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.

The P value is defined as the probability under the assumption of no effect or no difference (null hypothesis), of obtaining a result equal to or more extreme than what was actually observed. The P stands for probability and measures how likely it is that any observed difference between groups is due to chance. Being a probability, P can take any value between 0 and 1. Values close to 0 indicate that the observed difference is unlikely to be due to chance, whereas a P value close to 1 suggests no difference between the groups other than due to chance. Thus, it is common in medical journals to see adjectives such as “highly significant” or “very significant” after quoting the P value depending on how close to zero the value is.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.

While the results of this before and after study can provide some preliminary insight into the effects of the dietary intervention, the results should be viewed with great caution as they may be considered merely anecdotal. The lack of a control group contributes to confounding the data. Therefore, while the difference may be statistically significant and the confidence interval is compatible with a fall in the number of seizures after therapy, the results cannot be introduced as the standard without a control group to compare with.

Correlation is a bivariate analysis that measures the strength of association between two variables and the direction of the relationship.Pearson r correlation: Pearson r correlation is the most widely used correlation statistic to measure the degree of the relationship between linearly related variables. Pearson’s correlation coefficient is the test that measures the statistical relationship, or association, between two continuous variables. It is known as the best method of measuring the association between variables of interest because it is based on the method of covariance. It gives information about the magnitude of the association, or correlation, as well as the direction of the relationship.The non-parametric Spearman or Kendall rank correlation coefficient is used if neither variable has a normal distribution or the sample size is small (i.e. <20).

The sensitivity of a screening test can be described in a variety of ways, typically such as sensitivity being the ability of a screening test to detect a true positive, being based on the true positive rate, reflecting a test’s ability to correctly identify all people who have a condition, or, if 100%, identifying all people with a condition of interest by those people testing positive on the test.The specificity of a test is defined in a variety of ways, typically such as specificity is the ability of a screening test to detect a true negative, being based on the true negative rate, correctly identifying people who do not have a condition, or, if 100%, identifying all patients who do not have the condition of interest by those people testing negative on the test.Sensitivity=[a/(a+c)]×100Specificity=[d/(b+d)]×100a: True positiveb: False Positivec: False negatived: True negative

Power calculations are a important step in study design and preparation, but do not directly help with the interpretation of the results. They are used to determine how many subjects are needed in order to avoid errors in accepting or rejecting the null hypothesis. These calculations are not usually complex and for the best results, the power of the test should be set to above 80%.

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.

A case–control study (also known as case–referent study) is a type of observational study in which two existing groups differing in outcome are identified and compared on the basis of some supposed causal attribute. Case–control studies are often used to identify factors that may contribute to a medical condition by comparing subjects who have that condition/disease (the cases) with patients who do not have the condition/disease but are otherwise similar (the controls).
An odds ratio (OR) is a statistic that quantifies the strength of the association between two events, A and B. The odds ratio is defined as the ratio of the odds of A in the presence of B and the odds of A in the absence of B or vice versa.

A written protocol is important in clinical research as it helps to decrease bias with early findings as the process of the trial has been documented in advance. To show that the study has been properly undertaken before commencing, the investigators must document their names| they must describe the process, detail the analysis that will be undertaken, and provide a power calculation. The ethics committee does not always need to see the protocol.

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.

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

Case control studies are used to determine the relationship between exposure to a risk factor and the resultant outcomes. It finds patients in the general population who have a certain condition and retrospectively searches for past exposure to possible risk factors for the disease. Controls are people who do not have the disease found in the general population. This type of study is useful for rare diseases, and is less time consuming to conduct. While cohort studies can be used to study rare diseases they measure the relative risk of developing the disease over time based on exposure. Ecological or cross-sectional studies attempt take a snapshot of a whole population, and thus are inappropriate for rare diseases as larger sample numbers are needed. A randomised control trial is better suited to determine the effect of an intervention.

The Chi squared test is used to find the relationship between two variables, determining whether they are not independent of each other. This test of statistical significance allows you to determine the degree of confidence with which you can accept or reject the null hypothesis. The student t test compares the significant differences in data means, while rank correlation, linear regression and the correlation coefficient all help to measure the linear relationship between variables.

In the final result of this double blind study, 25% or one in four of patients who received the treatment responded positively. Though the difference is significant at P<0.05, it is better to present this as a significant difference at 0.4%. The number needed to treat (NNT) is defined as the inverse of the absolute risk reduction. Taking this as 0.25 (25%), the NNT is 1/0.25 = 4. However given the 95% confidence interval is between 10-50% for absolute risk reduction, the NNT with 95% CI is between 2 and 10. Therefore we cannot say with certainty that the NNT is at least 4.

The main result of a correlation is called the correlation coefficient (or r). It ranges from -1.0 to +1.0. The closer r is to +1 or -1, the more closely the two variables are related.If r is close to 0, it means there is no relationship between the variables. If r is positive, it means that as one variable gets larger the other gets larger. If r is negative it means that as one gets larger, the other gets smaller (often called an inverse correlation).

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.

If the 95% confidence interval contains zero (more precisely, the parameter value specified in the null hypothesis), then the effect will not be significant at the 0.05 level.If the 95% CI for the DIFFERENCE between the 2 groups contains the value 0, this means that the p-value will be greater than 0.05. Conversely, if the 95% CI does not contain the value 0, then the p-value will be strictly less than 0.05. The same applies when comparing groups using a ratio, such as an odds ratio or risk ratio. When using a RATIO instead of a DIFFERENCE, the situation of no difference between the 2 groups will be indicated by a value of 1 instead of 0. If the ratio equals to 1, the 2 groups are equal. Hence, if the 95% CI of the ratio contains the value 1, the p-value will be greater than 0.05. Alternatively, if the 95% CI does not contain the value 1, the p-value is strictly less than 0.05.

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.

Odds ratios are best described as the odds of an event in one group divided by the odds of the event in another. They form an alternative to the relative risk in case–control studies and are close to the relative risk when events are rare. The odds are the number of the event divided by the number without the event, which is less intuitive than the risk, which is the number with the event divided by the total. Odds ratios are therefore less intuitive than relative risks. Logistic regression analysis outputs variable coefficients which are the log of the odds ratio.

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