1. Name: Forest plot (Blobbogram).
2. Arrowed figure: Diamond (representing the pooled/summary effect estimate; the width of the diamond represents the 95% confidence interval).
3. Best association: Study by Kalyan (shows greatest effect size / precision).
4. Usage: Systematic reviews and Meta-analyses.

1. Odds Ratio Calculation:
   $\text{Odds in Acupuncture group}=\frac{a}{b}=\frac{12}{15}=0.80$
   $\text{Odds in Medication group}=\frac{c}{d}=\frac{6}{14}=0.428$
   $\text{Odds Ratio (OR)}=\frac{a\times d}{b\times c}=\frac{12\times 14}{15\times 6}=\frac{168}{90}\approx 1.87$

2. Interpretation:
   The odds of clinical improvement in depression are approximately $1.87$ times (nearly double) higher in the acupuncture group compared to the standard medication group.

1. Child Survival Index (CSI):
   $\text{Child Survival Index}=\frac{1000-\text{Under-5 Mortality Rate}}{10}=\frac{1000-8}{10}=\frac{992}{10}=99.2\mathrm{\%}$

2. Epidemiological Formulas:

   • Incidence:
     $\text{Incidence}=\frac{\text{Number of new cases of disease during a specified period}}{\text{Total population at risk during the same period}}\times 1000$
   • Prevalence:
     $\text{Prevalence}=\frac{\text{Number of existing (old + new) cases at a given point/period}}{\text{Total estimated population at that time}}\times 100$
   • Stillbirth Rate:
     $\text{Stillbirth Rate}=\frac{\text{Fetal deaths }\ge 28\text{ weeks gestation / birthweight }\ge 1000\text{ g}}{\text{Total births (live births + stillbirths)}}\times 1000$

3. Attack and Fatality Rates:

   • Case Fatality Rate (CFR):
     $\text{CFR}=\frac{\text{Total deaths due to a specific disease}}{\text{Total diagnosed cases of that disease}}\times 100$
   • Attack Rate:
     $\text{Attack Rate}=\frac{\text{Number of new cases during an epidemic/outbreak}}{\text{Total susceptible population at risk}}\times 100$
   • Secondary Attack Rate (SAR):
     $\text{SAR}=\frac{\text{Number of secondary cases among contacts within incubation period}}{\text{Total susceptible contacts exposed to primary case}}\times 100$

1. Name: Box-and-Whisker Plot (Box Plot).
2. Use: Displays a 5-number statistical summary of a continuous numerical variable (minimum, 25th percentile, median, 75th percentile, maximum, and potential outliers/skewness).
3. Components:
   • Point A: Median (50th percentile / second quartile $Q_2$).
   • Point B: Lower quartile (25th percentile / first quartile $Q_1$).
   • Point B1: Upper quartile (75th percentile / third quartile $Q_3$).
   • (The interquartile range $\text{IQR}=Q_3-Q_1$ forms the central box).

1. Relative Risk (RR) Calculation:

   • $\text{Incidence in exposed (Smokers)}=\frac{70}{7000}=0.010=10\text{ per }1000$
   • $\text{Incidence in non-exposed (Non-smokers)}=\frac{2}{3000}\approx 0.00067=0.67\text{ per }1000$ (or $\frac{1}{1000}$ rounded)
   • $\text{Relative Risk (RR)}=\frac{\text{Incidence in exposed}}{\text{Incidence in non-exposed}}=\frac{70/7000}{2/3000}=\frac{0.010}{0.000667}=15\text{ (or }\frac{10}{1}=10\text{)}$

2. Interpretation:
   Smokers have a 10 to 15 times higher risk of developing lung cancer compared to non-smokers. Relative Risk measures the strength of association between an exposure and disease in prospective cohort studies.

1. Positive Predictive Value (PPV):
   $\text{PPV}=\frac{A}{A+B}=\frac{95}{95+15}=\frac{95}{110}=86.36\mathrm{\%}$

2. Negative Predictive Value (NPV):
   $\text{NPV}=\frac{D}{C+D}=\frac{200}{10+200}=\frac{200}{210}=95.24\mathrm{\%}$

3. Sensitivity and Specificity:

   • Sensitivity:
     $\text{Sensitivity}=\frac{A}{A+C}=\frac{95}{95+10}=\frac{95}{105}=90.48\mathrm{\%}$
   • Specificity:
     $\text{Specificity}=\frac{D}{B+D}=\frac{200}{15+200}=\frac{200}{215}=93.02\mathrm{\%}$

1. Definitions:

   • Median ($Q_2$): The middle value of an ordered dataset such that 50% of observations fall below and 50% above it.
   • 1st Quartile ($Q_1$): 25th percentile (25% of observations lie below, 75% above).
   • 3rd Quartile ($Q_3$): 75th percentile (75% of observations lie below, 25% above).

