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3.11: Chapter Summary and Key Terms

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    The data we collect are characterized by their central tendency (where the values cluster), and their spread (the variation of individual values around the central value). We report our data’s central tendency by stating the mean or median, and our data’s spread using the range, standard deviation or variance. Our collection of data is subject to errors, including determinate errors that affect the data’s accuracy and indeterminate errors that affect its precision. A propagation of uncertainty allows us to estimate how these determinate and indeterminate errors affect our results.

    When we analyze a sample several times the distribution of the results is described by a probability distribution, two examples of which are the binomial distribution and the normal distribution. Knowing the type of distribution allows us to determine the probability of obtaining a particular range of results. For a normal distribution we express this range as a confidence interval.

    A statistical analysis allows us to determine whether our results are significantly different from known values, or from values obtained by other analysts, by other methods of analysis, or for other samples. We can use a t-test to compare mean values and an F-test to compare variances. To compare two sets of data you first must determine whether the data is paired or unpaired. For unpaired data you also must decide if you can pool the standard deviations. A decision about whether to retain an outlying value can be made using Dixon’s Q-test, Grubb’s test, or Chauvenet’s criterion.

    You should be sure to exercise caution if you decide to reject an outlier. Finally, the detection limit is a statistical statement about the smallest amount of analyte we can detect with confidence. A detection limit is not exact since its value depends on how willing we are to falsely report the analyte’s presence or absence in a sample. When reporting a detection limit you should clearly indicate how you arrived at its value.

    Key Terms

    alternative hypothesis

    box plot

    confidence interval

    detection limit

    dot chart

    Grubb’s test

    kernel density plot


    method error

    one-tailed significance test

    paired t-test

    probability distribution



    standard deviation


    type 1 error

    unpaired data


    central limit theorem

    constant determinate error

    determinate error



    limit of identification


    normal distribution


    personal error

    propagation of uncertainty


    sampling error

    standard error of the mean


    type 2 error


    binomial distribution

    Chauvenet’s criterion

    degrees of freedom

    Dixon’s Q-test


    indeterminate error

    limit of quantitation

    measurement error

    null hypothesis

    paired data


    proportional determinate error


    significance test

    Standard Reference Material

    two-tailed significance test


    This page titled 3.11: Chapter Summary and Key Terms is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey.

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