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Weighted Mean00:57

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While taking the arithmetic, geometric, or harmonic mean of a sample data set, equal importance is assigned to all the data points. However, all the values may not always be equally important in some data sets. An intrinsic bias might make it more important to give more weightage to specific values over others.
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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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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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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.
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The accurate values of population parameters such as population proportion, population mean, and population standard deviation (or variance) are usually unknown. These are fixed values that can only be estimated from the data collected from the samples. The estimates of each of these parameters are sample proportion, the sample mean, and sample standard deviation (or variance). To obtain the values of these sample statistics, data are required that have particular distribution and central...
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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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Updated: Sep 11, 2025

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The Democracy Effect: a weights-based estimation strategy.

Pedro Dal Bó1, Andrew Foster2, Kenju Kamei3

  • 1Brown University and NBER.

Journal of Economic Behavior & Organization
|August 13, 2025
PubMed
Summary
This summary is machine-generated.

Democracy can enhance policy effectiveness compared to imposed policies. A new estimation strategy, using population prevalence weights, simplifies analysis and eliminates selection effects under specific conditions.

Keywords:
C1C9D7Democracy effectExperimentMeasurementSelection effectVoting

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Area of Science:

  • Behavioral economics
  • Experimental economics
  • Political economy

Background:

  • Democratic policy selection may yield greater effects than exogenous imposition.
  • Previous estimation strategies require detailed voting data from exogenous treatments.

Purpose of the Study:

  • Introduce a simpler estimation strategy for the democracy effect.
  • Eliminate selection effects in estimating policy effectiveness under democracy.
  • Apply the new strategy to existing and novel experimental data.

Main Methods:

  • Develop a weights-based estimator using population prevalence.
  • Derive the statistical distribution of the new estimator.
  • Apply the estimator to Dal Bó et al. (2010) data and a new experiment.

Main Results:

  • The new strategy simplifies estimation by removing the need for exogenous treatment vote data.
  • A significant democracy effect was found in the Dal Bó et al. (2010) data.
  • No significant democracy effect was detected in the new experimental data.

Conclusions:

  • The weights-based estimation strategy is a viable alternative for analyzing democracy effects.
  • The democracy effect's presence may depend on experimental design and data availability.
  • Further research can explore the conditions under which selection effects are eliminated.