How to find products, that were only added to the shopping-cart to get free parcel? I‘m analysing shopping carts of a webshop and i‘m interested, if there are products, that are often used (more than random) to get the amount of an order over a specific cut-off to be free of parcel fees. 
I thought about:
Filtering out all orders that lie under the cutoff amount. Then take the other orders and look, if they fall under the cutoff-value if one product is omitted from the order. Then i could analyse what the most ordered items are that are used for this. 
Is this a good idea? How would i then test, if they are ordered more often than in any other order? 
 A: Your approach sounds useful. You essentially partition your entire set of baskets into subsets:


*

*Subset $A$ of baskets that do not contain the item you are looking at (let's call that $i$), are below the free shipping cutoff and would still be below the cutoff if $i$ were included

*Subset $B$ of baskets that contain $i$ and are below the cutoff

*Subset $C$ of baskets that do not contain $i$, are below the cutoff, but would be above the cutoff if $i$ were added

*Subset $D$ of baskets that do not contain $i$ and are above the cutoff

*Subset $E$ of baskets that contain $i$, are above the cutoff and would be below the cutoff if $i$ were not included

*Subset $F$ of baskets that contain $i$, are above the cutoff and would also be above the cutoff if $i$ were removed


You are essentially interested in whether $i$ is more prevalent where it makes a difference, i.e., in $C\cup E$, than where it does not make a difference, i.e., in $A\cup B\cup D\cup F$. You can assess this with a contingency table ("$i$ included vs. not included", against "$i$ makes a difference vs. not"),
#E   #B+#F
#C   #A+#D

You can assess whether the difference in proportions is significant using a standard $\chi^2$ test. However, if you do this across all (likely) tens or hundreds of thousands of items, you will run into standard multiple testing problems, so I wouldn't trust the $p$ values overmuch. Probably best just to calculate the $\chi^2$ statistic and look at your items in descending order of this statistic.
In addition, you will run into problems with the extreme slow movers, i.e., the Long Tail, which will essentially randomly pop up in cells of the table. Then again, you will likely not be able to do anything about these in a business sense, anyway. So it might be best to first filter for products that move "often" and only apply the method to those items.
(And: just looking at the table will also throw out items that are less likely to be included when they would have made a difference, simply by chance. So you probably want to filter your results set by whether the item is truly more prevalent in baskets where it makes a difference.)
