Biostatistics: A Complete Overview

from reportlab.lib.pagesizes import A4
from reportlab.lib.styles import getSampleStyleSheet, ParagraphStyle
from reportlab.lib.units import cm
from reportlab.lib import colors
from reportlab.platypus import (
    SimpleDocTemplate, Paragraph, Spacer, Table, TableStyle,
    HRFlowable, PageBreak, KeepTogether
)
from reportlab.lib.enums import TA_CENTER, TA_LEFT, TA_JUSTIFY
from reportlab.platypus import Image
import urllib.request
import os

OUTPUT = "/tmp/workspace/biostatistics-pdf/Biostatistics_Notes.pdf"

# ---------- Styles ----------
styles = getSampleStyleSheet()

TEAL      = colors.HexColor("#0D7377")
DARK_TEAL = colors.HexColor("#14A085")
LIGHT_BG  = colors.HexColor("#F0F8F7")
ACCENT    = colors.HexColor("#E8F5F4")
YELLOW    = colors.HexColor("#FFF8E1")
DARK_GRAY = colors.HexColor("#2C3E50")
MID_GRAY  = colors.HexColor("#5D6D7E")
TABLE_HDR = colors.HexColor("#0D7377")
TABLE_ALT = colors.HexColor("#EAF6F6")
RED_BOX   = colors.HexColor("#FDEDEC")
RED_BDR   = colors.HexColor("#E74C3C")
GREEN_BOX = colors.HexColor("#EAFAF1")
GREEN_BDR = colors.HexColor("#27AE60")

cover_title = ParagraphStyle("cover_title",
    fontSize=34, fontName="Helvetica-Bold",
    textColor=colors.white, alignment=TA_CENTER,
    spaceAfter=10, leading=42)

cover_sub = ParagraphStyle("cover_sub",
    fontSize=16, fontName="Helvetica",
    textColor=colors.HexColor("#D5F5E3"), alignment=TA_CENTER,
    spaceAfter=6)

cover_src = ParagraphStyle("cover_src",
    fontSize=10, fontName="Helvetica-Oblique",
    textColor=colors.HexColor("#A9DFBF"), alignment=TA_CENTER)

h1 = ParagraphStyle("h1",
    fontSize=20, fontName="Helvetica-Bold",
    textColor=colors.white, alignment=TA_LEFT,
    spaceBefore=4, spaceAfter=4, leading=26,
    backColor=TEAL,
    borderPad=(6, 10, 6, 10))

h2 = ParagraphStyle("h2",
    fontSize=14, fontName="Helvetica-Bold",
    textColor=TEAL, spaceBefore=14, spaceAfter=4,
    borderPad=2, leading=18)

h3 = ParagraphStyle("h3",
    fontSize=11, fontName="Helvetica-Bold",
    textColor=DARK_GRAY, spaceBefore=10, spaceAfter=3,
    leading=15)

body = ParagraphStyle("body",
    fontSize=10, fontName="Helvetica",
    textColor=DARK_GRAY, spaceAfter=6,
    leading=15, alignment=TA_JUSTIFY)

bullet = ParagraphStyle("bullet",
    fontSize=10, fontName="Helvetica",
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    leading=14, bulletIndent=6)

formula = ParagraphStyle("formula",
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    textColor=TEAL, backColor=ACCENT,
    spaceAfter=6, spaceBefore=4,
    leftIndent=20, rightIndent=20,
    borderPad=8, leading=16)

example_style = ParagraphStyle("example",
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note_style = ParagraphStyle("note",
    fontSize=9.5, fontName="Helvetica",
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    backColor=colors.HexColor("#EBF5FB"),
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    borderPad=6, leading=13)

mnemonic = ParagraphStyle("mnemonic",
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    backColor=colors.HexColor("#F5EEF8"),
    spaceAfter=4, spaceBefore=4,
    leftIndent=10, rightIndent=10,
    borderPad=6, leading=14)

sources_style = ParagraphStyle("sources",
    fontSize=8, fontName="Helvetica-Oblique",
    textColor=MID_GRAY, spaceAfter=3, leading=11)

# ---------- Helper: section header ----------
def section_header(num, title):
    return [
        Spacer(1, 10),
        Table([[Paragraph(f"{num}.  {title}", h1)]],
              colWidths=[17*cm],
              style=TableStyle([
                  ("BACKGROUND", (0,0), (-1,-1), TEAL),
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                  ("BOTTOMPADDING", (0,0), (-1,-1), 8),
                  ("LEFTPADDING", (0,0), (-1,-1), 14),
              ])),
        Spacer(1, 6),
    ]

def sub_header(text):
    return Paragraph(text, h2)

def sub_sub(text):
    return Paragraph(text, h3)

def para(text):
    return Paragraph(text, body)

def bul(text):
    return Paragraph(f"\u2022  {text}", bullet)

def form(text):
    return Paragraph(text, formula)

def ex(text):
    return Paragraph(f"\u25b6  {text}", example_style)

def note(text):
    return Paragraph(f"\u2139  {text}", note_style)

def mnemo(text):
    return Paragraph(f"\U0001f9e0  {text}", mnemonic)

def hr():
    return HRFlowable(width="100%", thickness=1, color=colors.HexColor("#BDC3C7"), spaceAfter=6, spaceBefore=6)

