University:
Montgomery College
Course:
MATH 117: Elements of Statistics
Academic year:

2020
Views:

424

Pages:

3
Author:

chondinny0r70

CHAPTER 17 - Robustness of procedures 17.7 – Robustness of the t-procedure A confidence interval or significance test is called robust if the confidence level or P-value does not change very much when the conditions for use of the procedure are violated. • Except in the case of small samples, the condition that the data are an SRS from the population of interest is more important than the condition that the population distribution is Normal. • Sample size less than 15: Use t procedures if the data appear close to Normal (roughly symmetric, single peak, no outliers). If the data are clearly skewed or if outliers are present, do not use t. • Sample size at least 15: The t procedures can be used except in the presence of outliers or strong skewness. • Large samples: The t procedures can be used even for clearly skewed distributions when the sample is large, roughly n ≥ 40. Theoretical conditions of t procedures: - SRS (this is the most important) - Population must be normally distributed If these two conditions are met, then t confidence intervals and t tests are exact IN PRACTICE No population is exactly normal Thus, no t-procedures has an exact distribution Explore the Shape of the sample: • Outliers are always a problem. We can’t use t-procedures in this case • Strong skewness are a problem when n < 40 • Strong skewness is not a problem when n = 40 or n > 40 because the Central Limit theorem applies