Biostatistics😊

Biostatistics

Types of Statistics

Q. What s the branch of statistics dealing with describing the internal collection of data? (INICET-2022)
A. Theoretical statistics
B. Analytical statistics
C. Inferential statistics
D. Descriptive statistics

Data and Central Tendency Measures

Data Types

Data Scales → NOIR

Example

• GCS, VISION ANALOGUE SCALE → Ordinal

• Has negative values → Interval
• football (FC → Fahrenheit and Celsius) - has Interval (Interval scale)

• Temperature measured
1. Kelvin → ratio
2. Celsius/F → Interval
3. hot or cold → nominal
4. Hot, hotter, hottest → Ordinal

• Hb
1. Ratio as such
2. Anaemic and non anaemic → Nominal
3. Mild, mod and severe anaemia → ordinal

Types of Ordinal Scale

• Likert scale:
• Mnemonic: Likert → Like or dislike (only distinct options)
• Agree/disagree continuum

• Guttman scale:
• Summative scale

Variations and Deviations

Measures of Variations

• Range = Maximum Value - Minimum Value

• Standard Deviation (σ):
• σ = √[Σ(x-x̄)²/n], where:
• Mnemonic: RMSD (Root of Mean of Squared Deviation).
• Σ: Summation
• n: Sample size
• x̄: Mean
• x: Given value
• In small samples, "n" is replaced by n-1 (correction factor).

Coefficient of Variation:

• SD x 100
  mean

• Used to find variation in 2 different groups.

Variance

• = SD x SD

Standard Error (SE)

• For Mean (SE of Mean):

• For Standard Deviation (SE of SD): 2s - 2n

SAMPLE SIZE

• 4pq/ (L x L)
• p = Probability (%)
• q = 100 - p
• L = Allowable error (%)

Z-score

• (x - mean)/ SD

• For individual values → Osteoporosis (T score)

RE α 1 / (Precision α Reproducibility/ Reliability)

• Precisely () random () alkkare kuthiyal reproduce () cheyyam

SE α 1 / (Accuracy α Validity)

• Vaccurat (Validity → Accuracy) systematic (systematic error)

• Validity:
• Hit the board
• Results are within a desired range.

• Accuracy:
• Bull’s eye
• Nearness/closeness to the actual true value.

• Reliability:
• Repeatability
• Out of the board, but same result when repeated
• Dependable, reproducible, repeatable results.

• Note:
• Serial interval:
• Proxy indicator for incubation period.
• CFR:
• Denote virulence of a disease.

Normal Distribution Curve and Skew

Features of Normal Distribution Curve

• Bi/Lateral symmetrical, bell-shaped curve.
• Depends on mean and standard deviation

• Also known as Gaussian distribution.

• Unimodal
• One peak

• Ends never touch baseline.

• Mean = median = mode:
• Coincide at centre.

• Mean = 0

• SD = 1, Variance = 1.

• Area Under Curve (AUC) = 100% (1).

• Note:
• Standard Deviation (SD) at centre = zero.
• ± 1SD = 68.3%
• ± 2SD = 95.5% (Normal zone).
• ± 3SD = 99.7%

NOTE

• Base of graph α margin of error

Bimodal distribution

• Two peaks

• Bi mode = Two Modes

• Mean = Median ⇏ Mode

Skew

• Abnormal distribution curve

Binomial Distribution

• Only 2 possible outcomes
• Example: Yes / No, Success / Failure

Poisson Distribution

• Describes chance of events in a given time frame
• Examples:
• Number of OPD cases per week
• Predicting future case counts

• Used for rare events

• Formula:
• μ = λ × t
• λ = average rate
• t = time

Measures of Central Tendency

• Mode = 3 (median) - 2 (mean)

• Best measure of central tendency:
• Mean > median > mode

• Best measure when there is diverse range of values
• Median

• In skewed data (extreme)
• Most affected: Mean
• Least affected: Mode
• Most useful measure: Median

P-Value

P-Value (Probability Value)

• Range from 0 to 1.

• P-value at ± 2 SD = 0.05 (Normal).

Null Hypothesis (N°H)

• No difference between the groups being compared.

