Online statistics tools, including a detection calculator, a kappa calculator and a Lin's concordance calculator are now accessible as Python 3.x code available at: https://github.com/niwa/statcalc
The following file contains corrections to the recent book: McBride, G.B. (2005). Using Statistical Methods for Water Quality Management: Issues, Problems and Solutions. Wiley, New York.
Download: McBride Book Corrections (March 2011) [PDF 40KB]
The Detection calculator
The Detection calculator is used to examine and calculate various properties of tests of three types of hypotheses: one-sided, point-null and equivalence. You can use either one or two groups of samples—all assuming random sampling from a normal distribution. For the first two types of hypothesis you can specify one of: the sample size, the significance level, the detectable effect size, and its detection probability. You specify any three of these and it calculates the remaining one. For equivalence tests only the detection probability can be calculated (further options will be added at a later date); its results are followed by an instructive graphical comparison of the effect of sample size on the detection probabilities for tests of the inequivalence hypothesis, the equivalence hypothesis, and the point-null hypothesis.
The "detection probability" is usually the more familiar "statistical power", except for the case of testing the inequivalence hypothesis (postulating that a difference lies beyond an "equivalence interval"); in that case it is the test’s "operating characteristic". You can download pdf files explaining the main features of all these tests.
The kappa calculator is used to assess the degree of agreement between two dichotomous variables. Such variables may have one of only two "values", e.g., presence or absence. It calculates the value of Cohen’s "kappa" (κ). A value of κ = 1 denotes perfect concordance, k = 0 denotes agreement by chance alone.
Lin’s concordance calculator is used to assess the degree of agreement between two continuous variables, such as chemical or microbiological concentrations. It calculates the value of Lin’s concordance correlation coefficient. Values of ±1 denote perfect concordance and discordance; a value of zero denotes its complete absence.
Statistical testing procedures for Cohen’s kappa and for Lin’s concordance correlation coefficient are included in the calculator. These procedures guard against the risk of claiming good agreement when that has happened merely by "good luck".
- Cohen, J. (1960). A coefficient of agreement for nominal scales. Educational and Psychological Measurement 20(1): 37–46.
- Fleiss, J.L. (1981). Statistical methods for rates and proportions, 2nd ed., Wiley, p. 218.
- Landis, J.R.; Koch, G.G. (1977). The measurement of observer agreement for categorical data. Biometrics 45: 255–268.
- Lin, L.I-K. (1989). A concordance correlation coefficient to evaluate reproducibility. Biometrics 45: 255–268.
- Lin, L.I-K. (2000). A note on the concordance correlation coefficient. Biometrics 56: 324–325.
- McBride, G.B. (2005). Using Statistical Methods for Water Quality Management: Issues, Problems and Solutions. Wiley, New York.
- Whyte, R.; Finlay, R. (1995). Monitoring the microbiological quality of drinking-waters. Water and Wastes in New Zealand (November): 43–45, 60.
- Zar, J. H. (1996). Biostatistical analysis. 3rd ed. Prentice Hall, Upper Saddle River, NJ. (and 4th edition in 1998).
The development of the kappa and Lin’s concordance calculator tools was funded by NZ Ministry of Health, the Foundation for Research, Science and Technology (FRST), and Environmental Diagnostics Ltd.