Chi-square test is used to determine the statistically significant different between categorical variables. It also determines the difference between expected frequencies and the observed frequencies.

Mann Whitney U test is used to determine the statistically significant different between two independent groups.

Wilcoxon’s test is the test of dependency. it determines the statistically significant difference between two dependent groups.

Student t-test is one of the most commonly used method to test the hypothesis. It determines the significant difference between the means of two different groups.

ANOVA (analysis of variance) is similar to student’s t-test.

ANOVA is a statistical method used to determines the statistically significant difference between the mean of more than two group. In this experiment as we are dealing with three different group, ANOVA is most suitable test to determine the difference between each groups.

The degree of correlation is summarised by the correlation coefficient (r). This indicates how closely the points lie to a line drawn through the plotted data. In parametric data this is called Pearson’s correlation coefficient and can take any value between -1 to +1. A correlation of -1.0 indicates a perfect negative correlation, and a correlation of 1.0 indicates a perfect positive correlation.

For example

r = 1 – strong positive correlation (e.g. systolic blood pressure always increases with age)

r = 0 – no correlation (e.g. there is no correlation between systolic blood pressure and age)

r = – 1 – strong negative correlation (e.g. systolic blood pressure always decreases with age)

Whilst correlation coefficients give information about how one variable may increase or decrease as another variable increases they do not give information about how much the variable will change. They also do not provide information on cause and effect.

In contrast to the correlation coefficient, linear regression may be used to predict how much one variable changes when a second variable is changed.

Recall bias introduced when participants in a study are systematically more or less likely to recall and relate information on exposure depending on their outcome status.

In procedure bias, the researcher decides assignment of a treatment versus control and assigns particular patients to one group or the other non-randomly. This is unlikely to have occurred in this case, although it is not mentioned specifically.

Self Selection or volunteer bias occur when those subjects are selected to participate in the study who are not the representative of the entire target population. those subjects may be from high socio-economic status and practice those activities or lifestyle that improves their health.

Lead-time bias occurs when a disease is detected by a screening test at an earlier time point rather than it would have been diagnosed by its clinical appearance. In this bias, earlier detection improves the survival time in the intervention group.

68% of the population will be found in one standard deviation (SD) above plus one SD below the mean. Two SDs above plus two SDs below the mean will include 95% of the population.

The median can be greater or less than the mean as it is simply the mid point of the data after the data is arranged. Half the data are above and half below the median .

The mode is a true score, unlike the mean or the median. It is the most common score or the score obtained from the largest number of subjects in any given data.

The null hypothesis states that there is no significant difference between two groups.

The alternative hypothesis states that there is a significant difference between two groups.

A type I error (false positive) occurs when a null hypothesis is rejected when it should be accepted.

A type II error (false negative) occurs when the alternative hypothesis is rejected when it should be accepted.

The probability determines the rejection of a null hypothesis.

The level of significance is set at p <0.05.

The normal distribution is a symmetrical, bell-shaped distribution in which the mean, median and mode are all equal.

In statistical terms, correlation is used to denote association between two quantitative variables.

The degree of association is measured by a correlation coefficient, denoted by r. The correlation coefficient is measured on a scale that varies from + 1 through 0 to – 1. Complete correlation between two variables is expressed by either + 1 or -1. When one variable increases as the other increases the correlation is positive; when one decreases as the other increases it is negative. Complete absence of correlation is represented by 0.

The two methods are not synonymous as correlation measures the degree of relationship between two variables whereas regression analysis is about how one variable affects another or what changes it has on the other variable. Both are also shown by a different graphical representation.

Incidence tells us about the number of new cases that have been reported while prevalence gives us the idea of existing cases.

In this particular instance, the parameter of the study i.e. the total number of cases has not changed thus the prevalence of the disease remains same. Although, more cases have been reported in the second instance as a result of which incidence has increased.

The question mentions a quantitative, ratio scale data set. The use of mean would be ideal under normal circumstances, however, in this situation median is preferred as it is less sensitive to the skewness of data. The median is usually preferred to other measures of central tendency when your data set is skewed (i.e., forms a skewed distribution)

The correlation coefficient gives us the idea about relation between two parameters. i.e. to what extent change in parameter A could prompt a change in parameter B. The numerical value of correlation coefficient could not be greater than 1.

