assumption of independence

USAGE SUMMARY

"assumption of independence" is a correct and usable phrase in written English.
It is usually used to refer to a nation's declaration that it is a separate, independent country. For example, "The assumption of independence by the United States of America in 1776 marked the beginning of a new era in world history."

✓ Grammatically correct

Science

Academia

Human-verified examples from authoritative sources

Exact Expressions

60 human-written examples

The assumption of independence made here is that each test is independent of one another.

Genome Medicine

So for the assumption of independence can be rejected with 99% confidence.

Stanford University

Classical tolerance design procedures are based on the assumption of independence of variables.

Mechanism and Machine Theory

This is a more realistic assumption than the assumption of independence exploited in the previous papers.

Statistics & Probability Letters

The two methods differ with regard to the definition of the risks and the assumption of independence.

Contemporary Clinical Trials

This can arise when the data come from different subpopulations or when the assumption of independence is violated.

Computational Statistics & Data Analysis

These results suggest that the current Executive-in-Chief exercises a profound influence over removal decisions, undermining the assumption of independence among administrative adjudicators.

Princeton University

MNL relies on the assumption of independence of irrelevant alternatives (IIA).

Urban Rail Transit

In many stochastic models, the assumption of independence among random variables is not plausible.

Journal of Inequalities and Applications

However, statistical tests are normally premised on the assumption of independence.

Large-scale Assessments in Education

However, conditional logit estimation relies on the assumption of independence from irrelevant alternatives (IIA).

Journal of Economic Structures

Expert writing Tips

Best practice

When using the "assumption of independence", clearly state which elements or variables are being treated as independent and why this assumption is reasonable within your specific context. Justify your decision, acknowledging potential limitations.

Common error

A common mistake is to apply the "assumption of independence" without adequately considering whether the variables might be related in some way. Always evaluate possible correlations before making this assumption to avoid skewed or inaccurate results.

Linguistic Context

The phrase "assumption of independence" functions as a noun phrase that introduces a foundational supposition for reasoning or calculation. As Ludwig states, this assumption is frequently encountered and can be crucial for model validity. Examples show it's use in stating a baseline condition that might later be challenged or relaxed.

Expression frequency: Very common

Frequent in

Science

75%

Academia

15%

Formal & Business

5%

Less common in

News & Media

1%

Encyclopedias

1%

Wiki

1%

Ludwig's WRAP-UP

The phrase "assumption of independence" is a cornerstone concept across diverse fields, particularly in statistics, science, and academia. Ludwig AI confirms it's a correct and commonly used phrase. It signifies a presupposition that elements or variables are unrelated, which simplifies analyses but demands careful validation. As demonstrated by the examples, the "assumption of independence" is frequently employed when constructing models or interpreting data. Violating this assumption can lead to inaccurate conclusions. Therefore, as discussed in the writing guidance, awareness of potential dependencies is crucial. When the "assumption of independence" is not valid, alternative methods that account for dependence, like "statistical independence", should be considered.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

Statistical independence

Emphasizes the statistical nature of the independence being assumed.

Independence hypothesis

Replaces "assumption" with "hypothesis", framing it as a testable proposition rather than a given condition.

Presumption of independence

Substitutes "assumption" with "presumption", suggesting a belief held before evidence is available.

Treating variables as independent

Focuses on the action of considering variables separate from one another in a model or analysis.

Condition of independence

Replaces "assumption" with "condition", focusing on the requirement that elements be independent.

Principle of independence

Elevates the "assumption" to a "principle", implying a fundamental rule or guideline.

Independent events

This is a shorter way to say that events are not related or do not influence each other.

Mutual exclusivity

Highlights that events cannot occur simultaneously, implying a form of independence.

Absence of correlation

Directly states that there is no statistical relationship between variables.

Lack of interdependence

Emphasizes the absence of a relationship where one element relies on another.

FAQs

What does the phrase "assumption of independence" mean in statistics?

In statistics, the "assumption of independence" means that the data points or variables being analyzed are not influenced by each other. Each data point is a separate, random occurrence.

Why is the "assumption of independence" important in statistical tests?

Many statistical tests, such as t-tests and chi-square tests, rely on the "assumption of independence". If this assumption is violated, the results of these tests may be invalid, leading to incorrect conclusions.

How can I test if the "assumption of independence" is valid?

There are various methods to test for independence, such as the Durbin-Watson test for autocorrelation in regression models or examining scatter plots for patterns indicating dependence. Domain knowledge and understanding of the data generation process are also crucial.

What are some alternatives to using tests that rely on the "assumption of independence"?

If the "assumption of independence" cannot be met, consider using non-parametric tests or methods that account for dependence, such as mixed-effects models or time series analysis. Another approach is to use "statistical independence".