error

(noun)

The difference between the population parameter and the calculated sample statistics.

Related Terms

Examples of error in the following topics:

  • Chance Error

    • Random, or chance, errors are errors that are a combination of results both higher and lower than the desired measurement.
    • While conducting measurements in experiments, there are generally two different types of errors: random (or chance) errors and systematic (or biased) errors.
    • A random error makes the measured value both smaller and larger than the true value; they are errors of precision.
    • In this case, there is more systematic error than random error.
    • In this case, there is more random error than systematic error.

  • Bias

    • Systematic, or biased, errors are errors which consistently yield results either higher or lower than the correct measurement.
    • While conducting measurements in experiments, there are generally two different types of errors: random (or chance) errors and systematic (or biased) errors.
    • 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 systematic error than random error.
    • In this case, there is more random error than systematic error.

  • Standard Error

    • In regression analysis, the term "standard error" is also used in the phrase standard error of the regression to mean the ordinary least squares estimate of the standard deviation of the underlying errors.
    • 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.

  • 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:

  • Computing R.M.S. Error

    • Root-mean-square error serves to aggregate the magnitudes of the errors in predictions for various times into a single measure of predictive power.
    • RMS error is the square root of mean squared error (MSE), which is a risk function corresponding to the expected value of the squared error loss or quadratic loss.
    • RMS error is simply the square root of the resulting MSE quantity.
    • We can find the general size of these errors by taking the RMS size for them:
    • $\displaystyle \sqrt { \frac { { \left( \text{error}\ 1 \right) }^{ 2 }+{ \left(\text{error}\ 2 \right) }^{ 2 }+\cdots +{ \left( \text{error n} \right) }^{ 2 } }{ n } }$.

  • Caveat Emptor and the Gallup Poll

    • Readers should pay close attention to a poll's margin of error.
    • The margin of error statistic expresses the amount of random sampling error in a survey's results.
    • So in this case, the absolute margin of error is 5 people, but the "percent relative" margin of error is 10% (10% of 50 people is 5 people).
    • If the exact confidence intervals are used, then the margin of error takes into account both sampling error and non-sampling error.
    • Also, if the 95% margin of error is given, one can find the 99% margin of error by increasing the reported margin of error by about 30%.

  • Type I and Type II Errors

    • The two types of error are distinguished as type I error and type II error.
    • Minimizing errors of decision is not a simple issue.
    • For any given sample size the effort to reduce one type of error generally results in increasing the other type of error.
    • An example of acceptable type I error is discussed below.
    • This is an example of type I error that is acceptable.

  • Working Backwards to Find the Error Bound or Sample Mean

    • Working Backwards to find the Error Bound or the Sample Mean
    • Subtract the error bound from the upper value of the confidence interval
    • Suppose we know that a confidence interval is (67.18, 68.82) and we want to find the error bound.
    • If we know the error bound: = 68.82 − 0.82 = 68
    • If we don't know the error bound: = (67.18 + 68.82)/2 = 68

  • Type I and II Errors

    • This type of error is called a Type I error.
    • The Type I error rate is affected by the α level: the lower the α level, the lower the Type I error rate.
    • It might seem that α is the probability of a Type I error.
    • This kind of error is called a Type II error.
    • Unlike a Type I error, a Type II error is not really an error.

  • Outcomes and the Type I and the Type II Errors

    • Each of the errors occurs with a particular probability.
    • α = probability of a Type I error = P(Type I error) = probability of rejecting the null hypothesis when the null hypothesis is true.
    • β = probability of a Type II error = P(Type II error) = probability of not rejecting the null hypothesis when the null hypothesis is false.
    • Notice that, in this case, the error with the greater consequence is the Type II error.
    • The error with the greater consequence is the Type I error.