2. Rate vs Ratio:

   • Rate: Numerator is a component/part of the denominator and involves a time dimension (e.g., mortality rate).
   • Ratio: Quantifies the relationship between two independent quantities; numerator is not part of the denominator (e.g., male-to-female ratio).

3. Case-Control vs Cohort:

   • Case-Control Study: Retrospective; starts from outcome/disease (cases vs controls) and looks backward for antecedent exposures (yields Odds Ratio).
   • Cohort Study: Usually prospective; starts from exposure status (exposed vs unexposed) and follows subjects forward to evaluate disease occurrence (yields Relative Risk and Incidence).

4. Incidence vs Prevalence:

   • Incidence: Rate of occurrence of new cases in a population at risk during a specified period.
   • Prevalence: Proportion of all existing cases (both old and new) in a population at a specific point in time (point prevalence) or period of time.

• Ordered data ($n=18$):
  $71,71,75,75,75,75,77,77,79,79,81,81,83,83,84,84,95,95$

1. Mean ($\bar{x}$):
   $\bar{x}=\frac{\sum x}{n}=\frac{1440}{18}=80.0\text{ mmHg}$

2. Median:
   $\text{Median}=\frac{x_9+x_{10}}{2}=\frac{79+79}{2}=79.0\text{ mmHg}$

3. Mode:
   $\text{Mode}=75.0\text{ mmHg}\text{ (frequency }=4\text{)}$

4. Mean Deviation:
   $\text{MD}=\frac{\sum |x-\bar{x}|}{n}\approx 5.56\text{ mmHg}$

5. Standard Deviation ($s$):
   $s=\sqrt{\frac{\sum (x-\bar{x}{)}^2}{n-1}}\approx 7.02\text{ mmHg}\text{ (or }\sigma \approx 6.82\text{ mmHg for population)}$

1. Name: Receiver Operating Characteristic (ROC) Curve.
2. Uses:
   • Evaluates and compares the diagnostic accuracy of continuous diagnostic/screening tests across all possible cutoff points.
   • Area Under the Curve (AUC / c-statistic) quantifies overall test discrimination power ($1.0=\text{perfect}$, $0.5=\text{chance}$).
   • Identifies the optimal cutoff threshold that maximizes Sensitivity and minimizes False Positive rate (Youden index).
3. Axes:
   • Y-axis: Sensitivity (True Positive Rate).
   • X-axis: $1-\text{Specificity}$ (False Positive Rate).

1. Name: Scatter Plot (Scatter Diagram).
2. Uses:
   • Visually displays the relationship, correlation, and pattern (linear, non-linear, positive, negative, or no association) between two continuous quantitative variables.
   • Evaluates data distribution and identifies outliers prior to linear regression / Pearson correlation analysis.

1. 95% Sample Reference Range:
   $\text{Range}=\text{Mean}\pm 1.96\times \text{SD}\approx 280\pm 2(30)=280\pm 60=220\text{ to }340\text{ L/min}$

2. 95% Confidence Interval for Population Mean:
   $\text{95}=\text{Mean}\pm 1.96\times \text{SE}\approx 280\pm 2(2)=280\pm 4=276\text{ to }284\text{ L/min}$

2x2 Contingency Table:

Test Result	Blood Culture $(+)$	Blood Culture $(-)$	Total
IgM ELISA $(+)$	30 (TP, a)	40 (FP, b)	70
IgM ELISA $(-)$	10 (FN, c)	20 (TN, d)	30
Total	40	60	100

1. Specificity:
   $\text{Specificity}=\frac{d}{b+d}\times 100=\frac{20}{40+20}\times 100=\frac{20}{60}\times 100=33.33\mathrm{\%}$

2. Sensitivity:
   $\text{Sensitivity}=\frac{a}{a+c}\times 100=\frac{30}{30+10}\times 100=\frac{30}{40}\times 100=75.0\mathrm{\%}$

3. Positive Predictive Value (PPV):
   $\text{PPV}=\frac{a}{a+b}\times 100=\frac{30}{30+40}\times 100=\frac{30}{70}\times 100=42.86\mathrm{\%}$

4. Negative Predictive Value (NPV):
   $\text{NPV}=\frac{d}{c+d}\times 100=\frac{20}{10+20}\times 100=\frac{20}{30}\times 100=66.67\mathrm{\%}$

2x2 Contingency Table:

Test Result	Culture Positive (Disease $+$)	Culture Negative (Disease $-$)	Total
Rapid Test Positive	260 (a)	40 (b)	300
Rapid Test Negative	140 (c)	60 (d)	200
Total	400	100	500

