Level 6 · Why each category gets returned

crosstab: a count grid from two columns

pd.crosstab is a shortcut for the most common pivot: counting how often each pair of values occurs. You pass the two columns directly:

pd.crosstab(web_sessions["device"], web_sessions["converted"])
# converted  False  True
# device
# desktop    13978   563
# mobile     21029   520
# tablet      3800   110

The first argument becomes the rows, the second the columns. Empty pairs are 0, not NaN, because a count of nothing is zero. It’s a function of the pandas module (pd.crosstab), not a DataFrame method, so the columns can even come from different tables as long as their rows line up.

normalize: shares instead of counts

Raw counts mislead when groups differ in size. Mobile had 520 conversions, close to desktop’s 563, but from far more sessions. The normalize argument divides by a total:

• normalize="index": each cell ÷ its row total. Every row adds up to 1. “Of mobile sessions, what share converted?”
• normalize="columns": each cell ÷ its column total. Every column adds up to 1. “Of converted sessions, what share were on mobile?”
• normalize=True (or "all"): each cell ÷ the grand total.

pd.crosstab(web_sessions["device"], web_sessions["converted"], normalize="index").round(3)
# converted  False   True
# desktop    0.961  0.039
# mobile     0.976  0.024
# tablet     0.972  0.028

Desktop converts at 3.9% against mobile’s 2.4%: the share tells the story the counts hid.

Choosing the direction

Say the question out loud and listen for “of”. “Of each category’s returns, what share is damaged?” divides by the category (row) total. “Of all damaged returns, what share is Furniture?” divides by the reason (column) total. The two give different numbers from the same counts, and both are correct answers to different questions.

margins=True adds an All row and column with the totals, which is a quick way to check the counts before you normalize: on the returns data the grand total is 1,673, every return in the table.

Getting the category

Returns don’t carry a category. Each return points to an order line (order_item_id), the line points to a product, and the product has the category. Two merges bring it in, and since every return matches exactly one line and every line one product, the row count stays at 1,673.

Common mistakes

• Normalizing in the wrong direction. Rows add up to 1 with "index", columns with "columns".
• Comparing raw counts across groups of very different sizes.
• Passing column names as strings, pd.crosstab("category", "reason"). crosstab takes the columns themselves, not their names.
• Reporting shares without the counts behind them. Furniture’s 45.6% damaged rests on only 103 returns; say so.