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Basic Statistics: Classical Measurement Theory

What is classical measurement theory? It’s a fancy way of saying, “How badly did we screw up our data?” Something a lot of statisticians find themselves saying daily (I’m just guessing. After all, I’m not a statistician myself).

No collected data is without errors. You might even say, “To err is data.” But just because it’s not perfect does not mean that it’s not useful – at least, if the errors are correctly identified. That’s what classical measurement theory helps with: identifying the errors.

Understand everything so far?

Let’s keep going.

Here’s the formula:

X = T + E

Here’s what you need to know: It requires three parts, observed measurementtrue score, and error. X represents the observed measurement, which is the sum of T (true score) and E (the error).

Let’s create an example. Let’s say you measure a cup of water. The measurement shows that the cup contains 8 ounces of water. However, you know that the true measure of water is 2 ounces less. You would then plug those numbers into the formula like so,

8 = 6 + 2

See? It’s simple. Unfortunately, both T and E are hypothetical, since in the real world you would never know the truth value of measurements, and can only make estimates about whether the data is correct or not.

Congratulations, you just took a baby step to be a master of statistics. Give yourself a pat on the back. You deserve it.

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