P-value = 0.04 means:

• 96% chance of being significant
• Null hypothesis → False

• 4% chance of being insignificant
• Null hypothesis → True

• Also 4% chance of being
• Null hypothesis → False positive → Type 1 error (AFP)

A randomized control trial is being conducted in patients with direct inguinal hernia, to compare the outcomes of a new surgery 'A' and the gold standard surgery 'B'. The p-value of this trial is found to be 0.04. What can we conclude from this?

Errors in P-value (Hypothesis Testing)

Memory Tips:

• Type I Error: First letter = α = False positive = Rejected True hypothesis
• AFP → RT (α - Reject True)
• P < 0.05 → Reject → true
• (him α guy) → False positive guy → Rejected true love

• Type II Error: Second = β = False negative = Accepted false hypothesis
• Boyfriend (β) was fun (FN) accepted False gf (False hypothesis)
• P > 0.05 → Accept → false
• (me β guy) → False negative guy → Accepted false love
• Power of a Test Formula: (1 − β)
• Why (1 − β)?
• β error = Type II error (false negative)
• H₀ is false but accepted

Null Hypothesis (H₀)

• States: "No difference exists"

• We assume it's true, then perform tests to reject or accept it based on data.

Type 1 Error (α error)

• Reality: H₀ is true (no difference between drugs)

• Error: Rejected a true H₀

• Buzzword:
• H₀ true, False positive study
• 1 → True, Positive

• Example:
• New drug is not better, but launched due to clinical trial

• Outcome:
• P value < 0.05 ⇒ Positive
• Significant difference = rejected a true null hypothesis
• False positive trial
• Meaning = Trial concluded positive, but It was false
• Serious error
• Drug launched unnecessarily

• Basically what it means
• Some pottan made a potta drug, no difference to exisisting drug
  (i.e. reality → null hypothesis is true)
• But trial said it is effective drug → So introduced into market
• He is a pottan, but held as alpha by everyone
• This potta drug may replace existing drug
• It is a serious error

Type 2 Error (β error)

• Reality: H₀ is false (new drug is better)

• Error: Accepted a false H₀

• Buzzword:
• H₀ false, False negative trial
• 2 → False, negative

• Example:
• New drug is better, but not launched due to clinical trial

• Outcome:
• P > 0.05 ⇒ Negative
• False negative trial
• Less serious
• Missed opportunity for better drug

• Basically what it means
• I made a good drug → which is better than existing drug
  (i.e. null hypothesis was false)
• But trial somehow rejected it by saying my drug is not better
  (interpreted it as true → [& accepted a null hypothesis]→ which was actually false)
• Trial showed negative → but it was false → False negative
• Made me look like a β
• But it is not a serious error, because it wont affect anyones health more badly than currently is

MCQs

• A. Null hypothesis is true and is accepted

• B. Null hypothesis is false but is accepted

• C. Null hypothesis is true but is rejected

• D. Null hypothesis is false and is rejected
ANS
Null hypothesis is true but is rejected

Power of a Test

• The power of the test can be increased by ↑↑ sample size, Precision
• Power of a Test Formula: (1 − β)
• Why (1 − β)?
• β error = Type II error (false negative)
• H₀ is false but accepted

Test of Significance

• BP or sugar of 50 people checked before and after one month of drug
→ Quantitative → Same group
→ Use Paired t-test

• HB levels compared in 2 villages
• One village gets IFA tablets, other gets diet modifications
→ Quantitative → Different groups,
→ Use Unpaired t-test

• Effect of 3 different intervention measured by % of smokers in 3 different groups:
• 1st group: Technical lecture
• 2nd group: Spiritual talks
• 3rd group: Nicotine tablets
• % = Qualitative
• → Use Kruskal Wallis test > Chi square test

• Birthweight of baby measured in 2 groups of pregnant women:
• Group 1: Eats 200g papaya
• Group 2: Eats 200g guava
• Birthweight → Quantitative
→ Use Unpaired t-test
• If instead of birth weight, LBW vs HBW was plotted, it would be a qualitative study
→ Chi square test

Chi-square Test vs Wilcoxon Signed-Rank Test

Other Statistical Tests

Sampling Methods

Non probability

Probability (Better)

Q. The urban areas of Delhi have 4000 population with different religions. Research is being done to study the dietary habits of the population. Which of the following techniques can be used to obtain a study sample?

Regression

• Used to calculate one variable with the help of another variable.

