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Related Concept Videos

Estimating Population Mean with Unknown Standard Deviation01:22

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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...
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Estimating Population Mean with Known Standard Deviation01:16

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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:
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Regression toward the mean (“RTM”) is a phenomenon in which extremely high or low values—for example, and individual’s blood pressure at a particular moment—appear closer to a group’s average upon remeasuring. Although this statistical peculiarity is the result of random error and chance, it has been problematic across various medical, scientific, financial and psychological applications. In particular, RTM, if not taken into account, can interfere when...
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Testing a Claim about Mean: Unknown Population SD01:21

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A complete procedure of testing a hypothesis about a population mean when the population standard deviation is unknown is explained here.
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What are Estimates?01:06

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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. 
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Estimating Population Standard Deviation01:26

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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...
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Appropriately estimating the standardized average treatment effect with missing data: A simulation and primer.

Samantha F Anderson1

  • 1Department of Psychology, Arizona State University, 950 S. McAllister Ave, Tempe, AZ, 85281, USA. samantha.f.anderson@asu.edu.

Behavior Research Methods
|December 22, 2022
PubMed
Summary
This summary is machine-generated.

Estimating the standardized average treatment effect (sATE) with missing data requires careful handling. Maximum likelihood and multiple imputation methods offer unbiased estimates, but model and variance choices are crucial, especially for small sample sizes.

Keywords:
Average treatment effectMaximum likelihoodMissing dataMultiple imputationStandardized mean difference

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Area of Science:

  • Statistics
  • Psychometrics
  • Biostatistics

Background:

  • Standardized average treatment effect (sATE) estimation is vital for interpreting randomized treatment studies and informing meta-analyses.
  • Missing outcome data in pretest-posttest randomized studies complicate unbiased sATE estimation, particularly due to its ratio structure (mean difference over standard deviation).

Purpose of the Study:

  • To compare the bias and accuracy of different missing data handling strategies for estimating the sATE in randomized pretest-posttest studies.
  • To investigate the impact of modeling choices within maximum likelihood and multiple imputation approaches on sATE estimation.

Main Methods:

  • A Monte Carlo simulation study was conducted under conditions of both homogeneity and heterogeneity of variance.
  • Evaluated various modeling choices, including analysis models, variance estimators, imputation algorithms, and pooling methods, within maximum likelihood and multiple imputation frameworks.
  • Examined specific missingness patterns relevant to pretest-posttest designs.

Main Results:

  • Both maximum likelihood and multiple imputation can yield largely unbiased sATE estimates.
  • Accuracy differences were primarily attributed to variations in bias.
  • Model and variance estimator choices significantly impact sATE estimation accuracy, particularly at smaller sample sizes (N=50).

Conclusions:

  • Careful selection of analysis models and variance estimators is recommended for accurate sATE estimation, especially with limited sample sizes.
  • The study provides practical recommendations and a software demonstration to improve sATE estimation in the presence of missing data.
  • A pedagogical explanation clarifies how specific methods introduce bias in the numerator and denominator of the sATE.