# ---------- Generic table builder ----------
def build_table(headers, rows, col_widths=None):
    if col_widths is None:
        col_widths = [17*cm/len(headers)] * len(headers)
    hdr_row = [Paragraph(f"<b>{h}</b>", ParagraphStyle("th",
        fontSize=9.5, fontName="Helvetica-Bold",
        textColor=colors.white, alignment=TA_CENTER, leading=12)) for h in headers]
    data = [hdr_row]
    for i, row in enumerate(rows):
        data.append([Paragraph(str(c), ParagraphStyle("td",
            fontSize=9, fontName="Helvetica",
            textColor=DARK_GRAY, leading=12)) for c in row])
    ts = TableStyle([
        ("BACKGROUND", (0,0), (-1,0), TABLE_HDR),
        ("ROWBACKGROUNDS", (0,1), (-1,-1), [colors.white, TABLE_ALT]),
        ("GRID", (0,0), (-1,-1), 0.5, colors.HexColor("#BDC3C7")),
        ("TOPPADDING", (0,0), (-1,-1), 5),
        ("BOTTOMPADDING", (0,0), (-1,-1), 5),
        ("LEFTPADDING", (0,0), (-1,-1), 7),
        ("RIGHTPADDING", (0,0), (-1,-1), 7),
        ("VALIGN", (0,0), (-1,-1), "MIDDLE"),
    ])
    return Table(data, colWidths=col_widths, style=ts, hAlign="LEFT")

# ---------- Download normal curve image ----------
img_path = "/tmp/workspace/biostatistics-pdf/normal_curve.png"
try:
    urllib.request.urlretrieve(
        "https://cdn.orris.care/cdss_images/c39869747094c8561f90f8f17758c9d8d4517297107f9e433d6f95463ff6982f.png",
        img_path)
    print("Image downloaded OK")
except Exception as e:
    print(f"Image download failed: {e}")
    img_path = None

# ---------- Document ----------
doc = SimpleDocTemplate(
    OUTPUT, pagesize=A4,
    leftMargin=2*cm, rightMargin=2*cm,
    topMargin=2*cm, bottomMargin=2*cm,
    title="Biostatistics Notes",
    author="Orris Medical")

story = []

# ===== COVER PAGE =====
story.append(Spacer(1, 1.5*cm))
cover_tbl = Table(
    [[Paragraph("BIOSTATISTICS", cover_title)],
     [Paragraph("Complete Study Notes", cover_sub)],
     [Paragraph("Normal Distribution  •  Hypothesis Testing  •  p-Value\n"
                "t-Test  •  Chi-Square Test  •  Errors  •  Central Tendency", cover_sub)],
     [Spacer(1, 12)],
     [Paragraph("Sources: Park's Textbook of Preventive & Social Medicine  |  "
                "Henry's Clinical Diagnosis  |  Goldman-Cecil Medicine  |  "
                "Barash Clinical Anesthesia  |  Miller's Review of Orthopaedics", cover_src)]],
    colWidths=[17*cm],
    style=TableStyle([
        ("BACKGROUND", (0,0), (-1,-1), TEAL),
        ("TOPPADDING", (0,0), (-1,-1), 14),
        ("BOTTOMPADDING", (0,0), (-1,-1), 14),
        ("LEFTPADDING", (0,0), (-1,-1), 20),
        ("RIGHTPADDING", (0,0), (-1,-1), 20),
        ("ROUNDEDCORNERS", [10]),
    ]))
story.append(cover_tbl)
story.append(Spacer(1, 0.8*cm))

# Quick-ref box on cover
qr_data = [
    [Paragraph("<b>Quick Reference</b>", ParagraphStyle("qrh", fontSize=11,
        fontName="Helvetica-Bold", textColor=TEAL))],
    [Paragraph("x̄ ± 1σ = 68.3%   |   x̄ ± 2σ = 95.4%   |   x̄ ± 3σ = 99.7%", ParagraphStyle("qr",
        fontSize=10, fontName="Courier-Bold", textColor=DARK_GRAY))],
    [Paragraph("p < 0.05 = Significant   |   Type I = False Positive (α)   |   Type II = False Negative (β)", ParagraphStyle("qr2",
        fontSize=9.5, fontName="Helvetica", textColor=DARK_GRAY))],
]
story.append(Table(qr_data, colWidths=[17*cm],
    style=TableStyle([
        ("BACKGROUND", (0,0), (-1,-1), ACCENT),
        ("BOX", (0,0), (-1,-1), 1.5, TEAL),
        ("TOPPADDING", (0,0), (-1,-1), 7),
        ("BOTTOMPADDING", (0,0), (-1,-1), 7),
        ("LEFTPADDING", (0,0), (-1,-1), 14),
    ])))
story.append(PageBreak())

