Basic Statistics

Descriptive Statistics
Inferential Statistics
Methods to Test Hypotheses



For anesthesiologists, a basic knowledge of statistics is necessary for rational interpretation of the literature. For those doing research, statistical concepts are critical in the planning, execution, presentation, and publication of studies. Few nonstatisticians will develop sufficient knowledge to resolve complex statistical issues; however, clinicians and investigators can avoid obvious errors and can consult with trained statisticians when additional expertise is needed. This synopsis will provide some basic vocabulary and help with the answers to several commonly asked statistical questions.

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Descriptive statistics: summarize a group of individual data points. A group constitutes a sample of an entire population. Categories of data are called variables (not parameters). Variables are classified as continuous, including both ratio scales and interval scales (e.g., cardiac output), or discontinuous, (e.g., five finger, six layers.) Ranked variables cannot be measured but can be ordered by magnitude (e.g., Glasgow Coma Scale). Categorical variables may be nominal or ordinal but have unmeasurable attributes (e.g., alive or dead.) Common definitions of descriptive statistics include:

where = sum, X = the value of an individual observation, X = the mean of all observations, and n = the number of observations.

If the data are normally distributed, 95% of all population members fall within about 2 standard deviations of the mean, i.e., if the mean t SD for systolic blood pressure is 110 10 mmHg, then 95% of systolic blood pressures are between 80 and 130 mmHg.

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Inferential statistics: allow generalizations to a population, based upon a sample; used to test hypotheses and evaluate estimates. The hypothesis of "no difference" is often called the null hypothesis.

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  1. Are two or more numbers different?



    (See table inside front cover of Glantz, SA. Primer of Bio-Statistics (4th Edition). McGraw-Hill, Inc., NY, NY, 1997.)

    Parametric data (normally distributed, continuous data): unpaired or paired t tests; ANOVA. Discontinuous data or non-normally distributed continuous data: Mann-Whitney rank-sum test (used in unpaired data); Wilcoxon signed-rank test (used with paired data); KruskalWallis statistic (used similarly to ANOVA). Categorical data: Chi-square analysis-of-contingency table for unpaired data or three or more groups of different individuals; McNemar's test for paired data.

  3. Are two or more responses different?



    Parametric data (normally distributed, continuous data): repeated measures ANOVA. Discontinuous data or non-normally distributed continuous data: Friedman statistic. Categorical data: Cochrane's Q for three or more treatments in the same individuals.

  5. Are statistically significant differences clinically important?



    Dependent on judgement and experience. For instance, if two anesthetics are associated with a statistically significant 3.0 mmHg difference in intracranial pressure in patients with brain tumors, that might be of little clinical importance.

  7. What is the meaning of a "zero numerator?"



    A common statistical question implicit in clinical practice: What is the implication of not observing a complication or an effect in a given population? ("What does it mean if I have never induced a pneumothorax in a series of subclavian central venous catheterizations?") The basic rule is that the actual incidence of that occurrence if the series were continued would be
    0 to 3
    where n is the number of events currently in the series.

  9. Are two or more numbers equivalent?



    The same approaches are used as in question I above. However, power analysis is essential in determining the confidence with which the evidence should be accepted (i.e., is the sample size sufficient to safely conclude that there is no difference?) A good conceptual comparison is the criminal justice system which provides a verdict of "not guilty" rather than "innocent."

    A special case is the determination of whether two measurement techniques are equivalent, in which the Bland-Altman approach (see above) is the preferable method.

  11. Are two or more responses the same?



    The same approach is used as in question 2 above. However, power analysis is essential in determining the confidence with which the evidence should be accepted (i.e., is the sample size sufficient to safely conclude that there is no difference?)

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Glanz, SA. Primer of Bio-Statistics (4th Edition). McGraw-Hill, NY, NY, 1997. Chapter references in (parentheses).
Scale of Measurement 2 treatment groups, different individuals 3+ groups, diff individuals Before and after a single treatment in same individuals Multiple treatments, same individuals Association between 2 variables
Interval (and drawn from normally distributed populations)* Unpaired t-test (4) Analysis of variance (ANOVA) (3) Paired t-test (9) Repeated-measures ANOVA (9) Linear regression and Pearson product-moment correlation; Bland-Altman analysis (8)
Nominal Chi-square analysis-of-contingency table (5) Chi-square analysis-of-contingency table (5) McNemar's test (9) Cochrane Q ** Contingency coefficients **
Ordinal Mann-Whitney rank-sum test (10) Kruskal-Wallis statistic (10) Wilcoxon signed-rank test (10) Friedman statistic (10) Spearman rank correlation (8)
Survival time Log-rank test or Gehan's test (11)
* If the assumption of normally distributed populations is not met, rank the observations and use the methods of data measured on an ordinal scale.
** Not included in this text.

REFERENCES (Annotated)

  1. Glanz, SA. Primer of Bio-Statistics (4th Edition). McGraw-Hill, NY, NY, 1997.



    An excellent general reference for a nonstatistician.

  3. Moses LE. Statistical concepts fundamental to investigations. N Engl J Med 1985;312:890-897.



    A good overview of how to use statistics in interpreting (and planning) research.

  5. Cupples LA, Heeren T. Schatzkin A, Cotton T. Multiple testing of hypotheses in comparing two groups. Ann Intern Med 1984;100:122-129.



    A good overview of multivariate testing (the kind of methodology that is used to answer questions such as "What factors correlate with postoperative myocardial infarction? "

  7. Bland JM, Altman DG. Statistical methods for assessing agreement between two methods of clinical measurement. The Lancet 1986;1:307.



    A widely cited reference for a fundamental type of question such as "What is the comparison between measurements of hemoglobin saturation done with arterial blood samples or pulse oximetry? "

  9. William on DF, Parker RA, Kendrick IS. The box plot: a simple visual method to interpret dataAnn Intern Med 1989;110:916.



    Advocates a new approach to the presentation of data that probably will become widely accepted (or required) over time.

  11. Hanley JA, Lippman-Hand A. If nothing goes wrong, is everything all right? JAMA 1983;249: 1743-1745.



    Well worth reading, even if you plan to interpret nothing other than your own clinical experience.

  13. Steel RGC, Torrie JH. Multiple comparisons in Steel RGC, Torrie JH (Eds.) Principles and Procedures of Statistics: a Biometrical Approach, 2nd Ed. McGraw-Hill Inc., NY, NY, 1980. Ch. 8, p 173-194.



    Math is a little heavy, but the commonly used tests are presented.

  15. Student. The probable error of a mean. Biometrika 1908;6:1-25.



    A classic. No, I don't know why no first or middle name is given.

  17. Derish PA. Biostatistics for Editors. CBE Views 1994;17:3-6.



    Concise overview.,

  19. Bailar JC, Mosteller F. Guidelines for statistical reporting in articles for medical journals. Annals of Internal Medicine 1988;108:266-273.
  20. Mills JL. Data Torturing. N Engl J Med 1993;329:1196-1199.
  21. Kubinski JA, Rudy TE, Boston JR- Research design and analysis: the many faces of validity. J Crit Care 1991;6:143-151.



    This reference and the two that follow are a series of readable papers that address important basic issues.

  23. Boston JP, Rudy TE, Kubinski JA. Multiple statistical comparisons: fishing with the right bait. J Crit Care 1991;6:211-220.
  24. Rudy TE, Kubinski JA, Boston JR. Multivariate analysis and repeated measurements: a premier. J Crit Care 1992;7:30-41.
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