a static proportion to a dynamic rate of change.

the degree to which

Emphasizes the extent or intensity of a change or effect, rather than a specific numerical ratio.

the extent to which

Highlights the range or scope of a change or influence.

the amount by which

Focuses on the absolute quantity of change, rather than the relative proportion.

the percentage increase of

Specifies an increase expressed as a percentage.

the fractional increase of

Specifies an increase expressed as a fraction.

the ratio in which

Focuses on the relationship between two quantities.

the fraction by which

Similar to proportion but emphasizes the part out of a whole.

the scaling factor of

Highlights the multiplicative factor that determines the change in size or magnitude.

the multiplier effect on

Describes how an initial change is amplified or magnified.

FAQs

How can I use "the proportion by which" in a sentence?

Use "the proportion by which" to describe the extent to which a quantity has changed relative to its original value. For example, "The proportion by which the budget increased was 20%."

What are some alternatives to "the proportion by which"?

You can use alternatives like "the rate at which", "the degree to which", or "the extent to which" depending on the specific context.

Is it better to use "the proportion by which" or "the percentage by which"?

Both phrases are grammatically correct, but "the percentage by which" is generally used when referring specifically to changes expressed as a percentage. "The proportion by which" is more general and can refer to any ratio or fraction.

What is the difference between "the proportion by which" and "the amount by which"?

"The amount by which" refers to the absolute difference between two quantities, while "the proportion by which" refers to the relative difference or the ratio of change. For example, if a price increased by $10, that's the amount; if it increased by 10%, that's the proportion.