Hãy xem xét một nghiên cứu đa trung tâm hợp tác lớn về hiệu quả của một liệu pháp điều trị ung thư mới. Một số lượng lớn chăm sóc được thực hiện để chuẩn hóa việc điều trị từ trung tâm đến trung tâm, nhưng nó là rõ ràng rằng thời gian tồn tại trung bình trên các liệu pháp mới | 82 STATISTICAL INFERENCE POPULATIONS AND SAMPLES Figure Quantile-quantile plot of heights of 928 adult children. Data from Galton 1889 . cumulative percentages plotted against the endpoints of the intervals in Figure produce the usual sigmoid-shaped curve. These data are now plotted on normal probability paper in Figure . The vertical scale has been stretched near 0 and 100 in such a way that data from a normal distribution should fall on a straight line. Clearly the data are consistent with a normal distribution model. SAMPLING DISTRIBUTIONS Statistics Are Random Variables Consider a large multicenter collaborative study of the effectiveness of a new cancer therapy. A great deal of care is taken to standardize the treatment from center to center but it is obvious that the average survival time on the new therapy or increased survival time if compared to a standard treatment will vary from center to center. This is an illustration of a basic statistical fact Sample statistics vary from sample to sample. The key idea is that a statistic associated with a random sample is a random variable. What we want to do in this section is to relate the variability of a statistic based on a random sample to the variability of the random variable on which the sample is based. Definition . The probability density function of a statistic is called the sampling distribution of the statistic. What are some of the characteristics of the sampling distribution In this section we state some results about the sample mean. In Section some properties of the sampling distribution of the sample variance are discussed. Properties of Sampling Distribution Result . If a random variable Y has population mean p and population variance Ơ2 the sampling distribution of sample means of samples of size n has population mean p and SAMPLING DISTRIBUTIONS 83 population variance Ơ2 n. Note that this result does not assume normality of the parent population. .
