Level 1 · Desktop versus mobile conversion

Conversion rate is a mean

A conversion rate is the share of visits that end in an order: conversions divided by visits. In pandas you do not need to count anything. converted is a True/False column, True counts as 1 and False as 0, so its mean is the share of True values:

web_sessions["converted"].mean()                       # 0.0298 overall
web_sessions.groupby("device")["converted"].mean()

device
desktop    0.038718
mobile     0.024131
tablet     0.028133

Desktop visits end in an order 3.87% of the time, mobile ones 2.41%. Always look at the counts too: 14,541 desktop sessions, 21,549 mobile, and only 3,910 tablet. Small groups have noisy rates.

Two ways to say “bigger”

The same gap can be written two ways, and mixing them up is one of the most common errors in reports.

• Absolute difference, in percentage points: 3.87% - 2.41% = 1.46 points.
• Relative lift, in percent: 3.87 / 2.41 - 1 = 0.60, so desktop converts 60% more often.

“Conversion rose 2%” is ambiguous: from 3.0% to 5.0% (2 points) or from 3.0% to 3.06% (2% relative)? Write “points” for absolute differences and ”% higher” for relative ones, and give the base rate.

What the gap does and doesn’t mean

The numbers say mobile visits convert less. They do not say the mobile site is worse. Mobile visitors browse on the bus, compare prices, and come back on a laptop to buy. A session-level rate cannot see that journey. Comparing groups that chose themselves (people pick their device) shows a difference, not its cause. Only a controlled test, where a coin decides who sees what, can tell you whether a change to the mobile site would move the number. That is what the rest of this chapter builds toward.

Common mistakes

• Lift from rounded rates. 0.0387 / 0.0241 - 1 gives 0.6058, not 0.6045. Round at the end.
• Points versus percent. A 1.46-point gap is a 60% lift. Say which one you mean.
• Averaging rates across groups. The overall rate is not the mean of the three device rates: (3.87 + 2.41 + 2.81) / 3 = 3.03%, but the real overall rate is 2.98%, because mobile has more sessions. Recompute from the rows.
• A rate without its count. A 6% rate on 50 sessions is three orders. Show n.

Interview note

“Our conversion went up 10%, is that good?” is a classic follow-up question. A strong answer asks whether that is 10% relative or 10 points, from what base, on how many sessions, and compared with what: the same period last year, or a randomly assigned control group.