based on the sample mean

USAGE SUMMARY

The phrase "based on the sample mean" is correct and usable in written English.
It can be used in statistical contexts when discussing calculations or conclusions derived from the average value of a sample. Example: "The results of the experiment were analyzed based on the sample mean to determine the overall trend."

✓ Grammatically correct

Science

Academia

Human-verified examples from authoritative sources

Exact Expressions

10 human-written examples

The process mean and variance response functions are then fitted based on the sample mean and variance obtained at each design point.

Computers & Industrial Engineering

The magnitude of the point estimate implies an increase in surgical discharges that is small in magnitude – about 40 annually, or about 1.8% (based on the sample mean).

Health Economics Review

That is, the WSE loss function based on the sample mean is more efficient than that using the sample median when no outlier exists.

EURASIP Journal on Advances in Signal Processing

Accordingly, the weighted squared error (WSE) loss function based on the sample mean is utilized in the line-of-sight (LOS) condition, where the sensor state is determined by the classical statistical testing [19, 20].

EURASIP Journal on Advances in Signal Processing

Thus, the proposed adaptive method utilizes the WSE based on the sample mean as the loss function if the testing result that the sensor is in the LOS condition is supported.

EURASIP Journal on Advances in Signal Processing

Then, the source position is determined by minimizing the sum of WSE loss functions based on the sample mean of the sensor expected to be in the LOS condition and sample median of the sensor determined to be in the LOS/NLOS state.

EURASIP Journal on Advances in Signal Processing

Human-verified similar examples from authoritative sources

Similar Expressions

50 human-written examples

This ambiguity issue appears more clearly with the formulation of (hat {sigma }_{p}^{2} tilde {mathbf {h}})) based on the sample means and variances: hat{sigma}_{p}^{2} tilde{mathbf{h}})=s^{2}_{p}+|bar{y}_{p}-mathbf{F}_{p}tilde{mathbf{h}}|^{2}, (11).

EURASIP Journal on Advances in Signal Processing

DLDA is robust against imbalanced class-size because the decision boundary for DLDA is based on the sample means and variances of the two classes which are independent of the ratio of class sizes.

BMC Medical Research Methodology

It is found that the distributions of the test statistics based on the weighted sample means are completely independent of the unknown variances.

Computational Statistics & Data Analysis

The experimenter may set the second stage sample sizes to in the treatment groups and to in the control group with the second-to-first-stage-ratios, based on the interim sample means.

Biometrical Journal

That means, based on the sampling theorem, that as long as the input frequency is below 10 kilohertz we get no aliasing.

Massachusetts Institute of Technology

Expert writing Tips

Best practice

When writing scientific or technical reports, ensure that you clearly define the term "sample mean" if your audience might not be familiar with statistical terminology. This will avoid confusion and enhance clarity.

Common error

Avoid using "based on the sample mean" loosely in non-statistical contexts. This phrase carries a specific statistical meaning, and using it metaphorically can confuse readers. For example, do not write 'The decision was based on the sample mean of opinions' if you haven't actually calculated an average from a defined sample.

Linguistic Context

The phrase "based on the sample mean" functions as a prepositional phrase that modifies a verb or noun. It indicates that an action, calculation, or conclusion is derived from the average value of a sample. According to Ludwig, this phrase is correct and usable in written English, typically appearing in technical or analytical contexts.

Expression frequency: Uncommon

Frequent in

Science

80%

Academia

20%

News & Media

0%

Less common in

Formal & Business

0%

Encyclopedias

0%

Wiki

0%

Ludwig's WRAP-UP

In summary, "based on the sample mean" is a prepositional phrase indicating that an analysis or conclusion relies on the average value of a sample. Ludwig AI confirms that this phrase is grammatically correct and suitable for written English, predominantly in scientific and academic contexts. When using this phrase, ensure clarity by clearly defining "sample mean" and avoid metaphorical usage. Related alternatives include "derived from the sample average" or "calculated using the sample mean", depending on the context. While the sample mean is a valuable statistic, it is important to consider whether it is the most appropriate measure for the data distribution. Ultimately, according to Ludwig, using "based on the sample mean" effectively requires a clear understanding of statistical concepts and their applications.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

derived from the sample average

Replaces "mean" with "average", implying a similar calculation but using a slightly different term.

calculated using the sample mean

Focuses on the calculation aspect, highlighting the use of the sample mean in a computation.

determined by the sample mean

Emphasizes the determination aspect, where the sample mean is a key factor in deciding or concluding something.

informed by the sample mean

Suggests that the sample mean provides insight or guidance, influencing a decision or conclusion.

dependent on the sample mean

Highlights that the result or outcome is reliant on the value of the sample mean.

a function of the sample mean

States that the phrase is mathematically related to the sample mean.

using the sample mean as a basis

Highlights the sample mean being the foundation or starting point.

with the sample mean as a reference

Positions the sample mean as a point of comparison or standard.

premised on the sample mean

Implies that the argument or conclusion starts with the sample mean as a premise.

grounded in the sample mean

Emphasizes that the conclusion or analysis is firmly rooted in the sample mean.

FAQs

How is "based on the sample mean" used in statistical analysis?

In statistical analysis, "based on the sample mean" indicates that a conclusion or calculation is derived from the average value of a subset (sample) of a larger population. For example, a hypothesis test might be "based on the sample mean" to infer properties about the entire population.

What are some alternatives to saying "based on the sample mean"?

You can use alternatives like "derived from the sample average", "calculated using the sample mean", or "determined by the sample mean" depending on the specific context and the nuance you want to convey.

Is it always appropriate to use the sample mean as a basis for analysis?

While the sample mean is a common and useful statistic, it's not always the most appropriate. The suitability depends on the data distribution and the presence of outliers. In some cases, the median or other measures of central tendency might be more robust. For example, you may use the median when your data have outliers.

What is the difference between "based on the sample mean" and "based on the population mean"?

"Based on the sample mean" refers to calculations or inferences drawn from the average of a subset of the population, while "based on the population mean" uses the average of the entire population. The sample mean is often used to estimate the population mean when data for the entire population are not available.