Standard deviation is defined as the measure of dispersion of a set of data from its mean. It measures the absolute variability of a distribution| the higher the dispersion or variability, the greater is the standard deviation and greater will be the magnitude of the deviation of the value from their mean.

Prevalence:

This is the proportion of individuals in a population who have a specific condition, disease, or attribute at a given point in time or over a specific period.

Incidence:

This is the number of new cases of a specific condition, disease, or attribute that develop in a population during a specified period of time.

Specificity:

This refers to the ability of a test to correctly identify those without the condition (true negative rate).

Sensitivity:

This refers to the ability of a test to correctly identify those with the condition (true positive rate).

Probability:

This is a measure of the likelihood that an event will occur. In the context of diseases, it can refer to the likelihood of developing a condition.

The Chi-squared test would have been a useful test to compare the proportions in the scenario. However, due to the small sample size, Fisher’s exact test can be applied to analyse the significance of the difference. Adequate information is not given to determine what sample sizes were used to test the efficacy of the treatment, and to tell whether the treatment should be discontinued without further analysis on the data.

The main aim of randomisation in a clinical trial is to remove the bias and avoid any potential confounding variables. While in double blind studies both the investigators and the patients are not aware of which group they belong in, being blind is not essential in carrying out a randomized study, nor is it essential that the randomisation be done away from the study centre. A placebo also does not facilitate randomisation, which can be done in single centre and multi-centre trials.

Crossover trials are characterized by the switching of study participants throughout the treatment groups, keeping a random order of switching. This randomization is important to determine any carry-over effect of different treatment modalities. The benefit of this study is the evaluation of the efficacy of various short-term treatment options for the relief of chronic conditions. The washout period is small in this type of study. Crossover studies are more efficient than the parallel studies, but they should be used according to the treatment options and outcomes.

Linear regression is a basic and commonly used type of predictive analysis. The overall idea of regression is to examine two things: (1) do a set of predictor variables do a good job in predicting an outcome (dependent) variable? (2) Which variables, in particular, are significant predictors of the outcome variable, and in what way do they–indicated by the magnitude and sign of the beta estimates–impact the outcome variable.These regression estimates are used to explain the relationship between one dependent variable and one or more independent variables. Three major uses for regression analysis are (1) determining the strength of predictors, (2) forecasting an effect, and (3) trend forecasting

The equation, lung function = 3.2 + (1.7 x height) is linear, but this does not necessarily mean that the relationship itself is linear. The equation is able to predict that taller individuals are more likely to have greater lung functions. No information is given on whether the coefficients and the R value are statistically significant.

Before the test, the patient was likely to have the disease being tested for. Their pre test odds were 2, making them twice as likely to have the disease. After testing positive, their pretest odds of 2 and the likelihood ratio of 3 are multiplied to produce 6 as the post test odds. The patient is now 6 times as likely to have the disease after the test. Likelihood ratios above 10 or below 0.1 are strong evidence to rule in and rule out a diagnosis. The negative likelihood ratio is not known here, but does not subtract from the interpretation of the outcomes in this patient.

The level of statistical significance is often expressed as a p-value between 0 and 1. The smaller the p-value, the stronger the evidence that you should reject the null hypothesis.A p-value less than 0.05 (typically ≤ 0.05) is statistically significant. It indicates strong evidence against the null hypothesis, as there is less than a 5% probability the null is correct (and the results are random). Therefore, we reject the null hypothesis, and accept the alternative hypothesis.However, this does not mean that there is a 95% probability that the research hypothesis is true. The p-value is conditional upon the null hypothesis being true is unrelated to the truth or falsity of the research hypothesis.A lower p-value is sometimes interpreted as meaning there is a stronger relationship between two variables. However, statistical significance means that it is unlikely that the null hypothesis is true (less than 5%).To understand the strength of the difference between two groups (control vs. experimental) a researcher needs to calculate the effect size.

An odds ratio (OR) is a measure of association between an exposure and an outcome. The OR represents the odds that an outcome will occur given a particular exposure, compared to the odds of the outcome occurring in the absence of that exposure. Odds ratios are most commonly used in case-control studies, however they can also be used in cross-sectional and cohort study designs as well (with some modifications and/or assumptions). Wherea = Number of exposed casesb = Number of exposed non-casesc = Number of unexposed casesd = Number of unexposed non-casesOR=(a/c) / (b/d) = ad/bc