# ===== 1. MEASURES OF CENTRAL TENDENCY =====
story += section_header("1", "Measures of Central Tendency")
story.append(para('The "average" gives a mental picture of the central value in a distribution. Three measures are commonly used in medical statistics:'))
story.append(Spacer(1, 6))

for title, content, adv, dis in [
    ("(a) The Mean (Arithmetic Mean)",
     "Sum all observations and divide by n.  Formula:  x̄ = Σx / n",
     "Easy to calculate and understand.",
     "Unduly influenced by extreme (outlier) values."),
    ("(b) The Median",
     "Arrange data in order; pick the middle value. If n is even, average the two middle values.",
     "Not affected by extreme values — more representative when outliers are present.",
     "Ignores the actual values of all observations except the middle."),
    ("(c) The Mode",
     "The most frequently occurring value in a distribution.",
     "Not affected by extreme items; easy to understand.",
     "Often not clearly defined. Seldom used in biological/medical statistics."),
]:
    story.append(KeepTogether([
        sub_sub(title),
        form(content),
        bul(f"<b>Advantage:</b> {adv}"),
        bul(f"<b>Disadvantage:</b> {dis}"),
        Spacer(1, 4),
    ]))

story.append(ex("Example (Mean): Diastolic BP of 10 individuals = 83, 75, 81, 79, 71, 95, 75, 77, 84, 90.  Total = 810.  Mean = 810/10 = 81.0"))
story.append(ex("Example (Median): Arranged: 71, 75, 75, 77, [79], 81, 83, 84, 95  →  Median = 79"))
story.append(ex("Example (Mode): In series 85,75,81,79,71,95,75,77,75,90...  75 occurs most often  →  Mode = 75"))

story.append(Spacer(1, 8))
story.append(note("In a perfectly normal distribution: Mean = Median = Mode. When extreme values are present, the Median is often more representative than the Mean."))

story.append(Spacer(1,6))
story.append(build_table(
    ["Measure", "Best For", "Affected by Outliers?"],
    [["Mean", "Normally distributed data", "YES"],
     ["Median", "Skewed data / outliers present", "NO"],
     ["Mode", "Most common value; nominal data", "NO"]],
    col_widths=[5*cm, 7.5*cm, 4.5*cm]
))
story.append(sources_style and Paragraph("Source: Park's Textbook of Preventive and Social Medicine, pp. 951-952", sources_style))

story.append(PageBreak())

# ===== 2. NORMAL DISTRIBUTION =====
story += section_header("2", "Normal Distribution")
story.append(para("The normal (Gaussian) distribution is a smooth, symmetrical, bell-shaped curve. When large biological data sets (e.g., haemoglobin values) are plotted, they approximate this curve. The shape depends on the mean (x̄) and standard deviation (σ)."))

story.append(Spacer(1, 6))
story.append(sub_header("Mathematical Formula"))
story.append(form("P(x) = (1 / σ√2π) × e^[-(x-x̄)² / 2σ²]"))

story.append(sub_header("Key Properties"))
for prop in [
    "Perfectly symmetrical about the mean",
    "Mean = Median = Mode (all coincide at the centre)",
    "Total area under the curve = 1 (100%)",
    "The tails extend to ±∞ but never touch the x-axis (asymptotic)",
    "Completely described by just two parameters: mean (x̄) and SD (σ)",
]:
    story.append(bul(prop))

story.append(Spacer(1,8))
story.append(sub_header("The 68-95-99.7 Rule  (Most Important!)"))

if img_path and os.path.exists(img_path):
    img = Image(img_path, width=10*cm, height=6*cm)
    story.append(Table([[img]], colWidths=[17*cm],
        style=TableStyle([("ALIGN",(0,0),(-1,-1),"CENTER")])))
    story.append(Spacer(1,4))

story.append(build_table(
    ["Range", "% of Values Included", "Clinical Meaning"],
    [["x̄ ± 1σ", "68.3%", "~2/3 of all values"],
     ["x̄ ± 2σ", "95.4%  (~95%)", "Used for reference ranges"],
     ["x̄ ± 3σ", "99.7%", "Almost all values"]],
    col_widths=[5*cm, 6*cm, 6*cm]
))
story.append(Spacer(1,6))

story.append(sub_header("Standard Normal Curve (Z-distribution)"))
story.append(para("There is only ONE standardized normal curve with mean = 0 and SD = 1. Any raw value is converted to a Z-score:"))
story.append(form("Z = (x - x̄) / σ"))
story.append(bul("Z tells you how many standard deviations a value is from the mean"))
story.append(bul("Used to find probabilities from normal distribution tables"))
story.append(ex("Example: Mean pulse = 72, SD = 2. Pulse of 80: Z = (80-72)/2 = 4. Probability of pulse ≥80 = only 0.003% (3 in 100,000)"))
story.append(note("Clinical application: Laboratory reference ranges are calculated as mean ± 2 SD, capturing the central 95% of healthy individuals."))
story.append(Paragraph("Source: Park's Textbook of Preventive and Social Medicine, pp. 952-954  |  Henry's Clinical Diagnosis, p. 130", sources_style))

story.append(PageBreak())

