## Solving Statistics: Scatter plots

# Background

This time there was no question about the statistics of a certain paper. Therefore, the editor asked me if I could elaborate on a specific type of figures for this edition of the AMSj: the scatter plot.

This time there was no question about the statistics of a certain paper. Therefore, the editor asked me if I could elaborate on a specific type of figures for this edition of the AMSj: the scatter plot.

The *distribution* of a continuous numerical variable tells you something about how likely each possible outcome or groups of outcomes will occur. The distribution of a continuous numerical variable can be described as normal or non-normal. A normal distribution is the name for a specific mathematical concept that follows a symmetric bell shaped curve and is completely defined by its mean and standard deviation. Approximately 68% of the observations fall between one standard deviation below and one standard deviation above the mean. And approximately 95% of the observations fall between two standard deviations below and two standard deviations above the mean. Normal distribution is an important term within the field of statistics. If you have a normal distribution you can perform a certain number of statistical tests that you cannot perform if your distribution is non-normal.^{1}

The performance of activities of daily living (ADL) at home is important for the recovery of older individuals after hip fracture. However, 20-90% of these individuals lose ADL function and never fully recover. Although exercise interventions have been proven to improve physical function, especially elderly do not seem to benefit from these interventions. In this prospective, stepped-wedge randomized controlled trial, care as usual [CaU] is compared to 1) occupational therapy (OT) with coaching based on cognitive behavioural treatment (CBT) [OTc], and 2) OT-CBT with sensor monitoring embedded [OTcsm]. More specifically, during 12 months, six nursing homes will start with providing CaU, then cross over to provide OTc and finally cross over to provide OTcsm. The timing of crossing over is randomized: two nursing homes will cross over for the first time after two months, two after four months and the last two after six months. OTc will always be provided for 4 months, CaU for two, four and siex months respectively, and OTcsm for six, four and two months. The primary outcome measure, perceived daily functioning, is measured 6 months after start of rehabilitation and compared to baseline functioning.^{1}

A correlation coefficient is a number that shows if there is an association between variables. It provides an indication of the association between two variables X and Y (1). Two types of correlations are commonly used for continuous, numerical data. These are Pearson’s correlation coefficient and Spearman’s rank correlation coefficient.

No statistical question this time. Partly because I wasn’t asked a question, but also because of a recent Science Cafe organised by the Young Statisticians of the Netherlands Society for Statistics and Operations Research. The subject of this evening was ‘To

A hypothesis test is a method of statistical inference on sets of random variables, such as Hand Eczema Severity Index (HECSI) scores obtained from patients with hand eczema following treatment with hand creams “handy help” or “silky smooth”. If the values of the HECSI are normally distributed, a researcher can use Student’s t-test to compare the mean HECSI scores in both groups. The null hypothesis is that the mean scores are equal in both groups and the alternative hypothesis that the mean scores are not equal.

As a junior researcher I noticed that there are different opinions on when to choose nonparametric tests (like the Mann-Whitney or Kruskal-Wllis test) over parametric tests (like the independent samples *t*-test or ANOVA). Most researchers know that this decision should be made based on the distribution of the data: parametric tests for normally distributed outcomes, nonparametric tests for non-normal data. Therefore, in every beginners course on Statistics different ways to test/assess normality are discussed (histograms, QQ-plots, the Kolgomorov-Smirnov test, and the Shapiro-Wilk test).

Researchers usually present the characteristics of the participants in each group at the start of a study in a table. This table is often the first table in a paper and, hence, called Table 1. This table gives the reader an overview of the study participants and examines whether the participants are similar to patients he or she encounters. The reader can also use the information in the table to judge whether the participants in the two groups were comparable. Sometimes the two groups differ with respect to relevant demographic and clinical characteristics. Then it is important to correct for these differences in further analyses and take them into account when interpreting the results of the study.

I am analyzing data from a small randomized controlled clinical trial with two arms. Should I test whether there are differences in baseline characteristics between the two groups and present the p-values in Table 1 of my manuscript? What do the results of these tests mean for further analysis that I carry out?

In a prospective cohort study to propose a novel ultrasound scoring system for hand and wrist joints (US10) for evaluation of patients with early rheumatoid arthritis (RA), the researchers also investigated inter-observer reliability between two readers. Images from 20 randomly chosen patients (of the 48 patients included in the study) were evaluated for the inflammation and joint damage parameters of the joints included in the US10 score (second and third MCPs and PIPs and wrists), yielding a total of 200 images. A trained rheumatologist preformed the initial US examination, he had eight years of experience in US and was blinded to all other study findings. The 2^{nd} evaluation of the ultrasound images was performed by a rheumatologist, with five years of experie

In order to identify parameters that influence myocardial perfusion, a total of 70 patients were included in a multivariable linear regression model. A total of 19 different predictors were considered, of which 18 were measured on patient level (for example gender, age, BMI, smoking, medication, blood pressure) and 1 on coronary artery level (diameter of the coronary artery at stenosis).