Maybe stupid questions, but if someone can clarify it, I will be very thankful.
The question is: if the normality assumption behind T test is „the sample mean is normal“, why can one decide whether this assumption is satisfied by checking the „normality of data“ at all?
sample size > 30 : according to central limit theorem „sample mean is normal“ independent of data distribution
sample size < 30 ? : normality test says data is normal => sample mean is normal??
sample size < 30 ?: normality test says data is not normal => sample mean is not normal??
(Normality test itself has low power when dealing with small sample size?)
The question is: if the normality assumption behind T test is „the sample mean is normal“, why can one decide whether this assumption is satisfied by checking the „normality of data“ at all?
sample size > 30 : according to central limit theorem „sample mean is normal“ independent of data distribution
sample size < 30 ? : normality test says data is normal => sample mean is normal??
sample size < 30 ?: normality test says data is not normal => sample mean is not normal??
(Normality test itself has low power when dealing with small sample size?)