Statistical analysis

[reading time: 4 minutes]

The statistical analysis uses mathematical methods to analyze the results obtained in scientific studies with numerical outcomes, and evaluates their relevance.

Statistics can be of a descriptive type (for example, it can answer the question: “How much of the population of a city is over sixty?”) or of an inferential type, ie, it can study data of a population sample to assess whether they can be generalized to the whole population.

Simplifying the subject as much as possible, and for illustrative purposes only, it can be stated that researchers engaged in a typical clinical study divide the starting population into two groups and pose a question, for example like: “Will the intervention we intend to apply cause a difference between those who receive it and those who do not receive it?”

For the purpose of conducting a study, the scientific procedure starts from the assumption that the null hypothesis (H0) will be true, that is, it is assumed that the question will have to be answered in the negative, that is, the action applied will have no effect. In this case, at the end of the experiment there will be no differences between the groups, or the differences detected will be only casual or too small.

Whereas, when the differences are sufficiently big, or, to use technical language, statistically significant, it will be possible to accept the so-called alternative hypothesis, that is, it will be possible to say that the differences between the two groups are not casual. If this happens the researcher can answer positively to the research question, concluding that the intervention causes a difference between those who receive it and those who do not.

In fact, statistical analysis is used to provide the appropriate tools to measure the differences between groups, in order to understand whether there actually is a statistically significant difference. 

In order to perform the calculations, researchers can resort to many types of statistical tests, each with different characteristics that would make it more adequate for analyzing specific types of data. For example, the squared Chi-test can be used to compare two ratios or two percentages, while the Student’s t test can be used to compare the means between two groups.

Let us hypothesize that a number of researchers engaged in an RCT have collected the datasets, ie, the different numerical values referred to a certain initial time and a certain final time (before and after the intervention provided by the study project), calculated for each of the subjects included in the study group and for each of the subjects in the control group.

If the precise conditions of applicability are met for each of the tests, a statistical analysis can be carried out. Its aim will be to evaluate if there is a difference between the groups and, if so, to quantify it. 

In other words, the statistical analysis has to allow the researchers to find a value of probability, or p-value, which would allow them to estimate that the observed difference between the study groups is unlikely to be merely casual.

The numerical value of this probability is measured by the p-value, which, being a probability as such, can only range from 0 to 1. If the p-value is equal to 1, it means that the null hypothesis is met, that is, that there are no differences between the groups. The smaller the p-value, the greater the probability that the results are not casual.

If the researchers set a statistical significance level of 5%, in order to reject the null hypothesis and accept the alternative hypothesis, the p-value must be less than 0.05 (ratio of 1/20). The calculation of the p-value is obtained through spreadsheets formulae or through statistical softwares.

As a practical example a study by Fornari et al.¹ is mentioned here:

This study involved the administration of OMTh, an acronym that represents the international wording to indicate Osteopathic Manipulative Therapy, that is, the osteopathic manipulative treatment administered by practitioners without a degree in medicine, as opposed to OMT, which is the treatment given by osteopathic physicians.

The 20 participants had to perform a 5-minute arithmetic task before a panel of three people (stressor), then half of them received a single session of OMTh.

Electrocardiographic recordings were made before and after the session, assessing heart rate and HRV, to establish the LF:HF ratio, considered an index of sympato-vagal balance. Saliva samples were also collected to determine the cortisol levels.

The statistical analysis revealed statistically significant differences (p < 0.05) between the study group, treated with craniosacral techniques, and the control group, which received a simulated therapy.

For more complete information please refer to the quoted article1, to the extensive literature on the subject and to the volume edited by Francesco Cerritelli and Diego Lanaro².

Bibliography

1. Fornari M, Carnevali L, Sgoifo A. Single Osteopathic Manipulative Therapy Session Dampens Acute Autonomic and Neuroendocrine Responses to Mental Stress in Healthy Male Participants. J Am Osteopath Assoc. 2017 Sep 1;117(9):559-567.
2. Cerritelli F, Lanaro D. Elementi di ricerca in osteopatia e terapie manuali. Napoli: Edises, 2018.