# ===== 3. HYPOTHESIS TESTING =====
story += section_header("3", "Hypothesis Testing")
story.append(para("Hypothesis testing is a formal statistical procedure to determine whether an observed difference between groups is real or merely due to chance."))

story.append(Spacer(1,6))
story.append(sub_header("The Two Hypotheses"))
story.append(build_table(
    ["Hypothesis", "Symbol", "Statement"],
    [["Null Hypothesis", "H₀", "There is NO difference between groups (e.g., drug has no effect)"],
     ["Alternative Hypothesis", "H₁ or Hₐ", "There IS a significant difference between groups"]],
    col_widths=[4.5*cm, 2*cm, 10.5*cm]
))
story.append(Spacer(1,8))

story.append(sub_header("Step-by-Step Process"))
steps = [
    ("Step 1", "State H₀ and H₁ clearly before collecting data"),
    ("Step 2", "Choose appropriate statistical test (t-test, chi-square, ANOVA, etc.)"),
    ("Step 3", "Set significance level α (usually 0.05)"),
    ("Step 4", "Collect data and calculate the test statistic"),
    ("Step 5", "Find the p-value from the test statistic"),
    ("Step 6", "If p < α → Reject H₀   |   If p ≥ α → Fail to reject H₀"),
]
step_data = [[Paragraph(f"<b>{s}</b>", ParagraphStyle("sn", fontSize=9.5, fontName="Helvetica-Bold",
    textColor=colors.white, alignment=TA_CENTER)),
    Paragraph(d, ParagraphStyle("sd", fontSize=9.5, fontName="Helvetica",
    textColor=DARK_GRAY))] for s,d in steps]
story.append(Table(step_data, colWidths=[3*cm, 14*cm],
    style=TableStyle([
        ("BACKGROUND",(0,0),(0,-1), DARK_TEAL),
        ("ROWBACKGROUNDS",(1,0),(1,-1),[colors.white, ACCENT]),
        ("GRID",(0,0),(-1,-1),0.5,colors.HexColor("#BDC3C7")),
        ("TOPPADDING",(0,0),(-1,-1),6),("BOTTOMPADDING",(0,0),(-1,-1),6),
        ("LEFTPADDING",(0,0),(-1,-1),8),("RIGHTPADDING",(0,0),(-1,-1),8),
        ("VALIGN",(0,0),(-1,-1),"MIDDLE"),
    ])))
story.append(Spacer(1,8))

story.append(sub_header("Choosing the Right Test"))
story.append(build_table(
    ["Type of Data", "Groups", "Statistical Test"],
    [["Continuous (means)", "2 groups", "Student's t-test"],
     ["Continuous (means)", "> 2 groups", "ANOVA (F-test)"],
     ["Categorical (counts/proportions)", "2+ groups", "Chi-square test"],
     ["Categorical (small counts)", "2 groups", "Fisher's Exact Test"],
     ["Ordinal", "2 groups", "Mann-Whitney U test"],
     ["Paired / before-after", "Same subjects", "Paired t-test"]],
    col_widths=[6*cm, 4*cm, 7*cm]
))
story.append(note("Key quote: 'The null hypothesis is never proven. We can end up thinking it is correct, but the test does not strictly lead to that conclusion — like a trial verdict of Not Guilty is not the same as Innocent.'  — Henry's Clinical Diagnosis"))
story.append(Paragraph("Source: Goldman-Cecil Medicine, pp. 2694-2696  |  Barash Clinical Anesthesia, p. 523", sources_style))

story.append(PageBreak())

# ===== 4. P-VALUE =====
story += section_header("4", "p-Value")
story.append(para("The p-value is the probability that the observed result (or one more extreme) could occur by chance alone, assuming the null hypothesis is true. It does NOT measure the size of an effect or the importance of a result."))

story.append(Spacer(1,6))
story.append(build_table(
    ["p-Value", "Normal Deviate", "Interpretation"],
    [["p < 0.05", "ND > 2", "SIGNIFICANT — less than 5% chance result is due to chance"],
     ["p = 0.05", "ND = 2", "Borderline significant (just at the threshold)"],
     ["p > 0.05", "ND < 2", "NOT significant — difference may be due to chance"]],
    col_widths=[3*cm, 4*cm, 10*cm]
))
story.append(Spacer(1,8))

story.append(sub_header("Key Concepts"))
for pt in [
    "The conventional threshold is <b>p &lt; 0.05</b> (5% significance level)",
    "p &lt; 0.05 means there is less than a 1 in 20 chance the result is due to random variation",
    "A smaller p-value = stronger evidence against H₀ (NOT a bigger effect)",
    "A 95% Confidence Interval that does NOT include zero (for differences) corresponds to p &lt; 0.05",
    "p-value only addresses chance — it does not address bias or confounding",
]:
    story.append(bul(pt))

