Channel conversion rates and traffic mix jointly determine the overall rate
Purchase conversion can rise for both search ads and social ads while falling across all advertising visits. Before reversing a website change, an advertising manager should examine the share of visits supplied by each channel. A larger share from a channel with a lower purchase rate can outweigh rising rates within both channels.
A reversal between subgroup comparisons and the aggregate comparison is known as Simpson’s paradox. Marketing research has examined how changes in subgroup rates and changes in group composition contribute to aggregate results. (Lipovetsky and Conklin on data aggregation)
Put conversion rates and session shares in the same table to investigate changes in visitor response alongside changes in the mix of visits. The practical method proposed here preserves the actual aggregate result and calculates a separate comparison using fixed traffic weights.
Both channels improve while overall conversion falls from 8.2% to 4.8%
For this example, the denominator is the number of advertising sessions and the numerator is the number of those sessions containing at least one purchase. A session represents a visit to the website. A person returning in a new session adds another visit; multiple purchases during one session count as one purchasing session.
Worked example with hypothetical figures
Compare two consecutive 30-day periods for the same website. Each session belongs to exactly one of two channels, search ads or social ads. Visits from other sources are excluded. Purchase definitions and channel classification remain the same across both periods.
| Channel | Earlier sessions | Earlier purchasing sessions | Earlier rate | Later sessions | Later purchasing sessions | Later rate |
|---|
| Search ads | 900 | 81 | 9% | 200 | 24 | 12% |
| Social ads | 100 | 1 | 1% | 800 | 24 | 3% |
| All advertising sessions | 1,000 | 82 | 8.2% | 1,000 | 48 | 4.8% |
Search conversion rises from 9% to 12%, and social conversion rises from 1% to 3%. Yet purchasing sessions fall from 82 to 48 and the overall rate declines. Every row is arithmetically consistent.
The mix has changed. Search sessions fall from 90% to 20% of advertising sessions, while social sessions rise from 10% to 80%. The increased weight of social traffic, which has the lower conversion rate in this example, pulls the aggregate down. These hypothetical figures establish no general ranking of search and social advertising.
Averaging the two rates gives a different result from the actual total
Calculate the overall rate as total purchasing sessions divided by total sessions. A simple average gives equal weight to channels even when their session counts differ.
For the earlier period, the simple average is (9% + 1%) / 2 = 5%. Actual purchasing sessions total 82 out of 1,000, so the aggregate advertising conversion rate is 8.2%. Calculating the actual overall result requires accounting for visit counts.
Equivalently, multiply each channel’s conversion rate by its share of all advertising sessions and add the results:
- Earlier period: 9% × 90% + 1% × 10% = 8.2%.
- Later period: 12% × 20% + 3% × 80% = 4.8%.
This is a weighted average, using session shares as weights. Both channel conversion rates and the distribution of sessions contribute to the overall rate.
Simpson’s original 1951 paper also demonstrates that associations within groups can differ from the association after pooling them. It discusses how the meaning of the classifications changes the interpretation of identical numerical tables. Creating more detailed tables alone leaves substantive interpretation unfinished. (Simpson’s original paper)
What happens when both periods use the same traffic mix?
To compare the rates without changing traffic weights, apply a common mix to both periods. Here, fix search at 90% and social at 10%, matching the earlier period, and recalculate the later period’s rate.
Later comparison rate = 12% × 90% + 3% × 10% = 11.1%.
The earlier rate using those same weights is 8.2%, making the difference 2.9 percentage points. Under the common 90% search and 10% social weighting, the later channel rates produce a higher aggregate.
The 11.1% figure is a comparison metric calculated with the earlier mix. The actual later-period share of advertising sessions containing a purchase remains 4.8%. The calculation also makes no prediction that channel conversion rates would stay unchanged if advertising volume were adjusted.
| Metric | Question answered | Later-period value |
|---|
| Actual conversion rate | What share of all advertising sessions contained a purchase? | 4.8% |
| Rate with fixed traffic weights | How do channel rates compare under the earlier traffic mix? | 11.1% |
Possible common weights include the earlier period’s mix or the combined mix across both periods. Choose the reference mix before calculating the comparison and apply identical weights to both periods. A channel with zero sessions has an undefined conversion rate; substituting 0% changes the meaning of the comparison.
What evidence supports budget decisions and page changes?
Budget decisions require advertising costs and purchase profitability alongside conversion rates. In this example, session totals remain constant while purchasing sessions fall, but advertising spend, order values, and costs of goods are absent. Conversion rates alone cannot justify stopping social ads. Match channel spending to profit from associated orders and assess whether additional spending can increase profit.
Evaluating a page change requires investigating why channel rates rose. Changes in prices, advertising search terms, or device mix can also affect the result. UC Berkeley’s statistics text explains confounding, where differences beyond the intervention affect outcomes, and presents randomized comparisons as a way to study an intervention’s effect. (UC Berkeley on comparisons and confounding)
Connect the following records to specific decisions:
- Record sessions and purchasing sessions by channel, then recalculate rates and traffic shares. When only the aggregate declines, calculate the contribution of the traffic mix before deciding to reverse a page change.
- Record changes to purchase tracking and channel classification. Recalculate affected periods under a common definition or select a different comparison period.
- To evaluate a page change, design an A/B test with randomized user assignment during the same period. Define the outcome and counting method in advance, and assess random variation.
Higher channel conversion rates describe an observed result. Establishing that a page change caused the increase requires additional investigation.
Keep the actual result visible when choosing what to improve
When the overall purchase rate falls, calculate both the share of sessions containing a purchase and the distribution of visits across channels. The actual rate describes business results; a fixed-weight rate compares channel rates under a common mix. Using both makes the work of assessing budget allocation and evaluating page changes more specific.
When editing a page, check that the advertised product, displayed price, and purchase links match its content, and correct discrepancies. Record what changed and the date so subsequent comparisons can identify the revisions.
SpreadSite is a no-code website builder that lets you create, publish, and update a website from Google Sheets using ready-made templates.
To create a website presenting the product details and prices used in your advertising, give SpreadSite a try!
Build a website with SpreadSite →
