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Incidence in exposed is 50/500 = 0.10 and in unexposed is 10/500 = 0.02; relative risk is the ratio 0.10/0.02 = 5.0.
Prevalence counts all existing cases (old and new) in a population at a defined moment, which is the standard way to express the total burden of a chronic disease. Incidence measures only new cases, and case fatality and attack rate describe outcome severity and outbreak spread respectively.
Sensitivity is true positives divided by all people with disease: 180/200 = 0.90, or 90%. It is computed only among the diseased and is unaffected by the number of disease-free people tested.
A prospective cohort measures exposure before the outcome occurs, so the temporal sequence is known. Case-control, cross-sectional and ecological designs generally cannot establish that exposure preceded disease at the individual level.
Case-control sampling selects on outcome, so the incidence in exposed and unexposed cannot be computed directly; the odds ratio is the estimable measure of association. It approximates the risk ratio only when the outcome is rare.
Standard deviation quantifies spread around the mean, whereas mean, median and mode are all measures of central location. Dispersion measures describe variability, not the typical value.
Random allocation distributes both measured and unmeasured confounders, on average, equally across arms, supporting a causal interpretation. It does not itself ensure blinding, change sample size requirements, or remove measurement error.
The p-value is the probability of observing data at least as extreme as those obtained, calculated under the assumption that the null hypothesis holds. It is not the probability that the null is true, nor a measure of effect size or replicability.
Direct standardization applies the standard population age weights to district age-specific death rates. With mortality increasing with age, giving more weight to older groups can raise the rate, consistent with a district younger than the standard population.
When prevalence is very low, the large number of disease-free people generates many false positives even with good specificity, so most positives are false and PPV is low. Predictive values depend on prevalence, unlike sensitivity and specificity.
Using prevalent cases preferentially includes those who survived long enough to be ascertained, and their exposure profile may differ from incident cases, producing prevalence-incidence bias. Recall and interviewer bias can occur in any interview study, and loss to follow-up applies to cohort designs.
A chi-square of 6.0 exceeds the 3.84 critical value for one degree of freedom at alpha 0.05, so the null hypothesis of no association is rejected. Degrees of freedom for a 2x2 table are (2-1)(2-1) = 1.
Matching forces controls to resemble cases on selected variables, preventing those variables from confounding the exposure-disease association. It does not alter disease prevalence, remove the need for controls, or eliminate random error.
A confidence interval spanning zero includes the null value, so the observed data do not exclude no effect in either direction. The interval describes a range of plausible values for the parameter, not the probability that a specific value is true.
Attributable risk is the difference in incidence between exposed and unexposed, representing the absolute excess risk due to exposure. Ratio measures such as the odds ratio and prevalence ratio express relative, not absolute, excess.
A single narrow peak occurring within one incubation period is typical of a brief common exposure affecting many people at once (point source). Propagated outbreaks show successive generations of cases, and continuing sources show a plateau.
Because the confidence interval excludes 1.0, the null hypothesis of no association is rejected at the 5% level. The interval also shows the estimate is imprecise, but significance is determined by exclusion of the null value.
The control group supplies the counterfactual comparison, allowing the effect of the intervention to be separated from background change. Its role is not to enlarge the sample, monitor delivery, or measure baseline prevalence.
The 95% confidence interval is the estimate plus or minus 1.96 standard errors, here 130 +/- 3.92, giving roughly 126 to 134 mmHg. The standard error, not the standard deviation, is used for the interval of the mean.
Lead-time bias arises because earlier detection advances the date of diagnosis without postponing death, artificially lengthening measured survival. Length bias and other biases involve selection of slower-growing cases or differential data collection.
Attributable fraction among the exposed equals (risk in exposed minus risk in unexposed) divided by risk in exposed: (0.20-0.10)/0.20 = 0.50, or 50%. It represents the proportion of disease in the exposed that would be avoided if the exposure were removed.
Kappa is (observed agreement minus chance agreement) divided by (1 minus chance agreement): (0.80-0.50)/(1-0.50) = 0.60. It corrects the crude agreement for agreement expected by chance.
Exponentiating a logistic regression coefficient yields an odds ratio, here adjusted for the other covariates in the model. It compares the odds of the outcome in the exposed with the unexposed.
Number needed to treat is the reciprocal of the absolute risk reduction; a value of 25 means 25 patients must be treated to prevent one additional adverse outcome. It reflects absolute benefit, not relative reduction or harm.
