Module 7: Statistics for Data Analysis | Data Analyst

"Statistics is the grammar of science." — Karl Pearson

Learning Objectives

By the end of this module, you will be able to:

Calculate and interpret descriptive statistics (central tendency, spread, shape)
Describe and apply probability distributions (normal, binomial, Poisson)
Perform hypothesis tests (t-test, chi-square, ANOVA) and interpret results
Calculate and explain confidence intervals
Distinguish correlation from causation and avoid common statistical pitfalls
Apply statistical thinking to real business problems

Why Statistics for Data Analysts?

Without statistics, analysis is sorting and plotting. With statistics you can say how surprised you should be by a gap, how wide plausible ranges are, and when noise looks like a pattern.

Goal	Statistical idea
Typical value?	Mean, median, trimmed mean
Uncertainty?	Standard error, confidence interval
Real difference?	Hypothesis test + effect size
Relationship?	Correlation (carefully)

Concept: A p-value is not “probability the null is true” — it’s how often you’d see data this extreme if the null story were true.

1. Descriptive Statistics

Measures of Central Tendency

Mean = balance point; median = middle sorted value; mode = most frequent. For skewed income-like data, median often matches “typical person” better than mean.

Measures of Spread

Range, variance, standard deviation (same units as data), IQR (Q3−Q1, robust). Coefficient of variation compares spread relative to the mean across scales.

Shape: Skewness and Kurtosis

Skewness: tail direction (>0 right-skew). Kurtosis: tail heaviness vs normal. Use plots — numbers alone lie softly.

2. Probability Distributions

Normal Distribution (Gaussian)

Bell curve; described by μ and σ. 68–95–99.7 rule for quick intuition. Many methods assume approximate normality; check with histograms / Q-Q plots.

Binomial Distribution

Count of successes in n fixed trials with probability p per trial — clicks, conversions, defectives.

Poisson Distribution

Count of rare events in fixed exposure — support tickets per hour, accidents per day. Mean ≈ variance at moderate λ.

Distribution	Question it models
Normal	Continuous, symmetric-ish
Binomial	Yes/no counts out of n
Poisson	Event counts in an interval

3. Hypothesis Testing

The Framework

H₀ = boring baseline (“no effect”). H₁ = what you seek. Pick α (often 0.05). Compute p-value; if p < α, reject H₀ — but always ask effect size and business meaning.

t-Test: Comparing Means

Two-sample for independent groups (A/B). Paired for before/after on same units. One-sample vs a benchmark.

Chi-Square Test: Comparing Proportions

Contingency tables — independence of two categoricals (segment vs tier).

ANOVA: Comparing 3+ Groups

Tests whether any group mean differs; follow with post-hoc pairwise tests and multiple-comparison correction if needed.

Situation	Test direction
Two independent groups	Two-sample t-test (or Welch if variances differ)
Same subjects twice	Paired t-test
3+ groups	ANOVA first, then corrected pairwise
Counts in categories	Chi-square / Fisher as appropriate

Fun Fact: Six pairwise t-tests at α=0.05 can easily yield ~26% chance of some false alarm — that’s why ANOVA + correction exists.

4. Confidence Intervals

A CI gives a range of plausible parameter values from your sample. Wider = more uncertainty or higher confidence level. For proportions, use normal approximation when counts are healthy.

Try This! State a 95% CI for a mean in plain English without saying “95% probability the truth is in the range” — use the repeat the study interpretation.

5. Correlation

Correlation vs. Causation

Pearson = linear association. Spearman = monotonic (rank-based). Neither implies X causes Y.

The Causation Trap

Confounders create spurious correlation (ice cream and drownings ↔ summer). Experiments, timing, and domain knowledge fight this.

6. Effect Size and Practical Significance

Huge samples make tiny differences “significant.” Report Cohen’s d (or similar) and ask: “Would we change a decision for this magnitude?”

Key Example: Classic pattern — t-test p-value plus a standardized effect size so you don’t confuse statistical and practical wins.

python

[object Object], numpy ,[object Object], np
,[object Object], scipy ,[object Object], stats

rng = np.random.default_rng(,[object Object],)
control = rng.normal(,[object Object],, ,[object Object],, ,[object Object],)
treatment = rng.normal(,[object Object],, ,[object Object],, ,[object Object],)

t_stat, p_value = stats.ttest_ind(control, treatment)
pooled = np.sqrt(
    (,[object Object], * control.std(ddof=,[object Object],) ** ,[object Object], + ,[object Object], * treatment.std(ddof=,[object Object],) ** ,[object Object],) / ,[object Object],
)
cohens_d = (treatment.mean() - control.mean()) / pooled

,[object Object],(,[object Object],)
,[object Object],(,[object Object],)
,[object Object],(,[object Object],)

Practice Exercises

Exercise 1: Descriptive Statistics Report (Beginner)

500 salaries: mean, median, std, IQR, skewness; histogram with mean/median marked; interpret mean vs median gap.

Exercise 2: A/B Test Analysis (Intermediate)

Two conversion rates with equal n: test significance and CI for difference.

Exercise 3: Distribution Fitting (Intermediate)

Histogram + Q-Q + Shapiro / KS for normality call.

Exercise 4: Multi-Group Comparison (Advanced)

Five locations: ANOVA, post-hoc, box plots.

Exercise 5: Full Statistical Report (Advanced)

Full stack: descriptives, tests, CIs, effect sizes, visuals, non-technical summary.

Mini-Project: Marketing Campaign Analysis

Four channels: describe conversions and revenue, chi-square on conversion, ANOVA on revenue, correlations spend↔outcome, CIs for ROI, one-page exec summary.

Key Takeaways

Describe before you infer; plots + summaries first.
Match distribution to data-generating story.
Pair p-values with effect sizes and CIs.
Correlation is not causation — hunt confounders.
“Significant” can still be negligible in business terms.

Resources for Further Learning

Key Takeaway

Summarize with mean/median/SD/IQR and always look at shape on a plot.
Pick tests that match variable types and study design (paired vs independent).
Report confidence intervals and effect sizes, not only p-values.
Treat correlation as a hint, not proof of causation.
Ask whether a statistically detectable change is large enough to act on.

Next up: Module 8 — Advanced Data Processing — level up your data wrangling with optimized Pandas and the blazing-fast Polars library.