story.append(Spacer(1,6))
story.append(sub_header("Clinical Example"))
example_tbl = Table([
    [Paragraph("<b>Transient Neurologic Symptoms</b>", ParagraphStyle("et", fontSize=9.5,
        fontName="Helvetica-Bold", textColor=colors.white, alignment=TA_CENTER))],
], colWidths=[17*cm], style=TableStyle([
    ("BACKGROUND",(0,0),(-1,-1), TABLE_HDR),
    ("TOPPADDING",(0,0),(-1,-1),6), ("BOTTOMPADDING",(0,0),(-1,-1),6),
]))
story.append(example_tbl)
story.append(build_table(
    ["Treatment", "Yes", "No"],
    [["Lidocaine", "9 (26%)", "26"],
     ["Bupivacaine", "1 (3%)", "34"]],
    col_widths=[6*cm, 5.5*cm, 5.5*cm]
))
story.append(ex("Chi-square = 5.72, df = 1, p = 0.017  →  p < 0.05  →  SIGNIFICANT difference in TNS rates between the two drugs."))
story.append(Paragraph("Source: Park's Textbook of Preventive and Social Medicine, p. 955  |  Barash Clinical Anesthesia, p. 523", sources_style))

story.append(PageBreak())

# ===== 5. ERRORS IN HYPOTHESIS TESTING =====
story += section_header("5", "Errors in Hypothesis Testing")
story.append(para("Even with careful statistical testing, two fundamental errors are possible. These are unavoidable in theory but can be minimised by good study design."))
story.append(Spacer(1,6))

# Type I
story.append(KeepTogether([
    Table([[Paragraph("TYPE I ERROR  (Alpha Error, α)", ParagraphStyle("t1h",
        fontSize=12, fontName="Helvetica-Bold", textColor=RED_BDR))]],
        colWidths=[17*cm], style=TableStyle([
            ("BACKGROUND",(0,0),(-1,-1), RED_BOX),
            ("BOX",(0,0),(-1,-1),1.5, RED_BDR),
            ("TOPPADDING",(0,0),(-1,-1),8), ("LEFTPADDING",(0,0),(-1,-1),12),
            ("BOTTOMPADDING",(0,0),(-1,-1),8),
        ])),
    Spacer(1,4),
    bul("Incorrectly <b>REJECTING</b> the null hypothesis"),
    bul("Concluding groups ARE different when they actually are NOT"),
    bul("= <b>False Positive</b>"),
    bul("Acceptable probability: <b>≤ 0.05 (5%)</b>  — this is the p-value threshold"),
    bul("Represented by: <b>α (alpha)</b>"),
    Spacer(1,6),
]))

# Type II
story.append(KeepTogether([
    Table([[Paragraph("TYPE II ERROR  (Beta Error, β)", ParagraphStyle("t2h",
        fontSize=12, fontName="Helvetica-Bold", textColor=GREEN_BDR))]],
        colWidths=[17*cm], style=TableStyle([
            ("BACKGROUND",(0,0),(-1,-1), GREEN_BOX),
            ("BOX",(0,0),(-1,-1),1.5, GREEN_BDR),
            ("TOPPADDING",(0,0),(-1,-1),8), ("LEFTPADDING",(0,0),(-1,-1),12),
            ("BOTTOMPADDING",(0,0),(-1,-1),8),
        ])),
    Spacer(1,4),
    bul("Incorrectly <b>FAILING TO REJECT</b> the null hypothesis"),
    bul("Concluding groups are NOT different when they actually ARE"),
    bul("= <b>False Negative</b>"),
    bul("Acceptable probability: <b>up to 20%</b>"),
    bul("Represented by: <b>β (beta)</b>"),
    bul("<b>Power = 1 − β</b>  (probability of correctly detecting a true difference)"),
    Spacer(1,6),
]))

