systematic error

(noun)

an error which consistently yields results either higher or lower than the correct measurement; accuracy error

Related Terms

  • random error
  • Accuracy
  • Precision

Examples of systematic error in the following topics:

  • Bias

    • Systematic, or biased, errors are errors which consistently yield results either higher or lower than the correct measurement.
    • Accuracy (or validity) is a measure of the systematic error.
    • If it is within the margin of error for the random errors, then it is most likely that the systematic errors are smaller than the random errors.
    • In this case, there is more random error than systematic error.
    • In this case, there is more systematic error than random error.
  • Chance Error

    • While conducting measurements in experiments, there are generally two different types of errors: random (or chance) errors and systematic (or biased) errors.
    • To better understand the outcome of experimental data, an estimate of the size of the systematic errors compared to the random errors should be considered.
    • Random errors are due to the precision of the equipment , and systematic errors are due to how well the equipment was used or how well the experiment was controlled .
    • In this case, there is more systematic error than random error.
    • In this case, there is more random error than systematic error.
  • Estimation

    • There is some level of error associated with it.
    • All measurements have some error associated with them.
    • Random errors occur in all data sets and are sometimes known as non-systematic errors.
    • Bias is sometimes known as systematic error.
    • The mean squared error (MSE) of $\hat { \theta }$ is defined as the expected value of the squared errors.
  • Chance Error and Bias

    • Chance error and bias are two different forms of error associated with sampling.
    • In statistics, a sampling error is the error caused by observing a sample instead of the whole population.
    • In sampling, there are two main types of error: systematic errors (or biases) and random errors (or chance errors).
    • Random error always exists.
    • These are often expressed in terms of its standard error:
  • Standard Error

    • The standard error and the standard deviation of small samples tend to systematically underestimate the population standard error and deviations.
    • This is due to the fact that the standard error of the mean is a biased estimator of the population standard error.
    • The relative standard error (RSE) is simply the standard error divided by the mean and expressed as a percentage.
    • If one survey has a standard error of $10,000 and the other has a standard error of $5,000, then the relative standard errors are 20% and 10% respectively.
    • Paraphrase standard error, standard error of the mean, standard error correction and relative standard error.
  • Estimating the Accuracy of an Average

    • The standard error of the mean is the standard deviation of the sample mean's estimate of a population mean.
    • Note that the standard error and the standard deviation of small samples tend to systematically underestimate the population standard error and deviations because the standard error of the mean is a biased estimator of the population standard error.
    • In particular, the standard error of a sample statistic (such as sample mean) is the estimated standard deviation of the error in the process by which it was generated.
    • If the standard error of several individual quantities is known, then the standard error of some function of the quantities can be easily calculated in many cases.
    • Evaluate the accuracy of an average by finding the standard error of the mean.
  • Checking the Model and Assumptions

    • Different response variables have the same variance in their errors, regardless of the values of the predictor variables.
    • In practice, this assumption is invalid (i.e., the errors are heteroscedastic) if the response variables can vary over a wide scale.
    • In order to determine for heterogeneous error variance, or when a pattern of residuals violates model assumptions of homoscedasticity (error is equally variable around the 'best-fitting line' for all points of x), it is prudent to look for a "fanning effect" between residual error and predicted values.
    • That is, there will be a systematic change in the absolute or squared residuals when plotted against the predicting outcome.
    • Error will not be evenly distributed across the regression line.
  • Model Assumptions

    • This means, for example, that the predictor variables are assumed to be error-free; that is, they are not contaminated with measurement errors.
    • In order to determine for heterogeneous error variance, or when a pattern of residuals violates model assumptions of homoscedasticity (error is equally variable around the 'best-fitting line' for all points of $x$), it is prudent to look for a "fanning effect" between residual error and predicted values.
    • This is to say there will be a systematic change in the absolute or squared residuals when plotted against the predicting outcome.
    • Error will not be evenly distributed across the regression line.
    • Independence of errors.
  • Properties of Sampling Distributions

    • This standard deviation is called the standard error of the mean.
    • For the case where the statistic is the sample mean, and samples are uncorrelated, the standard error is:
    • To be specific, assume your sample mean is 125 and you estimated that the standard error of the mean is 5.
    • A statistical study can be said to be biased when one outcome is systematically favored over another.
    • Describe the general properties of sampling distributions and the use of standard error in analyzing them
  • Decision and Conclusion

    • A systematic way to make a decision of whether to reject or not reject the null hypothesis is to compare the p-value and a preset or preconceived α (also called a "significance level").
    • A preset α is the probability of a Type I error (rejecting the null hypothesis when the null hypothesis is true).
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