Introduction
In today's competitive business landscape, intuition is no longer sufficient for making critical decisions. Companies that leverage statistical analysis to inform their strategies consistently outperform those that rely on experience or instinct.
The story that follows demonstrates how a systematic statistical approach from descriptive analytics to hypothesis testing can provide clear, evidence-based answers to complex business questions. More importantly, it shows how understanding statistical concepts like effect size, statistical power, and potential errors can prevent costly mistakes and unlock growth opportunities.
The Business Problem
A retail company operating both online and physical stores wanted to answer three key questions:
- How are sales performing over time?
- How reliable are insights drawn from the data?
- Does running a marketing campaign actually increase revenue per transaction? The company had three years of transaction data, including revenue, store type, region, and whether a marketing campaign was used. The goal was to use statistics to support decision-making.
Step by Step Statistical Analysis
Before testing anything, you need to know what your data looks like. This is called descriptive statistics.
What We Calculated:
Central Tendency (The "Average")
- Mean revenue: 8272 per transaction
- Median revenue: 7723 per transaction The mean is higher than the median, which tells us some transactions are very high (outliers). The median is often more "typical".
Distribution Shape
Skewness and kurtosis show that most transactions are low to moderate, but there are some very high transactions pulling the average up. The distribution looks like this:
Visualize the Data
Numbers are important, but pictures tell stories. We created four key visualizations:
Revenue Over Time (Line Chart)
What we found is that revenue has seasonal peaks and valleys. December is high (holidays), and January is low (post holiday slump).
Why this matters: If we only compared December to January, we'd think campaigns work miracles. But it might just be Christmas shopping.
Revenue by Store Type (Bar Chart)
Online transactions are actually more valuable on average, even though physical stores sell more volume.
Revenue by Region (Box Plot)
Nairobi: Highest median revenue but most variable
Rift Valley: Most consistent (narrow box)
Western & Coast: Lower median but good campaign response
Business Insight: One marketing strategy won't fit all regions. We need customisation.
Units Sold vs. Revenue (Scatter Plot)
This showed that campaigns don't just increase volume, they increase the value per unit sold. Customers buy more expensive items during campaigns.
Check for Bias (Sampling)
TYPES OF BIAS:
1. SELECTION BIAS
- Urban areas systematically differ from rural areas
- Higher income, different shopping behaviors
- Better infrastructure and internet connectivity
2. GEOGRAPHIC BIAS
- Rural regions completely excluded
- Cannot generalize findings to entire market
3. SOCIOECONOMIC BIAS
- Urban customers have different purchasing power
- Product preferences may differ
BUSINESS IMPACT
- Revenue estimates would be overstated
- Marketing effectiveness could be overestimated
- Regional strategy would be incomplete
- Expansion decisions would lack empirical foundation
RECOMMENDED SAMPLING METHOD:
STRATIFIED RANDOM SAMPLING:
- Divide population into strata (regions, store types)
- Randomly sample proportionally from each stratum
- Ensures all segments are represented
- Maintains natural population distribution
- Allows both overall and stratum-specific analysis
Apply Statistical Theorems
Law of Large Numbers
We tested sample sizes from 10 to 1,000 transactions:
Central Limit Theorem
Even though individual transactions are all over the place (skewed distribution), when we take many samples and average them, the averages form a nice, normal bell curve.
Hypothesis Testing
A key business question examined was:
Does running a marketing campaign increase average revenue per transaction?
A one-tailed independent samples t-test was conducted to compare revenues from transactions with and without a marketing campaign.
The results showed:
- A large t-statistic
- A p-value far below the 5% significance level
This led to rejecting the null hypothesis and concluding that marketing campaigns significantly increase average revenue per transaction.
Business implication:
Statistical testing provides objective evidence to support or challenge strategic initiatives, reducing reliance on intuition alone.
Errors and Interpretation
Statistical decisions are subject to error:
A Type I error would mean concluding the campaign works when it does not, leading to wasted marketing budgets.
A Type II error would mean failing to detect a real effect, causing missed revenue opportunities.
Recognizing these risks allows businesses to balance caution with opportunity.
Type II error is worse because:
- Lost revenue is permanent
- Competitors gain market share
- Recovery is expensive
Effective size and Power
Although the campaign effect was statistically significant, the calculated Cohen’s d indicated a small to medium effect size. This means that while the campaign works, its impact per transaction is modest.
A statistically insignificant result could still matter in practice if:
- The effect is small but consistent
- The business operates at large scale
- The sample size is insufficient
Business implication:
Statistical significance should be interpreted alongside effect size and business context. Collecting more data can improve confidence and guide optimization rather than abandonment of strategies.
### Conclusion
This case study illustrates that statistics is far more than an academic exercise. When applied correctly, it enables businesses to:
- Understand performance realistically
- Measure risk and variability
- Test strategic decisions objectively
- Avoid costly cognitive and sampling biases
By integrating descriptive statistics, visualization, sampling theory, probability laws, and hypothesis testing, organizations can make evidence-based decisions that are both statistically sound and commercially meaningful.
In an increasingly competitive environment, businesses that leverage statistics effectively gain a decisive advantage not by predicting the future perfectly, but by making better decisions under uncertainty.
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