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70 T.S. Riall

incidence of Crohn’s disease occurring most commonly in patients in their teens/twenties and patients in their sixties. For this type of distribution, the mean is not a useful or descriptive measure.

Measures of Spread

While the mean provides useful information, you will have more information if you have an idea of the spread (disper- sion or variation) of the observations around the mean. The range is the difference between the smallest and largest observation. It is common to give maximum and minimum values, which are more useful than the range. The range is used to emphasize extreme values.

Standard deviation (SD) is the most commonly used mea- sure of variation in medicine. It describes how observations cluster around the mean, and it is the basis for many statisti- cal tests used to compare means between groups. For each observation, the deviation from the mean is calculated and squared. The sum of the squared deviations for all observa- tions is divided by the number of observations minus one. This value is called the variance. The square root of the vari- ance is the SD. Regardless of the distribution of the data, at least 75% of observations lay between the mean plus 2 SDs and the mean minus 2 SDs. If a distribution is bell-shaped or normal, it has special characteristics: 67% of observations in a normal distribution lie between the mean ± 1 SD, 95% lie between the mean ± 2 SD,and 99.7% lie between the mean ± 3 SD. If the mean is smaller than two standard deviations, the data are probably skewed. Mean and SD are best used when the data are symmetric.

A percentile is the percentage of distribution that is at or below a particular number. Percentiles are commonly used to determine the “normal” ranges of laboratory values. Values lower than the 2.5 percentile and higher than the 97.5 percen- tile (greater or less than 2 SD from the mean) are considered outliers or abnormal values.The interquartile range is the dif- ference between the 25th and 75th percentile (or first and

Chapter 5.  Analyzing Your Data

71

third quartiles) and specifies the central 50% of observations. Percentiles and interquartile ranges are used when the median is used for ordinal or skewed data, or when the mean is used with the goal is to compare individual observations with a set of norms.

Comparison of Numeric Variables

Bivariate analysis is used to assess the relationship of a single independent variable (predictor) and a single dependent variable (outcome). Statistical tests for comparing means of continuous variables that are normally distributed include the student’s t-test for two independent groups and the paired t-test for paired samples. If the continuous variable is not normally distributed, nonparametric tests are used.These tests include the Wilcoxon rank sum test (also known as the Mann–Whitney U test) for two independent groups and the Wilcoxon signed-rank test for paired samples. Two groups of data are independent if the values in one group do not pro- vide any information about the values in the other group. Analysis of variance (ANOVA) is used to compare means among three or more normally distributed, independent groups. When comparing three or more groups, the P-value (corresponding to an F-test) indicates an overall significant difference and not differences between any two groups. To determine differences between any two groups, you need to do post-hoc comparison tests to perform multiple, pairwise comparisons including Tukey, Bonferroni, Newman–Keuls, and Fisher tests. The Kruskal–Wallis test is used to compare medians for three more independent groups in which the means are not normally distributed.

Comparison of Categorical Values

Categorical variables are expressed as proportions and can be demonstrated in 2 × 2 tables for two independent groups up to r x c tables for n independent groups. Chi-square tests

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