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Related Concept Videos

Estimating Population Standard Deviation01:26

Estimating Population Standard Deviation

When the population standard deviation is unknown and the sample size is large, the sample standard deviation s is commonly used as a point estimate of σ. However, it can sometimes under or overestimate the population standard deviation. To overcome this drawback, confidence intervals are determined to estimate population parameters and eliminate any calculation bias accurately. However, this only applies to random samples from normally distributed populations. Knowing the sample mean and...
What are Estimates?01:06

What are Estimates?

It isn't easy to measure a parameter such as the mean height or the mean weight of a population. So, we draw samples from the population and calculate the mean height or mean weight of the individuals in the sample. This sample data acts as a representative measure of the population parameter. These sample statistics are known as estimates. 
The estimate for the mean of a sample is denoted by ͞x, whereas the mean of the population is designated as μ. Further, parameters such as the mean,...
Prediction Intervals01:03

Prediction Intervals

The interval estimate of any variable is known as the prediction interval. It helps decide if a point estimate is dependable.
However, the point estimate is most likely not the exact value of the population parameter, but close to it. After calculating point estimates, we construct interval estimates, called confidence intervals or prediction intervals. This prediction interval comprises a range of values unlike the point estimate and is a better predictor of the observed sample value, y. 
The...
Estimating Population Mean with Unknown Standard Deviation01:22

Estimating Population Mean with Unknown Standard Deviation

In practice, we rarely know the population standard deviation. In the past, when the sample size was large, this did not present a problem to statisticians. They used the sample standard deviation s as an estimate for σ and proceeded as before to calculate a confidence interval with close enough results. However, statisticians ran into problems when the sample size was small. A small sample size caused inaccuracies in the confidence interval.
William S. Gosset (1876–1937) of the Guinness...
Estimating Population Mean with Known Standard Deviation01:16

Estimating Population Mean with Known Standard Deviation

To construct a confidence interval for a single unknown population mean μ, where the population standard deviation is known, we need sample mean as an estimate for μ and we need the margin of error. Here, the margin of error (EBM) is called the error bound for a population mean (abbreviated EBM). The sample mean is the point estimate of the unknown population mean μ.
The confidence interval estimate will have the form as follows:
(point estimate - error bound, point estimate + error bound)
The...
Testing a Claim about Standard Deviation01:19

Testing a Claim about Standard Deviation

A complete procedure to test a claim about population standard deviation or population variance is explained here.
The hypothesis testing for the claim of population standard deviation (or variance) requires the data and samples to be random and unbiased. The population distribution also must be normal. There is no specific requirement on the sample size as the estimation is based on the chi-square distribution.
As a first step, the hypothesis (null and alternative) concerning the claim about...

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Related Experiment Video

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A Tactile Automated Passive-Finger Stimulator (TAPS)
19:44

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Published on: June 3, 2009

Improving progress test score estimation using bayesian statistics.

Chris Ricketts1, Rana Moyeed

  • 1Institute of Clinical Education, Peninsula Medical School, University of Plymouth, Plymouth, UK.

Medical Education
|April 20, 2011
PubMed
Summary
This summary is machine-generated.

A Bayesian statistical approach improves student progress test scores by reducing measurement error. This method smooths scores, enhancing consistency and better identifying students needing support.

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Area of Science:

  • Educational Measurement
  • Statistical Modeling

Background:

  • Progress tests track student knowledge growth but are prone to measurement error.
  • Previous test results offer valuable data to mitigate current measurement inaccuracies.

Purpose of the Study:

  • To investigate a Bayesian statistical approach for reducing measurement error in student progress tests.
  • To leverage prior test information to improve score estimation and consistency.

Main Methods:

  • Developed a Bayesian model incorporating results from preceding tests to update current scores and standard error of measurement (SEM).
  • Extended the model to include all available previous test results.

Main Results:

  • The Bayesian model produces an exponentially weighted combination of test scores, smoothing results over time.
  • Including all previous tests doubled the effective sample size, reducing measurement error by 30%.

Conclusions:

  • A Bayesian approach enhances score estimates and reduces SEMs in progress testing.
  • This method is practical for large student cohorts and frequent testing, improving student rank ordering and identification of those needing remediation.