Statistics for clinicians. 5. Interval data (I).

Interval data may be discrete or continuous. They are usually summarized by the average (arithmetic mean). Sometimes, for example when the possible values in a series change by a constant multiple, we need to use the geometric mean. To obtain the overall or mean percentage of a series of percentage values, we need to calculate their weighted mean. The variability of observations in a sample is measured by the standard deviation, and the variability of sample means is measured by the standard error of mean. Confidence interval is a range which contains the population mean with a known probability. It is obtained by deducting from the sample mean, and adding to it, "t" times the SEM, the value of "t" depending on the desired confidence level (1-P) and the sample size (N). The significance of difference between the mean of two sets of unpaired interval data (MA-MB) is tested by Student's t-test. If the data are paired, the significance of the mean difference (MD) is tested by paired t-test. Ordinal data, ie, grades and ranks, may be analyzed by means of the t-test which is more sensitive and allows more refined analyses if needed.

Statistics for clinicians. 3. Nominal data (II)

When the percentage occurrence of an event in a series of groups shows a linear trend, the standard chi-square test may not reveal its significance. The data should then be analyzed by z-test for a linear trend. When the results of several similar experiments show a trend in favor of one group, but the differences in individual studies are not significant, the data from all studies can be analyzed together by the z-test for significance of the trend. In some studies, patients need to be followed up for long periods for the occurrence of an event. Here, we are interested not only in the frequency of the event, but also how soon it occurs or how long it is delayed. For this purpose the data should be analyzed by the life table method (also known as the logrank method or the Mantel-Haenszel method). Diagnostic tests are usually evaluated by their sensitivity and specificity. However, what is also important for a clinician is their predictive value, which depends on the prevalence of the condition.

Statistics for clinicians. 2. Nominal data (I).

Nominal data consist of items assigned to well defined classes. They are presented as a proportion or percentage of the total. From a sample percentage we can estimate the population percentage with a desired degree of confidence, using standard error of the percentage as a measure of chance variation. We can compare the difference in percentage between two groups by means of the z-test or the chi-square test. If the number of observations is less than 40, Fisher's test is preferable to the chi-square test. When chi-square test is done on 2x2 tables, Yates' correction is recommended. For tables larger than a 2x2, Yates' correction is not used. When testing paired data for significance of difference, we need to use McNemar's modification of Chi-square test. Chi-square test is useful not only to test the significance of differences but also to test the significance of an association between attributes.

Statistics for clinicians. 1. Introduction.

Statistics is a way of thinking about variable events. The relative frequency with which an event occurs is called its probability (P). By convention, events with a probability of 5% or less (P less than = 0.05) are considered rare or "significant". Data may be of nominal (categories), ordinal (grades), or interval/ratio type (measurements). Statistical methods are helpful for: summarizing data; making estimates for populations; defining "normal" range; testing association between attributes; measuring correlation between variables; computing one variable in terms of others; and testing the significance of differences between groups.