error bound

(noun)

The margin or error that depends on the confidence level, sample size, and the estimated (from the sample) proportion of successes.

Examples of error bound in the following topics:

  • 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

  • Summary of Formulas

    • ( lower value,upper value ) = ( point estimate − error bound,point estimate + error bound )
    • Formula 8.2: To find the error bound when you know the confidence interval
    • error bound = upper value − point estimate OR error bound = (upper value − lower value)/2

  • Changing the Confidence Level or Sample Size

    • Increasing the confidence level increases the error bound, making the confidence interval wider.
    • Decreasing the confidence level decreases the error bound, making the confidence interval narrower.
    • If we increase the sample size n to 100, we decrease the error bound.
    • If we decrease the sample size n to 25, we increase the error bound.
    • Decreasing the sample size causes the error bound to increase, making the confidence interval wider.

  • Calculating the Sample Size n

    • If researchers desire a specific margin of error, then they can use the error bound formula to calculate the required sample size.
    • The error bound formula for a population mean when the population standard deviation is known is $EBM = z_{\frac{\alpha }{2}} \cdot (\frac{\sigma }{\sqrt{n}})$
    • The formula for sample size is $n = \frac{z^2\sigma ^2}{EBM^2}$ , found by solving the error bound formula for n
    • A researcher planning a study who wants a specified confidence level and error bound can use this formula to calculate the size of the sample needed for the study.

  • Lab 2: Confidence Interval (Place of Birth)

    • Calculate the confidence interval and the error bound. i.
    • Error Bound:

  • Practice 3: Confidence Intervals for Proportions

    • Would the error bound become larger or smaller?
    • Using the same p' and n = 80, how would the error bound change if the confidence level were increased to 98%?
    • If you decreased the allowable error bound, why would the minimum sample size increase (keeping the same level of confidence)?

  • Homework

    • Calculate the error bound.
    • Calculate the error bound.
    • Calculate the error bound.
    • Calculate the error bound.
    • Calculate the error bound.

  • Practice 1: Confidence Intervals for Means, Known Population Standard Deviation

    • Would the error bound become larger or smaller?
    • Using the same mean, standard deviation and sample size, how would the error bound change if the confidence level were reduced to 90%?

  • Which Standard Deviation (SE)?

    • Although they are often used interchangeably, the standard deviation and the standard error are slightly different.
    • The standard error is the standard deviation of the sampling distribution of a statistic.
    • However, the mean and standard deviation are descriptive statistics, whereas the mean and standard error describes bounds on a random sampling process.
    • Despite the small difference in equations for the standard deviation and the standard error, this small difference changes the meaning of what is being reported from a description of the variation in measurements to a probabilistic statement about how the number of samples will provide a better bound on estimates of the population mean, in light of the central limit theorem.
    • Standard error should decrease with larger sample sizes, as the estimate of the population mean improves.

  • Standard Error

    • This is due to the fact that the standard error of the mean is a biased estimator of the population standard error.
    • However, while the mean and standard deviation are descriptive statistics, the mean and standard error describe bounds on a random sampling process.
    • Despite the small difference in equations for the standard deviation and the standard error, this small difference changes the meaning of what is being reported from a description of the variation in measurements to a probabilistic statement about how the number of samples will provide a better bound on estimates of the population mean.
    • 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.