Types of Data Analytics – Lecture Notes

Historical Context & Big Picture

• Data‐analytics practices began in the late 1960s when computational power became available to run algorithms at scale.

• All analytic work, regardless of domain (business, health-care, engineering), is ultimately “algorithm implementation on data.”

The Four Core Types of Data Analytics

• Past-focused analytics
  • Descriptive (What happened?)
  • Diagnostic (Why did it happen?)

• Future-focused analytics
  • Predictive (What will happen?)
  • Prescriptive (How should it be handled/treated?)

• Remember the sequence: Descriptive → Diagnostic → Predictive → Prescriptive.

Descriptive Analytics

Purpose

• Provide a factual summary of events: counts, totals, averages, distributions.

• Used heavily in Assignment 1 and the upcoming quiz.

Statistical Toolkit (Measures of Central Tendency)

• Mean (Average) $\text{Mean}=\frac{\sum<em>{i=1}^n x</em>i}{n}$

• Median
  • Sort data ascending, choose the middle.
  • Even sample: average the two central values.

• Mode
  • Most frequently occurring value.

Additional Position Metrics

• Percentile – Proportion of the population scoring below a given value (e.g., 95th percentile ⇒ 95 % of observations fall below).

• Quartiles (Q1 – Q4)
  • Q1 = top 75–99 %
  • Q2 = 50–74 %
  • Q3 = 25–49 %
  • Q4 = 0–24 %

Measures of Dispersion

• Range $\text{Range}=x<em>{\max}-x</em>{\min}$

• Variance $\sigma^2 = \frac{\sum<em>{i=1}^n (x</em>i-\bar{x})^2}{n}$

• Standard Deviation $\sigma=\sqrt{\sigma^2}$

• Inter-quartile Range (IQR) $\text{IQR}=Q<em>3-Q</em>1$

Worked Mini-Example (Even-sized set)

Data: 53 58 69 70 … (20 values).
• Mean = (Σ values)/20.
• Median = average of 10th & 11th values (69 & 70).
• Mode = 53 (most frequent).

Diagnostic Analytics

Goal

• Move from “what” to “why” by isolating root causes.

Four Canonical Techniques

1. Drill-Down Analysis
   • Top-down approach (e.g., Country → State → City → Suburb).
   • Used to localise a fault or a disease focus.

2. Data Mining Workflow

   1. Gather raw data from multiple sources.

   2. Data preparation: remove noise & outliers.

   3. Feature extraction ("mining" the most informative patterns).

   4. Analyse & interpret (classification, clustering, etc.).
      • Health example: classifying cough sounds into Normal, Asthma, COVID, Heart-failure.
      • Business example: identify profit-making versus loss-making products.

3. Correlation Analysis
   • Measures linear association between two variables.
   • Coefficient range $-1 \le r \le 1$
   – $r\approx1$: strong positive trend
   – $r\approx0$: no trend
   – $r\approx -1$: strong negative trend.
   • Statistical significance usually accepted at $p\le0.05$.
   • Watch for outliers – points far outside the main cloud that distort $r$.

4. Causal (Causality) Analysis
   • Focus on cause → effect (not just correlation).
   • Examples
   – Study hard ⇒ good grades.
   – Caffeine intake ⇒ increased alertness.
   – Ad spend ⇒ higher sales.
   • Must rule out confounding third-variables (non-spuriousness).
   • Demonstrated via controlled experiments or advanced statistical tests.

Data Typology & Preparation

Raw vs Processed

• Raw data: direct sensor output (e.g., ECG voltages, microphone waveform).

• Processed data: cleaned, digitised, features extracted.

High-level Categories

1. Categorical (Qualitative)
   • Nominal – unordered labels (gender, ice-cream flavour).
   • Ordinal – ordered categories (low/med/high salary, primary → tertiary education).

2. Numerical (Quantitative)
   • Discrete – distinct counts (daily stock index, unit sales).
   • Continuous – measured on an infinite scale (speech waveform, heart signal).

Analog-to-Digital Reminder

• Computers analyse only discrete values.

• Continuous signals are sampled & quantised by an A/D converter before storage or analysis (e.g., Zoom audio, scanned photographs).

Outliers Defined

• Data points lying far outside the main distribution (e.g., single blue dot way off trend line).

• Often indicate noise, measurement error, or exceptional cases; routinely removed during data preparation.

Predictive & Prescriptive Analytics

(Future-Oriented – heavy use of Machine Learning)

Regression vs Classification

• Regression – predict continuous quantity (price, temperature).

• Classification – assign item to discrete category (spam / not-spam, diseased / healthy).

Linear Regression

• Best-fit straight line $y = mx + c$ across data points.

• Used when relationship is approximately linear.

Polynomial Regression

• Fit higher-order curve $y = a<em>0 + a</em>1x + a_2x^2 + \dots$.

• Captures curved trends and usually reduces residual error.

Logistic Regression (Sigmoid-Based Classification)

• Model: $\sigma(z)=\frac{1}{1+e^{-z}}$ (S-shaped curve).

• Decision rule: \sigma(z) < 0.5 \Rightarrow 0, $\sigma(z) \ge 0.5 \Rightarrow 1$.

• Excellent when data cluster into two regions not separable by a straight line.

Probabilistic Modeling – Bayes’ Theorem

• Fundamental rule for conditional probability:
  $P(A|B)=\frac{P(B|A)\,P(A)}{P(B)}$

Classic Card Example (Queen of Diamonds)

• $P(\text{Queen}) = 4/52$, $P(\text{Diamond}) = 13/52$, $P(\text{Diamond}|\text{Queen}) = 1/4$.

• $P(\text{Queen}|\text{Diamond}) = \frac{1/4 \times 4/52}{13/52} = 1/13$.

Weather Example

• $P(\text{Cloudy}) = 0.4$, $P(\text{Rain}) = 0.2$, $P(\text{Cloudy}|\text{Rain}) = 0.85$.

• $P(\text{Rain}|\text{Cloudy}) = \frac{0.85 \times 0.2}{0.4} = 0.425$ (42.5 % chance of rain when it’s cloudy).

Relevance

• Underpins naïve-Bayes classifiers and probabilistic reasoning used in predictive/prescriptive analytics.

Health Informatics Perspective

• Intersection of large health data sets + analytical techniques + domain expertise.

• Five pillars for successful projects:

  1. Data quality & volume ("Big data").

  2. Domain knowledge (clinicians: pulmonologists for lung data, cardiologists for heart data, etc.).

  3. Appropriate techniques (stats, data mining, ML).

  4. Ethical compliance – informed consent & approvals.

  5. Visualisation & communication of results.

Course & Assessment Links

• Quiz: Due $13^{\text{th}}$ June – worth 10 %.

• Assignment 1: Released 30 June – statistical description + correlation/diagnostic analyses (~25 %).

• Understanding today’s lecture content is critical for Assignment 1 success (mean/median/mode, variance, correlation, regression basics).

Quick Reference – Key Terms

• Descriptive / Diagnostic / Predictive / Prescriptive

• Mean, Median, Mode, Percentile, Quartile, Range, Variance, $\sigma$

• Drill-down, Data Mining, Correlation ($r$), Causality

• Categorical (Nominal, Ordinal) vs Numerical (Discrete, Continuous)

• Linear/Polynomial/Logistic Regression, Classification vs Regression

• Sigmoid function $\sigma(z)$, Bayes’ Theorem

• Outlier, Noise, Analog-to-Digital (A/D) conversion

These notes condense every concept, example, deadline, and methodological detail discussed in the lecture, providing a ready-to-study replacement for the original transcript.