Ecological studies analyse aggregated data, so an association between group averages may not reflect the individual-level relationship, a problem known as the ecological fallacy. Rates can be calculated and randomization is not part of ecological design.
Incidence rate measures new cases arising in a population over a defined period, with the population at risk in the denominator. Prevalence counts existing cases at a point or over a period, not new ones.
Skewed data are best summarized by the median with the interquartile range, which are resistant to extreme values. Mean and standard deviation are unduly influenced by outliers in skewed distributions.
Prevalence is the number with the condition divided by the total population examined: 100/500 = 0.20, or 20%. The denominator must be the whole sample, not only the smokers.
A cross-sectional study assesses exposure and outcome simultaneously, so the temporal order between them cannot be determined. Cohort studies and trials follow participants forward in time or reconstruct exposure before outcome.
The odds ratio is (a/c)/(b/d) = (120/80)/(120/280) = 1.5/0.4286 = 3.0. It compares the odds of exposure among cases with the odds of exposure among controls.
Relative risk is the incidence in exposed divided by incidence in unexposed: (80/1000)/(20/1000) = 0.08/0.02 = 4.0. It expresses how many times more likely disease is among the exposed.
Positive predictive value depends on prevalence as well as on sensitivity and specificity, and it declines sharply when disease is rare because most positive results are false positives. Sensitivity and specificity are intrinsic test characteristics independent of prevalence.
Because the confidence interval includes zero, the data are compatible with no true difference at the 5% significance level. The interval also extends to a clinically meaningful benefit, so the trial is inconclusive rather than proof of equivalence.
The rate is 60/3000 = 0.02 per person-year, which multiplied by 1000 gives 20 per 1000 person-years. Person-time denominators are used when follow-up duration varies between individuals.
Controls should be drawn from the same underlying population as the cases so that exposure distribution is comparable apart from disease status. This is the principle of comparable selection, which limits selection bias.
An independent samples t-test compares means of two unrelated groups when the outcome is approximately normal. The paired t-test applies only to matched or repeated measurements.
A correlation of -0.75 indicates a fairly strong negative linear relationship, meaning higher activity tends to accompany lower body mass index. Correlation quantifies association only and does not establish causation.
Funnel plot asymmetry, especially when small studies cluster on one side, suggests that studies with null or unfavourable results were not published. This is a classic graphical signal of publication bias.
Power is the probability of detecting a true effect, and higher power requires a larger sample to reduce the chance of a type II error. Increasing power from 80% to 90% therefore increases the required sample size.
The standardized incidence ratio is observed divided by expected: 45/30 = 1.5, meaning 50% more cases occurred than would be expected from the reference rates. Values above 1 indicate excess incidence.
Prevalence counts all existing cases (old and new) in a population at a defined moment, so it expresses the burden of disease at a point in time. Incidence measures new cases over a period and case fatality describes deaths among cases.
Attributable risk (risk difference) is the incidence in the exposed minus the incidence in the unexposed, giving the absolute excess risk due to exposure. The odds ratio and prevalence ratio are relative measures and do not give absolute excess.
Low specificity means many people without disease test positive, and when prevalence is low these false positives dominate, so the positive predictive value falls. Sensitivity affects the detection of true cases, not the proportion of positives who are truly diseased.
A prospective cohort follows exposed and unexposed people forward in time, so exposure is documented before outcome, establishing temporality. Case-control and cross-sectional designs assess exposure and outcome at similar times and cannot confirm sequence.
Consistency, meaning replication of the association in different populations and by different designs, supports causality by making confounding and bias less likely. Sample size, measurement tools and p values affect precision but not the causal interpretation.
Random allocation distributes both measured and unmeasured confounders evenly between groups so that differences in outcome can be attributed to the intervention. It does not affect sample size, measurement bias or blinding.
Primary prevention acts before disease occurs by removing or reducing exposure or increasing resistance, as with vaccination. Screening and early treatment act on existing but asymptomatic disease, and rehabilitation acts after disease has caused disability.
When a sufficient proportion of a population is immune, chains of transmission are interrupted, indirectly protecting those who are not immune. It does not act through individual protection of vaccinated people, whose immunity is direct.
Live attenuated vaccines such as MMR can replicate and cause disease in severely immunocompromised people, so they are contraindicated. Inactivated and toxoid vaccines do not carry this risk.
Infant mortality rate reflects the combined effect of socioeconomic conditions, nutrition, environment and health care on a vulnerable group, making it a sensitive summary measure of population health. The other options describe health system inputs or resources rather than health outcomes.