A basic question on Hypothesis testing: what is the difference between test statistic (T) and observed statistic (t)? And if observed statistic is a population parameter and test statistic is a sample parameter; shouldn’t observed statistic always be the pick for the value (if we know it already) that decides if our hypothesis is correct?

Second Question was if alpha increases, both my Power of test (i.e. probability of rejecting a false null hypothesis) and my Type I error are increasing. Is that desirable? video mentions some form of trade off between the 2 but I couldn’t wrap my head the trade off. a short example would really help.

Hi @ninadmehta34

T is calculated from the sample data to evaluate the hypothesis, while t is the actual value we get from the sample for comparison. Observed statistics are not population parameters, they represent what we observe in the sample. If we knew the population parameter, we wouldn’t need hypothesis testing as we’d already have certainty.

Increasing alpha raises the probability of rejecting a false null hypothesis but also increases the risk of a `False Positive`

(balancing sensitivity against accuracy).

Hope it helps! Feel free to ask if you need further assistance.

I understand now. Thank you, Alireza.

You’re welcome, happy to help!