story.append(sub_header("The 2×2 Decision Table"))
err_data = [
    [Paragraph(""), Paragraph("<b>H₀ True\n(no real difference)</b>",
        ParagraphStyle("eh", fontSize=9.5, fontName="Helvetica-Bold", textColor=colors.white, alignment=TA_CENTER)),
     Paragraph("<b>H₀ False\n(real difference exists)</b>",
        ParagraphStyle("eh2", fontSize=9.5, fontName="Helvetica-Bold", textColor=colors.white, alignment=TA_CENTER))],
    [Paragraph("<b>Reject H₀</b>", ParagraphStyle("er", fontSize=9.5, fontName="Helvetica-Bold",
        textColor=colors.white)),
     Paragraph("❌  Type I Error (α)\nFalse Positive", ParagraphStyle("ec", fontSize=9, fontName="Helvetica",
        textColor=RED_BDR, alignment=TA_CENTER)),
     Paragraph("✅  Correct Decision\nTrue Positive (Power)", ParagraphStyle("ec2", fontSize=9, fontName="Helvetica",
        textColor=GREEN_BDR, alignment=TA_CENTER))],
    [Paragraph("<b>Fail to Reject H₀</b>", ParagraphStyle("er2", fontSize=9.5, fontName="Helvetica-Bold",
        textColor=colors.white)),
     Paragraph("✅  Correct Decision\nTrue Negative", ParagraphStyle("ec3", fontSize=9, fontName="Helvetica",
        textColor=GREEN_BDR, alignment=TA_CENTER)),
     Paragraph("❌  Type II Error (β)\nFalse Negative", ParagraphStyle("ec4", fontSize=9, fontName="Helvetica",
        textColor=RED_BDR, alignment=TA_CENTER))],
]
story.append(Table(err_data, colWidths=[4.5*cm, 6.25*cm, 6.25*cm],
    style=TableStyle([
        ("BACKGROUND",(0,0),(0,-1), TEAL),
        ("BACKGROUND",(1,0),(-1,0), TEAL),
        ("ROWBACKGROUNDS",(1,1),(-1,-1),[ACCENT, colors.white]),
        ("GRID",(0,0),(-1,-1),0.5,colors.HexColor("#BDC3C7")),
        ("TOPPADDING",(0,0),(-1,-1),8), ("BOTTOMPADDING",(0,0),(-1,-1),8),
        ("LEFTPADDING",(0,0),(-1,-1),8), ("RIGHTPADDING",(0,0),(-1,-1),8),
        ("VALIGN",(0,0),(-1,-1),"MIDDLE"),
    ])))
story.append(Spacer(1,8))
story.append(note("Because falsely concluding a treatment works when it does not (Type I) is more serious than the reverse, α is set stricter (5%) than β (20%).  Power of 80% is standard for well-designed clinical trials."))
story.append(Paragraph("Source: Goldman-Cecil Medicine, p. 2698  |  Henry's Clinical Diagnosis, p. 130  |  Miller's Review of Orthopaedics, pp. 110-120", sources_style))

story.append(PageBreak())

# ===== 6. t-TEST =====
story += section_header("6", "The t-Test (Student's t-Test)")
story.append(para("The t-test is the most common method for comparing a <b>continuous variable between two groups</b>. It was devised by William Gosset (under the pseudonym 'Student') while working for the Guinness brewery."))

story.append(Spacer(1,6))
story.append(sub_header("Formula"))
story.append(form("t = (x̄₁ - x̄₂) / [SDc × √(1/n₁ + 1/n₂)]"))
story.append(build_table(
    ["Symbol", "Meaning"],
    [["x̄₁, x̄₂", "Mean values of group 1 and group 2"],
     ["n₁, n₂", "Number of observations in each group"],
     ["SDc", "Combined (pooled) standard deviation of both groups"],
     ["t", "The test statistic — compared against t-distribution tables"]],
    col_widths=[3*cm, 14*cm]
))

story.append(Spacer(1,8))
story.append(sub_header("Types of t-Test"))
story.append(build_table(
    ["Type", "When to Use", "Example"],
    [["Independent (Unpaired)", "Two separate, unrelated groups", "Males vs Females (Hb levels)"],
     ["Paired", "Same subjects measured twice", "BP before and after treatment"],
     ["One-sample", "Compare one group mean to a known value", "Sample mean vs population mean"]],
    col_widths=[4.5*cm, 6.5*cm, 6*cm]
))

story.append(Spacer(1,8))
story.append(sub_header("Assumptions for Validity"))
for pt in [
    "Data must be approximately <b>normally distributed</b>",
    "Approximately <b>equal sample sizes</b> in each group",
    "<b>Variances</b> of the groups should be equivalent (homogeneity of variance)",
    "Observations must be <b>independent</b> of each other (no patient counted twice)",
    "Data must be <b>continuous</b> (not categorical counts)",
]:
    story.append(bul(pt))

story.append(Spacer(1,6))
story.append(sub_header("Degrees of Freedom & Interpretation"))
story.append(para("Degrees of freedom (df) = n₁ + n₂ − 2"))
story.append(para("Once the t-statistic and df are known, look up the p-value in t-distribution tables:"))
story.append(bul("If <b>p &lt; 0.05</b>  →  Reject H₀  →  Means are significantly different"))
story.append(bul("If <b>p ≥ 0.05</b>  →  Fail to reject H₀  →  No significant difference detected"))

story.append(Spacer(1,6))
story.append(ex("Example: Hemoglobin in males (mean 15.1 g/dL, SD 0.96, n=36) vs females (mean 13.2 g/dL, SD 0.80, n=49). t = 9.898, p < 0.001 → Highly significant difference in Hb between sexes."))
story.append(note("When cell sizes are very unequal or variances differ significantly, use <b>Welch's t-test</b> instead, which does not assume equal variances."))
story.append(Paragraph("Source: Henry's Clinical Diagnosis and Management by Laboratory Methods, pp. 154-155", sources_style))

story.append(PageBreak())