Linear regression, using a technique called curve fitting, allows us to make predictions regarding a certain variable.

Correlation coefficient gives us an idea whether or not the two parameters provide have any relation of some sort or not i.e. does change in one prompt any change in other?

9 & 27 can be obtained by subtracting and adding 9 from the mean. 9 is three times the standard deviation and we know that 99.7% values lie within 3 standard deviations from the mean. We can find the interval for 99.7% to verify in the following way:

For 99.7% confidence interval, you can find the range as follows:

1. Multiply the standard error by 3.

2. Subtract the answer from mean value to get the lower limit.

3. Add the answer obtained in step 1 from the mean value to get the upper limit.

4. The range turns out to be 9-27 kg.

Being the part of a meta analysis, forest plots are more valued as evidence then randomised control trials.

The notion that forest plots can only be used if the results are substantial is not true. They are good indicators of the significance of the data. If the diamond intersects the central line, the data is rendered significant. It also aggregates means and confidence intervals from studies conducted in the past which makes the study much more reliable as errors associated with individual studies tend to have less of an impact in this way.

The suggestion that forest plots are primarily used for qualitative data is factually incorrect. Forest plots require numerical values to function.

All in all, forest plots help us in determining whether or not there is a significant trend in that particular field of study.

Standard error can be calculated by the following formula:

Standard Error= (Standard Deviation)/√(Sample Size)
= (12) / √(64)
= 12 / 8
= 1.5

When the association among any two classes of object is defined by the presence of a third entity it is termed as indirect association. For an instance, the age of the employee may affect the rate of pay, which would have implications on job satisfaction. So, in this example, an indirect relationship between age and job satisfaction exists due to a third party i.e. rate of pay.

Number needed to treat is a measure of the impact of a treatment or intervention that is often used to communicate results to patients, clinicians, the public and policymakers. It states how many patients need to be treated for one additional patient to experience an adverse outcome (e.g. a death).

It is calculated as the inverse of the absolute risk reduction and is rounded to the next highest whole number.

The absolute risk reduction is 8% (16% – 8%). 100/8 = 12.5, so rounding up the next integer this gives at NNT of 13. i.e. you would need to give the new drug to 13 people to ensure that you prevented one death.

Variance and standard deviation indicate the dispersion of the plot from mean value and thus are not really helpful in summarizing the mean.

Range is the difference between maximum and minimum value that is 45 in this case.

The mean in this case is 6.2 due to the presence of an outlier 45. In the presence of outlier mean can be misleading as it is quite sensitive to skewness in data.

Mode is the most frequent value. In this case mode has 4 values: 0,1,2,4.

In case of skewedness, median is the most apt representative of the mean as it is not affected by outliers. In this case since the data set has even values i.e. 10. Median is the average of the 5th & 6th entry after arranging the data in ascending order like that in case of the question (0,0,1,1,2,2,3,4,4,45). This turns out to be 2.

Its known that 68.3% of the total values of a normally distributed variable are found within a range of 1 standard deviation from the mean which makes the range to be 4.3 to 4.9 mmol/L.

Also known as the “product limit estimate’’, the Kaplan-Meier survival plot is used to estimate the true survival function from the collected data.

Using this plot, probabilities of occurrence of an event at a certain point in time can be computed. The successive probabilities are multiplied by any earlier computed probabilities to get the final estimate. For a given population, the survival probability at any particular time on the plot = (number of subjects living at the start – number of subjects who died)/number of subjects living at the start.

The description of a scatter plot is a graphical representation using Cartesian coordinates to display values for more than two variables for data set. It is used for to assess the relationship between 2 different variables.

For establishing a cause effect relationship, following criteria must be met:

1. Coherence & Consistency

2. Temporal Precedence

3. Specificity

As can be seen, sensitivity (The probability of a positive test) is not among these deciding factors..

The correct answer is the mean, median and mode of normally distributed data are the same value. This is as a result of the bell shaped curve which is equal on both sides.

The bell-shape indicates that values around the mean are more frequent in occurrence than the values farther away.

In a normal distribution:
1) +/- one standard deviation of the mean accounts for 68% of the data.
2) +/- two standard deviations of the mean accounts for 95% of the data.
3) +/- three standard deviations of the mean accounts for 99.7% of the data.

