Medicine and numbers

11.10.2021:
In some studies, the researcher wants to compare three or more groups. This could, for example, be a randomised controlled trial including several treatments. In this case, it will be relevant to conduct pairwise comparisons between the groups. If the study includes three groups – A, B and C – up to three pairwise comparisons can be conducted in the form of hypothesis tests. And, if the study includes four groups – A, B, C and D – up to six pairwise comparisons are possible: A-B, A-C, A-D, B-C, B-D and C-D. When there are several hypotheses, it will be relevant to control for the family-wise...

28.09.2021:
It is quite common to investigate multiple hypotheses in a single study, which increases the probability of Type I errors. This can be dealt with in various ways. A researcher may have various reasons for testing multiple hypotheses in the same study, for example to investigate the effect on several outcome variables, compare more than two groups or undertake separate analyses for sub-groups. Different adjustment methods Consider a study where six hypothesis tests are performed. If all tests are made at a significance level of 5 %, each of them will have a 5 % probability of making a Type I...

07.06.2021:
Many hypotheses in medical research are in principle one-sided, for example in a randomised, controlled trial that investigates whether a new type of clinical treatment has a better effect than treatment as usual. So why are two-sided hypothesis tests used? Let us assume, for example, that we register the number of successful outcomes, meaning the number of patients who recover from the disease, in two separate treatment groups. The null hypothesis (H0) is that the probability of success is the same in both groups. But what is the alternative hypothesis? This is a trial that seeks to...

28.08.2020:
Many studies include ordinal data, such as the integers from 1 to 4. Can the mean or median be a relevant summary measure for such data? Ordinal scales, often called Likert scales, are frequently used in medical research and many other fields. One example is the following question in the Nord Trøndelag Health Study (HUNT): 'How is your health at the moment?'. The response alternatives are 'Poor', 'Not so good', 'Good', and 'Very good', which we will number from 1 to 4. The categories are ordinal, since higher categories reflect better self-rated health. But the 'distances' between the...

11.06.2020:
Mean and standard deviation are frequently used measures of central tendency and variability in data from scale variables. If data are not normally distributed, some researchers prefer reporting median and quartiles instead. But the mean and standard deviation have useful properties and can be relevant also when data are not normally distributed. Let us first consider the normal distribution, which is shown in Figure 1. If data are normally distributed, approximately 16 % of the observations will be lower than one standard deviation under the mean, and approximately 84 % of the observations...

26.03.2020:
In a randomised controlled trial there should be no systematic differences in background variables between the groups before treatment. But sometimes it can be sensible to adjust for some pre-defined variables in the statistical analyses. In some studies there are background variables which are strong predictors for the outcome variable. In an observational study, the distribution of background variables often differs between the groups. Such variables may act as confounders, and cause bias in the estimated effect unless they are adjusted for in the analysis. In a randomised controlled trial...

09.03.2020:
In a randomised controlled trial there should be no systematic differences between the groups before treatment. Still, some researchers choose to significance test for possible differences in background variables. This is superfluous, and can be misleading. An important strength of randomised controlled trials is the fact that background variables, for example age and sex, is randomly distributed between the treatment groups. According to the CONSORT guidelines, baseline demographic and clinical characteristics should be reported separately for each group (1). Table 1 shows an example which is...

17.02.2020:
How do we quantify the results of a study? Is the effect measured on the original scale or a standardised effect size most relevant? Reindal and colleagues (1) studied age for onset of independent walking. For children diagnosed with autism spectrum disorder, the mean age (standard deviation) was 14.74 (4.28) months, and for children without autism spectrum disorder, it was 13.76 (2.88) months. The difference was therefore 14.74–13.76 = 0.98 months. This is the effect size measured on the original scale, also called unstandardised effect size. In addition, the authors report a standardised...

23.05.2019:
In a longitudinal study, data on one or more time points may be missing for some participants. 'Last observation carried forward' is a simple method for imputing missing values, but it has serious weaknesses. Missing data may arise from participants dropping out of the study, or temporarily failing to appear at one or more time points. One method for handling missing data in longitudinal studies is called 'Last observation carried forward' (LOCF). In studies with one measurement at baseline and one after, the method can be termed 'Baseline observation carried forward' (BOCF). These methods are...

26.02.2019:
Is statistics a foreign language, like German, Latin or Mandarin? Using numbers to tell stories is a cornerstone of medical research. Clinical researchers translate observations of blood, sugar, sweat and tears into numbers and categories that can be analysed using statistical methods. They exchange experiences, empirical data and results with their peers through tables, figures and statistical analyses in scientific articles, at conferences and in textbooks. But although statistics is central to acquiring and disseminating medical knowledge, few clinicians have statistics as their primary...