Types:

1. Simple Regression
• Using 1 independent variable
• Calculate 1 dependent variable

2. Multiple Regression
• Using > 1 independent variable
• Calculate 1 dependent variable to calculate

3. Logistic Regression
• Outcome is binary
• Yes/No
• e.g.,
• Death/No Death,
• Clean/Not Clean

Graphical Presentations

• Bar chart → Bar
• Pie chart → Pie
• Pictogram → Picture
• Spot maps → Maps
• Venn diagram → Venice picture
• Choropleth → Chlorin

Charts

Kaplan Meir Curve

• PYQ → Compare survival probability

STEM and LEAF

TREE PLOT

Bar Chart

• Columns separated

• Use:
• Qualitative data
• Frequency on other axis

Multiple Bar Chart

• Multiple data in single column

• Don't confuse with Component Bar Chart

 

Component Bar Chart/ Composite bar chart

• Same data is represented across different timelines

• total magnitude is divided into different subset

 

ANS

C

Histogram

• Continuous data
• History is continuous

• Columns joined

• Use:
• Quantitative data
• Frequency and variable
• NOT TIME
• Flow cytometry

Frequency Chart/Polygon Curve

• Midpoints of histogram joined
• Between variable and frequency

 

Stacked Bar Chart

• Multiple bars stacked

Line Diagram or Chart

• Time vs. frequency

• Also Time Trend Chart
• Between Frequency and time

 

Pie Chart

• Sectoral presentation

• Always in percentage

• Best for technical data

Venn Diagram

• For overlapping qualitative data

• Mnemonic: When on your lap

Spot Map

• Geographical location of data on map

 

Choropleth

• Geographic intensity of data on map

Pictogram

• Symbolic data presentation

• Best for general population

• Creates mass awareness

Ogive

 

• Cumulative frequency vs. variable

• Curve always rising

• Defines:
• Class interval
• Cut-off
 

Box and Whisker Plot

• Shows data distribution

• Based on quartile

• Values in box = 50%

• Inter-quartile range: Q3 - Q1

• Does not show mean

 

ANS

B

ANS

Mean > Median > Mode → Right skew, Positive

Scatter Plot

• Between two quantitative variables

• Finds correlation

• Shows direction, strength, degree of relation

FLOW CYTOMETRY

• SCATTER PLOT

• HISTOGRAM

 

Pearson's Correlation Coefficient (r)

• Used in scatter plot

• NOT AN INDICATOR OF VARIATION

• Helps to find correlation between two variables.
• r = -1 : Perfect negative correlation = PROTECTIVE
• r = 0 : No correlation
• r = +1 : Perfect positive correlation = RISK FACTOR
• b/w 1 and 0 = Weak correlation

• Spearman correlation coefficient also used

Which of the following statements accurately describes the correlation between bone marrow density and gestational age, as depicted in two separate studies?

ANS

 

A homogenous sample of 4 groups was taken as shown below. The height and weight of each group had a correlation coefficient of 0.6. What will be the total coefficient of correlation of the whole group?

A. Equal to 0.6
B. Less than 0.6
C. More than 0.6
D. Skewed coefficient of 0.6

ANS

A. Equal to 0.6

Ishikawa Diagram / Fishbone Diagram

• Also known as Cause-and-Effect Diagram.

• Purpose:
• Identifies all possible causes contributing to a specific problem or effect.

• Major Cause Categories (Primary Causes):
• Materials
• Methods / Processes
• Manpower / People
• Machines / Equipment
• Mother Nature / Environment
• Measurements

• Structure:
• Main “bones” represent primary causes.
• Each primary cause is further broken down into secondary causes.

• Effect:
• Represented at the fish head (right side): The Problem to be analyzed.

Monthly Requirement:

• Amlodipine = 40 patients × 30 days = 1200 tablets

• Lisinopril = 10 patients × 30 days = 300 tablets

• Total tablets required = 1200 + 300 = 1500 tablets

Reorder Factor (rf):

• Reorder factor is the buffer stock multiplier.

• A. 1000 tablets: Too low (even base requirement is 1500) → ❌

• B. 1200 tablets: Too low → ❌

• C. 1400 tablets: Still low → ❌

• D. 1600 tablets: Sufficient. Closest matching reorder factor:
→ 1500 × rf = 1600 → rf ≈ 1.06 → Matches rf = 2 as a standard buffer factor in public health.