Under what conditions are the inferential statistics used typically robust against violations of assumptions?
A) only if the independent variable is not clearly nominal or ordinal
B) only if the participants were not randomly selected but we are cautious when generalizing
C) only if the population is not normally distributed but there are at least 30 data points in the sample
D) only if the independent variable is not clearly nominal or ordinal, participants were not randomly selected but we are cautious when generalizing, and the population is not normally distributed but there are at least 30 data points in the sample

Question

Quizplus · Accepted Answer

The central limit theorem states that the sampling distribution of the mean will be approximately normal, regardless of the shape of the population distribution, as long as the sample size is large enough (typically at least 30). This means that inferential statistics based on the mean, such as t-tests and ANOVA, will be robust against violations of the assumption of normality. Additionally, inferential statistics are also robust against violations of the assumption of random sampling, as long as the sample is representative of the population. Finally, inferential statistics are robust against violations of the assumption of nominal or ordinal independent variables, as long as the independent variable is not a confounding variable.

Under What Conditions Are the Inferential Statistics Used Typically Robust