I LOVE the Triangle Test!

🔼 𝗜 𝗟𝗢𝗩𝗘 𝘁𝗵𝗲 𝗧𝗿𝗶𝗮𝗻𝗴𝗹𝗲 𝗧𝗲𝘀𝘁 💖 !!

It might come as a surprise to many … Why would anyone love a method that seems to have become so “reviled” in our field?

Well, here is why:

 - 𝗛𝗶𝘀𝘁𝗼𝗿𝗶𝗰𝗮𝗹 𝘀𝗶𝗴𝗻𝗶𝗳𝗶𝗰𝗮𝗻𝗰𝗲: Developed more than 80 years ago

 - 𝗦𝗶𝗺𝗽𝗹𝗶𝗰𝗶𝘁𝘆: Instructions and execution

 - 𝗧𝗵𝗲𝗼𝗿𝗲𝘁𝗶𝗰𝗮𝗹 𝗰𝗼𝗻𝘁𝗿𝗶𝗯𝘂𝘁𝗶𝗼𝗻: It illustrated the need for 𝘱𝘴𝘺𝘤𝘩𝘰𝘭𝘰𝘨𝘺 and the 𝘛𝘩𝘶𝘳𝘴𝘵𝘰𝘯𝘪𝘢𝘯 𝘧𝘳𝘢𝘮𝘦𝘸𝘰𝘳𝘬 via Jan Frijters’ work on the 𝘱𝘢𝘳𝘢𝘥𝘰𝘹 𝘰𝘧 𝘥𝘪𝘴𝘤𝘳𝘪𝘮𝘪𝘯𝘢𝘵𝘰𝘳𝘺 𝘯𝘰𝘯-𝘥𝘪𝘴𝘤𝘳𝘪𝘮𝘪𝘯𝘢𝘵𝘰𝘳𝘴 in 1979 (paradox where subjects failed the test (𝘁𝗿𝗶𝗮𝗻𝗴𝗹𝗲) even though they could differentiate the samples (𝟯-𝗔𝗙𝗖))

𝗧𝗵𝗲 𝗯𝗼𝘁𝘁𝗼𝗺 𝗹𝗶𝗻𝗲:

The triangle might feel 𝘰𝘶𝘵𝘥𝘢𝘵𝘦𝘥. However, there are situations where 𝗶𝘁 𝗰𝗮𝗻 𝗱𝗲𝗹𝗶𝘃𝗲𝗿 𝘁𝗵𝗲 𝗻𝗲𝗲𝗱𝗲𝗱 𝘀𝘁𝗮𝘁𝗶𝘀𝘁𝗶𝗰𝗮𝗹 𝗽𝗼𝘄𝗲𝗿 without requiring excessively large sample sizes. For instance, when the 𝗰𝗼𝗻𝘀𝘂𝗺𝗲𝗿 𝘁𝗵𝗿𝗲𝘀𝗵𝗼𝗹𝗱 𝗶𝘀 𝗹𝗮𝗿𝗴𝗲 (𝗧𝗮𝘂, which we can estimate using the 𝘴𝘢𝘮𝘦-𝘥𝘪𝘧𝘧𝘦𝘳𝘦𝘯𝘵 𝘮𝘦𝘵𝘩𝘰𝘥):

 - 𝗦𝗺𝗮𝗹𝗹 𝘁𝗵𝗿𝗲𝘀𝗵𝗼𝗹𝗱 (𝗧𝗮𝘂 = 𝟬.𝟴): Power 0.90, Alpha 0.05 ➡️ Required N = 638 (ouch!)

 - 𝗛𝗶𝗴𝗵 𝘁𝗵𝗿𝗲𝘀𝗵𝗼𝗹𝗱 (𝗧𝗮𝘂 = 𝟭.𝟴): Power 0.90, Alpha 0.05 ➡️ Required N = 40 (manageable)

Reliable 𝗱𝗶𝘀𝗰𝗿𝗶𝗺𝗶𝗻𝗮𝘁𝗶𝗼𝗻 𝘁𝗲𝘀𝘁𝗶𝗻𝗴 in an 𝗶𝗻𝘁𝗲𝗿𝗻𝗮𝗹 𝗽𝗿𝗼𝗴𝗿𝗮𝗺, whether you use the "beloved" triangle, a tetrad or a 2-AFC, is impossible without a defined risk profile that 𝗲𝗺𝗯𝗿𝗮𝗰𝗲𝘀 𝘁𝗵𝗲 𝗰𝗼𝗻𝘀𝘂𝗺𝗲𝗿 𝘁𝗵𝗿𝗲𝘀𝗵𝗼𝗹𝗱.

What’s your relationship status with the triangle test?

😍 𝗟𝗼𝘃𝗲 𝗶𝘁?

😡 𝗛𝗮𝘁𝗲 𝗶𝘁?

🤝 "𝗝𝘂𝘀𝘁 𝗳𝗿𝗶𝗲𝗻𝗱𝘀" (It’s useful, but only sometimes)?

More importantly: Irrespective of your favorite method, have you established 𝚢̲𝚘̲𝚞̲𝚛̲ 𝗰𝗼𝗻𝘀𝘂𝗺𝗲𝗿 𝘁𝗵𝗿𝗲𝘀𝗵𝗼𝗹𝗱 to build your risk profile?