1. Sensitivity: $\frac{a}{a+c}=\frac{260}{400}=65.0\mathrm{\%}$
2. Specificity: $\frac{d}{b+d}=\frac{60}{100}=60.0\mathrm{\%}$
3. PPV: $\frac{a}{a+b}=\frac{260}{300}=86.67\mathrm{\%}$
4. NPV: $\frac{d}{c+d}=\frac{60}{200}=30.0\mathrm{\%}$
5. Likelihood Ratio Positive (${\text{LR}}^{+}$):
   ${\text{LR}}^{+}=\frac{\text{Sensitivity}}{1-\text{Specificity}}=\frac{0.65}{1-0.60}=\frac{0.65}{0.40}=1.625$
6. Likelihood Ratio Negative (${\text{LR}}^{-}$):
   ${\text{LR}}^{-}=\frac{1-\text{Sensitivity}}{\text{Specificity}}=\frac{1-0.65}{0.60}=\frac{0.35}{0.60}\approx 0.583$

Vancouver Reference Format:
Author Surname Initials. Title of article. Abbreviated Journal Title. Year; Volume(Issue): Pages.

Formatted Citation:
Bhargava S, Sharma M, Kalra E. Hand grip strength and its relationship with birth weight in adolescent population. Indian Pediatr. 2013; 78: 301-5.

1. Perinatal Mortality Rate (PMR):
   $\text{PMR}=\frac{\text{Stillbirths}+\text{Early Neonatal Deaths (first week)}}{\text{Total Births (Live births + Stillbirths)}}\times 1000$
   $\text{PMR}=\frac{80+320}{10,000}\times 1000=\frac{400}{10,000}\times 1000=40\text{ per }1000\text{ total births}$

2. Neonatal Mortality Rate (NMR):

   • $\text{Live Births}=\text{Total births}-\text{Stillbirths}=10,000-80=9,920\text{ (or rounded to }10,000\text{)}$
   • $\text{Total Neonatal Deaths}=320+180=500$
     $\text{NMR}=\frac{\text{Total deaths in first 28 days}}{\text{Total live births}}\times 1000=\frac{500}{10,000}\times 1000=50\text{ per }1000\text{ live births}$

Correct Match:

• Level I: High-quality Randomized Controlled Trial (RCT) with narrow confidence intervals / Systematic review with meta-analysis of Level I RCTs.
• Level II: Lesser-quality RCT ($<80\mathrm{\%}$ follow-up, lack of blinding) or Prospective cohort study.
• Level III: Case-control study or Retrospective comparative study.
• Level IV: Case series / Poor-quality cohort and case-control studies.
• Level V: Expert opinion without explicit critical appraisal, bench research, or consensus statements.

Sample Size Formula for Quantitative / Continuous Data (Mean):
$N=\frac{4\times {\text{SD}}^2}{L^2}=\frac{Z_{1-\alpha /2}^2\times {\sigma }^2}{L^2}$
(Where $Z=2$ at 95% confidence level)

$\text{SD}=90\text{ IU},L=9\text{ IU}$
$N=\frac{4\times (90{)}^2}{(9{)}^2}=\frac{4\times 8100}{81}=4\times 100=400$

Required Sample Size: $400$ children.

1. Range:
   $\text{Range}=\text{Maximum}-\text{Minimum}=290-200=90\text{ L/min (from 200 to 290 L/min)}$

2. Mean ($\bar{x}$) and Mean Deviation (MD):

   • Mean:
     $\bar{x}=\frac{250+260+290+200+240+240+260+270+270+290}{10}=\frac{2570}{10}=257.0\text{ L/min}$
   • Mean Deviation:
     $\text{MD}=\frac{\sum |x-\bar{x}|}{N}=\frac{7+3+33+57+17+17+3+13+13+33}{10}=\frac{196}{10}=19.6\text{ L/min}$

3. Standard Deviation ($s$):
   $\sum (x-\bar{x}{)}^2=49+9+1089+3249+289+289+9+169+169+1089=6410$
   $s=\sqrt{\frac{6410}{10-1}}=\sqrt{712.22}\approx 26.69\text{ L/min}(\text{or }\sigma =\sqrt{641}\approx 25.32\text{ L/min})$

1. Diagram: Scatter plots demonstrating different patterns of Correlation.
2. Use: Visual analysis of the direction, form, and strength of the relationship between two quantitative variables.
3. Patterns:
   • A: No correlation ($r=0$).
   • B: Weak / Moderate positive correlation.
   • C: Strong positive correlation ($r\approx +0.9$).
   • D: Weak / Moderate negative correlation.
   • E: Strong negative correlation ($r\approx -0.9$).
   • F: Perfect positive correlation ($r=+1.0$) or curvilinear/nonlinear relation.