# ===== 7. CHI-SQUARE TEST =====
story += section_header("7", "Chi-Square Test  (χ²)")
story.append(para("The chi-square test is used for <b>categorical (nominal/count) data</b>. It tests whether observed frequencies differ significantly from expected frequencies — i.e., whether an association exists between two categorical variables."))

story.append(Spacer(1,6))
story.append(sub_header("Formula"))
story.append(form("χ² = Σ [(O − E)² / E]"))
story.append(build_table(
    ["Symbol", "Meaning"],
    [["O", "Observed frequency in each cell (actual data counts)"],
     ["E", "Expected frequency (calculated from row/column totals assuming H₀)"],
     ["Σ", "Sum across all cells of the contingency table"],
     ["χ²", "The test statistic compared to chi-square distribution tables"]],
    col_widths=[2*cm, 15*cm]
))

story.append(Spacer(1,8))
story.append(sub_header("Degrees of Freedom"))
story.append(form("df = (r − 1) × (c − 1)"))
story.append(bul("r = number of rows,  c = number of columns"))
story.append(bul("For a standard 2×2 table:  df = (2-1)(2-1) = 1"))
story.append(bul("Critical χ² value at df=1, p=0.05  =  <b>3.84</b>  (must memorise)"))

story.append(Spacer(1,8))
story.append(sub_header("Step-by-Step Worked Example (Whooping Cough Vaccines)"))
story.append(build_table(
    ["Vaccine", "Attacked", "Not Attacked", "Total", "Attack Rate"],
    [["A (Observed)", "22", "68", "90", "24.4%"],
     ["B (Observed)", "14", "72", "86", "16.2%"],
     ["Total", "36", "140", "176", "20.4%"]],
    col_widths=[4*cm, 3*cm, 3.5*cm, 3*cm, 3.5*cm]
))
story.append(Spacer(1,4))
steps_chi = [
    "Set H₀: No difference between vaccine A and vaccine B.",
    "Calculate expected values: E(A attacked) = 90 × (36/176) = 90 × 0.204 = 18.36",
    "Apply formula: χ² = (22-18.36)²/18.36 + (68-71.55)²/71.55 + (14-17.54)²/17.54 + (72-68.37)²/68.37",
    "χ² = 0.72 + 0.17 + 0.71 + 0.19 = 1.79",
    "df = (2-1)(2-1) = 1.  Critical value at p=0.05 = 3.84",
    "1.79 < 3.84  →  p > 0.05  →  Fail to reject H₀  →  No significant difference between vaccines.",
]
for i, s in enumerate(steps_chi, 1):
    story.append(bul(f"<b>Step {i}:</b> {s}"))

story.append(Spacer(1,8))
story.append(sub_header("Assumptions and Conditions"))
story.append(build_table(
    ["Condition", "Requirement"],
    [["Minimum expected frequency", "Each cell must have E ≥ 5 (some say ≥ 2)"],
     ["Data type", "Must be counts/frequencies (not means or percentages)"],
     ["Independence", "Observations must be independent"],
     ["When E < 5", "Use Fisher's Exact Test instead"],
     ["When comparing >2 groups", "Chi-square can still be used (larger tables)"]],
    col_widths=[7*cm, 10*cm]
))

story.append(Spacer(1,8))
story.append(sub_header("2×2 Contingency Table Template"))
cont_data = [
    [Paragraph(""), Paragraph("<b>Outcome +</b>", ParagraphStyle("ch",fontSize=9.5,fontName="Helvetica-Bold",textColor=colors.white,alignment=TA_CENTER)),
     Paragraph("<b>Outcome −</b>", ParagraphStyle("ch2",fontSize=9.5,fontName="Helvetica-Bold",textColor=colors.white,alignment=TA_CENTER)),
     Paragraph("<b>Total</b>", ParagraphStyle("ch3",fontSize=9.5,fontName="Helvetica-Bold",textColor=colors.white,alignment=TA_CENTER))],
    [Paragraph("<b>Exposed</b>",ParagraphStyle("cr",fontSize=9.5,fontName="Helvetica-Bold",textColor=colors.white)),
     Paragraph("a",ParagraphStyle("cc",fontSize=11,fontName="Courier-Bold",textColor=TEAL,alignment=TA_CENTER)),
     Paragraph("b",ParagraphStyle("cc2",fontSize=11,fontName="Courier-Bold",textColor=TEAL,alignment=TA_CENTER)),
     Paragraph("a+b",ParagraphStyle("ct",fontSize=9,fontName="Courier",textColor=DARK_GRAY,alignment=TA_CENTER))],
    [Paragraph("<b>Unexposed</b>",ParagraphStyle("cr2",fontSize=9.5,fontName="Helvetica-Bold",textColor=colors.white)),
     Paragraph("c",ParagraphStyle("cc3",fontSize=11,fontName="Courier-Bold",textColor=TEAL,alignment=TA_CENTER)),
     Paragraph("d",ParagraphStyle("cc4",fontSize=11,fontName="Courier-Bold",textColor=TEAL,alignment=TA_CENTER)),
     Paragraph("c+d",ParagraphStyle("ct2",fontSize=9,fontName="Courier",textColor=DARK_GRAY,alignment=TA_CENTER))],
    [Paragraph("<b>Total</b>",ParagraphStyle("cr3",fontSize=9.5,fontName="Helvetica-Bold",textColor=colors.white)),
     Paragraph("a+c",ParagraphStyle("ct3",fontSize=9,fontName="Courier",textColor=DARK_GRAY,alignment=TA_CENTER)),
     Paragraph("b+d",ParagraphStyle("ct4",fontSize=9,fontName="Courier",textColor=DARK_GRAY,alignment=TA_CENTER)),
     Paragraph("n",ParagraphStyle("ct5",fontSize=11,fontName="Courier-Bold",textColor=TEAL,alignment=TA_CENTER))],
]
story.append(Table(cont_data, colWidths=[4.5*cm, 4*cm, 4*cm, 4.5*cm],
    style=TableStyle([
        ("BACKGROUND",(0,0),(0,-1), TEAL),
        ("BACKGROUND",(1,0),(-1,0), TEAL),
        ("ROWBACKGROUNDS",(1,1),(-1,-1),[ACCENT, colors.white]),
        ("GRID",(0,0),(-1,-1),0.5,colors.HexColor("#BDC3C7")),
        ("TOPPADDING",(0,0),(-1,-1),8), ("BOTTOMPADDING",(0,0),(-1,-1),8),
        ("LEFTPADDING",(0,0),(-1,-1),8), ("RIGHTPADDING",(0,0),(-1,-1),8),
        ("VALIGN",(0,0),(-1,-1),"MIDDLE"),
    ])))
story.append(bul("Expected value for cell 'a' = (a+b)(a+c) / n"))

