a critical value of

USAGE SUMMARY

The phrase "a critical value of" is correct and usable in written English.
It is typically used in mathematical, statistical, or scientific contexts to refer to a specific value that is significant for analysis or decision-making. Example: "In hypothesis testing, the critical value of the test statistic determines whether to reject the null hypothesis."

✓ Grammatically correct

Science

Human-verified examples from authoritative sources

Exact Expressions

60 human-written examples

Then (3.2). is a critical value of.

Boundary Value Problems

A critical value of permeability was identified.

Energy

Thus, we can state a critical value of temperature Tc.

Journal of Theoretical and Applied Physics

Thus, c is a critical value of (J ucirc x)).

Boundary Value Problems

then c is a critical value of φ.

Journal of Inequalities and Applications

In particular, a critical value of the frequency is found.

Combustion and Flame

If is bounded from below, then is a critical value of.

Advances in Difference Equations

Then if ϕ satisfies the ( P S ) c -condition, c is a critical value of ϕ.

Boundary Value Problems

If Σ n ≠ ∅ and c n ∈ R, then c n is a critical value of I.

Boundary Value Problems

Then, if Φ satisfies the ( PS ) c -condition, c is a critical value of Φ.

Advances in Difference Equations

Then (c= inf_{X} f(x)) is a critical value of f.

Boundary Value Problems

Expert writing Tips

Best practice

When using "a critical value of", ensure the context clearly defines what makes the value critical. Explain the consequences of exceeding or falling below this value.

Common error

Avoid using "a critical value of" without specifying the units of measurement or the context in which it's considered critical. Ambiguity can lead to misinterpretation and incorrect application.

Linguistic Context

The phrase "a critical value of" functions as a noun phrase that modifies another noun, often a parameter or variable. It indicates a specific value that is significant for analysis, decision-making, or understanding a phenomenon. Ludwig provides numerous examples across various scientific domains.

Expression frequency: Very common

Frequent in

Science

95%

Formal & Business

3%

News & Media

2%

Less common in

Academia

0%

Encyclopedias

0%

Wiki

0%

Ludwig's WRAP-UP

In summary, the phrase "a critical value of" is a grammatically correct and very common phrase primarily used in scientific and technical contexts. It denotes a significant threshold or boundary, as confirmed by the examples provided by Ludwig. While it's essential to define the context and units of measurement for clarity, this phrase is invaluable for identifying pivotal points in various systems. Ludwig AI confirms that its usage is appropriate and widespread in scholarly and technical literature. Alternative phrasing includes "a threshold value for", "a crucial parameter of", or "a decisive level of" depending on the precise nuance desired.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

a threshold value for

Replaces "critical" with "threshold", emphasizing a boundary that must be crossed.

a crucial parameter of

Substitutes "value" with "parameter", highlighting a key factor or variable.

a decisive level of

Uses "decisive" instead of "critical", focusing on the importance in making a decision.

a significant point in

Emphasizes the "point" aspect, implying a specific location or instance of importance.

an essential measurement for

Changes "value" to "measurement", suggesting a quantifiable metric of significance.

a turning point regarding

Emphasizes change, like a moment after which the trend changes

a breaking point for

Implies a limit of stress or pressure where failure occurs

a pivotal quantity in

Highlights that the value is a magnitude or amount

a determinant number of

Shows that the number fixes or condition something

a key benchmark of

Implies a parameter by which others can be measured.

FAQs

How is "a critical value of" used in statistical analysis?

In statistics, "a critical value of" a test statistic is a threshold used to determine whether the results of a test are statistically significant. If the test statistic exceeds this value, the null hypothesis is rejected.

What's the difference between "a critical value of" and a threshold?

While both terms indicate a boundary, "a critical value of" often implies a statistical or mathematical significance, while a threshold is a more general term for a level or point at which something changes. You could also use "a threshold value for" in some contexts.

Can "a critical value of" be subjective?

Yes, the determination of what constitutes "a critical value of" can be subjective and depends on the specific context, goals, and priorities. However, the interpretation of that value should be as objective as possible.

What are some alternatives to saying "a critical value of"?

Depending on the context, you can use phrases such as "a threshold value for", "a crucial parameter of", or "a decisive level of".