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.

Relative risk is the probability of an outcome occurring in an exposed group as compared to the probability of that outcome in an unexposed group. In the scenario given, 50% of the children exposed developed the disease while only 10% of the children who were unexposed developed the disease. The relative risk was therefore 50/10=5. There is no further information about whether the study was controlled, the confidence interval, or the type of study. It therefore cannot be confirmed whether the chemical is causative and if it should be avoided.

To quantify differences between percentages you can use Fisher’s exact test.Odds ratios, relative risks and number needed to treat are ways of quantifying differences between percentages in two groups, however are not in themselves significance tests.

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).

A cohort study is a particular form of longitudinal study that samples a cohort (a group of people who share a defining characteristic, typically those who experienced a common event in a selected period, such as birth or graduation), performing a cross-section at intervals through time.
The relative risk (RR) or risk ratio is the ratio of the probability of an outcome in an exposed group to the probability of an outcome in an unexposed group. Relative risk is used in the statistical analysis of the data of experimental, cohort and cross-sectional studies, to estimate the strength of the association between treatments or risk factors, and outcomes.

Case control studies are observational studies which retrospectively determine whether a patient might have been exposed to a risk factor for a certain disease, as compared to a control group from the general population. They can be used for a range of outcomes as well as rare diseases. One of the biggest problems with this type of study is recall bias. Research subjects may selectively remember factors that are more predictive of the disease outcome when compared to the control group. All studies should have prior power calculations before the study commences.

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.

Relative risk = (Incidence in exposed group)/incidence in unexposed group). So in this case RR = (50/100)/(50/200) = 2.

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

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.