story.append(Paragraph("Source: Park's Textbook of Preventive and Social Medicine, pp. 956-957  |  Henry's Clinical Diagnosis, pp. 154-155", sources_style))
story.append(PageBreak())

# ===== SUMMARY + MNEMONICS =====
story += section_header("8", "Summary & Exam Mnemonics")

story.append(sub_header("t-Test vs Chi-Square — At a Glance"))
story.append(build_table(
    ["Feature", "t-Test", "Chi-Square (χ²)"],
    [["Data type", "Continuous (means)", "Categorical (counts)"],
     ["Tests for", "Difference between means", "Association between variables"],
     ["Groups", "Exactly 2 groups", "2 or more groups"],
     ["Key assumption", "Normal distribution", "Expected frequency ≥ 5"],
     ["Degrees of freedom", "n₁ + n₂ − 2", "(r−1)(c−1)"],
     ["When assumptions fail", "Use Mann-Whitney U test", "Use Fisher's Exact Test"]],
    col_widths=[5.5*cm, 5.75*cm, 5.75*cm]
))

story.append(Spacer(1,10))
story.append(sub_header("Key Values to Memorise"))
story.append(build_table(
    ["Value", "Meaning"],
    [["p < 0.05", "Statistically significant (5% significance level)"],
     ["x̄ ± 1σ = 68.3%", "Normal distribution: 68% within 1 SD"],
     ["x̄ ± 2σ = 95.4%", "Normal distribution: 95% within 2 SD (used for reference ranges)"],
     ["x̄ ± 3σ = 99.7%", "Normal distribution: 99.7% within 3 SD"],
     ["χ² critical (df=1) = 3.84", "Threshold for significance in a 2×2 chi-square test"],
     ["Type I (α) ≤ 0.05", "False positive — set as significance level"],
     ["Type II (β) ≤ 0.20", "False negative — power = 1 - β ≥ 0.80"],
     ["Z = (x − x̄) / σ", "Standard normal variate formula"]],
    col_widths=[6.5*cm, 10.5*cm]
))

story.append(Spacer(1,10))
story.append(sub_header("Mnemonics"))
mnemonics = [
    "ALPHA = ALARM  →  Type I error = you falsely SET OFF the alarm (False Positive)",
    "BETA = BLIND   →  Type II error = you are BLIND to a real difference (False Negative)",
    "1-2-3 Rule: 1SD=68%, 2SD=95%, 3SD=99.7%  (remember: 68-95-99.7)",
    "Chi-square: O vs E  →  'Did what we Observed match what we Expected?'",
    "t-test = means, chi-square = counts  →  'Tall people have means; count sheep'",
    "p < 0.05 = probably not chance   |   p > 0.05 = probably chance",
]
for m in mnemonics:
    story.append(mnemo(m))

story.append(Spacer(1,10))
story.append(hr())
story.append(Paragraph(
    "Sources: Park's Textbook of Preventive and Social Medicine  |  "
    "Henry's Clinical Diagnosis and Management by Laboratory Methods  |  "
    "Goldman-Cecil Medicine  |  Barash, Cullen, and Stoelting's Clinical Anesthesia, 9e  |  "
    "Miller's Review of Orthopaedics 9th Edition",
    sources_style))

# ---------- Build ----------
doc.build(story)
print(f"PDF saved to: {OUTPUT}")