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4.S: Evaluating Analytical Data (Summary)

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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 affecting its precision. A propagation of uncertainty allows us to estimate how these determinate and indeterminate errors will 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 precisions. To compare two sets of data you must first determine whether the data is paired or unpaired. For unpaired data you must also decide if the standard deviations can be pooled. 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 when deciding to reject an outlier.

    Finally, the detection limit is a statistical statement about the smallest amount of analyte that 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.

    4.9.1 Key Terms

    alternative hypothesis
    binomial distribution
    box plot
    central limit theorem
    Chauvenet’s criterion
    confidence interval
    constant determinate error
    degrees of freedom
    detection limit
    determinate error
    Dixon’s Q-test
    dot chart
    Grubb’s test
    indeterminate error
    kernel density plot
    limit of identification
    limit of quantitation
    measurement error
    method error
    normal distribution
    null hypothesis
    one-tailed significance test
    paired data
    paired t-test
    personal error
    probability distribution
    propagation of uncertainty
    proportional determinate error
    sampling error
    significance test
    standard deviation
    standard error of the mean
    Standard Reference Material
    two-tailed significance test
    type 1 error
    type 2 error
    unpaired data


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