normal approximation

(noun)

The process of using the normal curve to estimate the shape of the distribution of a data set.

Related Terms

Examples of normal approximation in the following topics:

  • The normal approximation breaks down on small intervals

    • Caution: The normal approximation may fail on small intervals The normal approximation to the binomial distribution tends to perform poorly when estimating the probability of a small range of counts, even when the conditions are met.
    • With such a large sample, we might be tempted to apply the normal approximation and use the range 69 to 71.
    • However, we would find that the binomial solution and the normal approximation notably differ:
    • TIP: Improving the accuracy of the normal approximation to the binomial distribution
    • The tip to add extra area when applying the normal approximation is most often useful when examining a range of observations.

  • Introduction to evaluating the normal approximation

    • Many processes can be well approximated by the normal distribution.
    • While using a normal model can be extremely convenient and helpful, it is important to remember normality is always an approximation.
    • Testing the appropriateness of the normal assumption is a key step in many data analyses.
    • The observations are rounded to the nearest whole inch, explaining why the points appear to jump in increments in the normal probability plot.

  • Non-normal point estimates

    • We may apply the ideas of confidence intervals and hypothesis testing to cases where the point estimate or test statistic is not necessarily normal.
    • The sample size is too small for the normal approximation to be valid;
    • The point estimate tends towards some distribution that is not the normal distribution.
    • For each case where the normal approximation is not valid, our first task is always to understand and characterize the sampling distribution of the point estimate or test statistic.

  • Calculating a Normal Approximation

    • In this atom, we provide an example on how to compute a normal approximation for a binomial distribution.
    • The following is an example on how to compute a normal approximation for a binomial distribution.
    • The area in green in the figure is an approximation of the probability of obtaining 8 heads.
    • For these parameters, the approximation is very accurate.
    • Approximation for the probability of 8 heads with the normal distribution.

  • The Normal Approximation to the Binomial Distribution

    • The process of using the normal curve to estimate the shape of the binomial distribution is known as normal approximation.
    • The process of using this curve to estimate the shape of the binomial distribution is known as normal approximation.
    • The importance of the normal curve stems primarily from the fact that the distribution of many natural phenomena are at least approximately normally distributed.
    • The normal approximation to the binomial distribution for 12 coin flips.
    • Note how well it approximates the binomial probabilities represented by the heights of the blue lines.

  • Evaluating the Normal approximation exercises

    • Do these data appear to follow a normal distribution?
    • Do these data appear to follow a normal distribution?
    • The superimposed normal curve approximates the distribution pretty well.
    • The points on the normal probability plot also follow a relatively straight line.
    • The data appear to be reasonably approximated by the normal distribution.

  • Probability Histograms and the Normal Curve

    • Many different types of distributions can be approximated by the normal curve.
    • Approximately normal distributions occur in many situations, as explained by the central limit theorem.
    • How can we tell if data in a probability histogram are normal, or at least approximately normal?
    • If the graph is approximately bell-shaped and symmetric about the mean, you can usually assume normality.
    • A normal probability plot is a graphical technique for normality testing--assessing whether or not a data set is approximately normally distributed.

  • Conclusion

    • Many distributions in real life can be approximated using normal distribution.
    • If the graph is approximately bell-shaped and symmetric about the mean, you can usually assume normality.
    • A normal probability plot is a graphical technique for normality testing--assessing whether or not a data set is approximately normally distributed.
    • We study the normal distribution extensively because many things in real life closely approximate the normal distribution, including:
    • The data points do not deviate far from the straight line, so we can assume the distribution is approximately normal.

  • Change of Scale

    • In order to consider a normal distribution or normal approximation, a standard scale or standard units is necessary.
    • In order to consider a normal distribution or normal approximation, a standard scale or standard units is necessary.
    • In the case of normalization of scores in educational assessment, there may be an intention to align distributions to a normal distribution.
    • Normalization can also refer to the creation of shifted and scaled versions of statistics, where the intention is that these normalized values allow the comparison of corresponding normalized values for different datasets.
    • Explain the significance of normalization of ratings and calculate this normalization

  • Normal Approximation to the Binomial

    • In the section on the history of the normal distribution, we saw that the normal distribution can be used to approximate the binomial distribution.
    • This section shows how to compute these approximations.
    • For these parameters, the approximation is very accurate.
    • The accuracy of the approximation depends on the values of N and π.
    • Approximating the probability of 8 heads with the normal distribution