Work up bias involves comparing the novel diagnostic test with the current standard test. A portion of the patients undergo the standard test while others undergo the new test as the standard test is costly. The result can be alteration in specify and sensitivity.

Recall bias is specifically appropriate to the case control studies that is when ever the memories retrieved by the participants differ in accuracy.

Not publishing the results of a valid study just because they are negative or uninteresting can be termed as publication bias.

When information gathering is ill suited with respect to time i.e. collecting the data regarding a fatal disease many years after the death of its patients, it is termed as Late – look bias.

The case in point is an instance of lead time bias when upon comparing two tests, one is able to detect the condition earlier than the other but the overall outcome doesn’t change. There is a possibility that this will make the survival rates for the newer test look more promising.

Phase 2 trials involve patients that are suffering from the disease under study and are associated with determining the efficiency and the optimum dosage of the drug.

Phase 0 trials assist the scientists in studying the behaviour of drugs in humans by micro dosing patients. They are used to speed up the developmental process. They have no measurable therapeutic effect and efficiency.

Phase 1 is associated with assessing whether a drug is safe to use or not. The process is extensive and can take up to several months. It also involves healthy participants (less than 100) that are paid to take part in the study. The side effects upon increasing dosage are also addressed by the study. The effects the drug has on humans including how its absorbed, metabolized and excreted are studied. Approximately 70% of the drugs pass this phase.

Phase 0 trials assist the scientists in studying the behaviour of drugs in humans by micro dosing patients. They are used to speed up the developmental process. They have no measurable therapeutic effect and efficiency.

Level 1 – High-quality randomised controlled trial with statistically significant difference or no statistically significant difference but narrow confidence intervals (prospective controlled)

Level 2 – Prospective comparative study (prospective uncontrolled)

Level 3 – Case-control study, retrospective comparative study (retrospective controlled)

Level 4 – Case series (retrospective uncontrolled)

Level 5 – Expert opinion.

ANOVA is based upon within group variance (i.e. the variance of the mean of a sample) and between group variance (i.e. the variance between means of different samples). The test works by finding out the ratio of the two variances mentioned above. (Commonly known as F statistic).

Boyle’s law is correctly stated as it states that the volume of a gas of known mass is inversely proportional with absolute pressure, at a constant temperature.

Beer’s law states that radiation absorption by a solution of known thickness and concentration is identical to that of a solution of double thickness and half concentration.

Bougner’s (or Lambert’s) law states that every layer with the same thickness will absorb the same amount of radiation as it passes through.

Graham’s law states that the diffusion rate of a gas is inversely related to the square root of its molecular weight.

Raoult’s law states that the reduction of a solvent’s vapour pressure is directly proportional to the solute’s molar concentration.

Funnel plot is essentially a scatterplot of the effect of treatment against a particular measure of study precision. Its primal purpose is to serve as a visual aid and help in detection of bias or systematic heterogenity.

In general practice, majority of phase 3 trials and some of the trials conducted in phase 2 are randomized. Because phase 4 trials require a huge sample size, they are not randomized as much. The primal reason behind conducting phase 3 trials is to test the efficiency and safety in a significant sample population. At this point it is assumed that the drug is effective up to a certain extent.

During a case-control study, subjects that exhibit outcomes of interest are compared with those who don’t show the expected outcome. The extent of exposure to a particular risk factor is then matched between cases and controls. If the exposure among cases surpasses controls, it becomes a risk factor for the outcome that is being studied.

Pilot studies are conducted on a lower and much smaller level, to assess if a randomized controlled trial of the crucial components of a study will be plausible.

Phase 4 trials are the ones that are conducted after its established that the drug is effective and is approved by the regulating authority for use. These trials are concerned with the side effects and potential risks associated with the long term usage of the drug.

Randomized controlled trails will be analysed by the intention-to-treat (ITT) approach. It provides unbiased comparisons among the treatment groups. ITT analyses are done to avoid the effects of dropout, which may break the random assignment to the treatment groups in a study.

ITT analysis is a comparison of the treatment groups that includes all patients as originally allocated after randomization.

In order to include such participants in an analysis, outcome data could be imputed which involves making assumptions about the outcomes in the lost participants.