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Chemistry LibreTexts

4.11: Chapter Summary and Key Terms

  • Page ID
    220686
  • Summary

    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

    mean

    method error

    one-tailed significance test

    paired t-test

    probability distribution

    range

    sample

    standard deviation

    tolerance

    type 1 error

    unpaired data

    bias

    central limit theorem

    constant determinate error

    determinate error

    error

    histogram

    limit of identification

    median

    normal distribution

    outlier

    personal error

    propagation of uncertainty

    repeatability

    sampling error

    standard error of the mean

    t-test

    type 2 error

    variance

    binomial distribution

    Chauvenet’s criterion

    degrees of freedom

    Dixon’s Q-test

    F-test

    indeterminate error

    limit of quantitation

    measurement error

    null hypothesis

    paired data

    population

    proportional determinate error

    reproducibility

    significance test

    Standard Reference Material

    two-tailed significance test

    uncertainty

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