1. Standard Deviation, Relative Risk, Confidence Intervals, Chi-Squared & P values

Standard Deviation (SD)

• SD tells you how spread out the values are around the mean.
• If weight = 6.7 kg ± 0.9 SD → most babies weigh between 5.8–7.6 kg.
• ±1 SD = 68% of values
• ±2 SD = 95%
• ±3 SD = 99.7%

Relative Risk (Risk Ratio)

Used in cohort studies (comparing two groups followed over time).

• RR < 1 → treatment/exposure reduces risk
• RR > 1 → increases risk
• RR = 1 → no difference
• MUST check 95% CI: if CI includes 1 → not significant.

Confidence Interval (CI)

• Tells you the likely range of the true population value.
• Example: RR = 0.74 (95% CI 0.58–0.94)
• CI does NOT include 1 → statistically significant
• Means the longer needle truly reduces reactions.

Chi-Squared Test (χ²)

• Used to compare proportions (e.g., reaction vs no reaction).
• Tests whether the difference between groups is likely real or due to chance.
• Do NOT interpret χ² value — always look at P value.

P value

• P = 0.05 → 1 in 20 chance result is due to chance → “significant”
• P = 0.001 → 1 in 1000 chance → “very highly significant”
• Example: Needle trial P = 0.009
• Only 9 in 1000 chance the difference is random → highly significant.

Clinical Message:

Longer needle reduced local reactions, RR = 0.74, CI excludes 1, P < 0.01.

2. Odds Ratios & Confidence Intervals

Odds vs Risk

• Risk = event / total
• Odds = event / non-event

Used mainly in case–control studies & meta-analysis.

Odds Ratio (OR)

• OR > 1 → event more likely in exposed group
• OR < 1 → event less likely
• OR = 1 → no difference
• MUST check CI: CI including 1 → NOT significant.

Example (Warfarin vs Aspirin)

• OR for vascular death = 1.1 (CI 0.52–2.32)
• CI includes 1 → not statistically significant.

Even if OR looks important, if CI includes 1 → throw it away.

3. Correlation & Regression

Correlation (r)

Measures strength of linear association:

• r = +1 → perfect positive
• r = –1 → perfect negative
• r = 0 → no linear relationship

Rule of thumb:

• 0–0.2 → very weak
• 0.2–0.4 → weak
• 0.4–0.6 → moderate
• 0.6–0.8 → strong
• 0.8 → very strong (check for errors!)

Spearman vs Pearson

• Spearman → non-parametric (skewed data)
• Pearson → normally distributed data

Regression

Regression creates the best-fit line to PREDICT values.

Equation: y = a + bx

• b = regression coefficient (slope)
• a = constant (where line hits y-axis)

Example: Antibiotic prescribing vs resistance

rs = 0.20

• Very weak correlation.
• P = 0.001 → statistically significant BUT clinically weak.

Regression coefficient = 0.019

• Reducing prescribing by 20% reduces resistance by ONLY 1%.
• Clinically unhelpful despite statistical significance.

Clinical Message:

Weak association → reducing prescribing alone won’t meaningfully reduce resistance.

4. Survival Analysis & Risk Reduction

Kaplan–Meier Curves

• Show probability of remaining event-free over time.
• Steps drop when events occur.
• Compare two curves visually.

Log-rank Test

• Compares two survival curves formally.
• P < 0.05 → survival significantly different.

Cox Regression (Hazard Ratio)

• HR < 1 → treatment reduces risk
• HR > 1 → increases risk
• HR = 1 → no difference
• Check CI — CI must NOT include 1.

Risk Reduction Measures

• RRR = relative reduction in risk
• ARR = absolute reduction in risk
• NNT = how many must be treated for one benefit
• Lower NNT is better.

Example: Ramipril HOPE Study

Risk of stroke:

• Ramipril: 3.36%
• Placebo: 4.86%

Risk Ratio = 0.69

• 31% relative risk reduction (RRR)

ARR = 1.5%

NNT = 100 / 1.5 = 67

Clinical Message:

Ramipril reduces stroke risk (RRR 31%), but NNT = 67 over 4.5 years → modest real-world benefit.

5. Sensitivity, Specificity & Predictive Values

Build the 2×2 table

Sensitivity = A / (A + C)

“How good is the test at detecting disease?”

High sensitivity → few false negatives.

Specificity = D / (B + D)

“How good is the test at excluding disease?”

High specificity → few false positives.

Predictive Values

Depend on prevalence.

Positive Predictive Value (PPV) = A / (A + B)

Likelihood patient actually has disease if test is positive.

Negative Predictive Value (NPV) = D / (C + D)

Likelihood patient does NOT have disease if test is negative.

Likelihood Ratio (LR)

LR+ = Sensitivity / (1 – Specificity)

• LR > 10 → very strong evidence
• LR < 0.1 → strong evidence against disease

Example: MI rule-out

• Sensitivity = 97.2%
• Specificity = 93%
• PPV = 66%
• NPV = 99.6%
• LR+ = 13.8

Clinical Message:

A negative test rules out MI very safely (NPV 99.6%).

FULL SUMMARY (All 5 in One Page)