Define the terms “valid” and “reliable” as they relate to statistics. Can a test be reliable and not valid or vise versa? Why or why not?

And yes, they can be one but not the other.

In statistics, the terms "valid" and "reliable" are often used when assessing the quality of measurements or tests.

Valid: Validity refers to the degree to which a statistical measurement or test accurately measures or predicts what it is intended to measure or predict. In other words, a valid measure is one that provides valid and accurate results that reflect the concept or construct being measured. Validity ensures that conclusions drawn from the data are logically sound and meaningful.

Reliable: Reliability refers to the consistency and stability of a statistical measurement or test over repeated administrations under the same conditions. A reliable measure or test produces consistent and dependable results. If you were to measure the same thing multiple times using a reliable test, you would expect to get similar results each time.

Can a test be reliable and not valid or vice versa? Yes, it is possible for a test to be reliable but not valid, and vice versa. Here's why:

1. Reliable but not valid: A test can be reliable if it consistently produces the same results under the same conditions. However, it may not be valid if it does not actually measure what it is intended to measure. For example, if you are using a thermometer to measure body temperature, and the thermometer consistently shows a temperature that is slightly higher than the actual body temperature, the results would be reliable (consistently higher), but not valid (not accurately measuring body temperature).

2. Valid but not reliable: A test can be valid if it accurately measures what it is intended to measure. However, it may not be reliable if it produces inconsistent or unstable results over repeated measurements. For example, if you are using a bathroom scale to measure body weight, and the scale provides accurate measurements, but the readings fluctuate significantly from one measurement to another, it would be valid (measuring weight accurately) but not reliable (inconsistent results).

In summary, while both validity and reliability are important concepts in statistics, a measurement or test can be reliable without being valid, and vice versa. It is ideal to have measures or tests that are both valid and reliable to ensure accurate and consistent results.

Here's an excellent summary.

http://web.cortland.edu/andersmd/STATS/valid.html