StatisticsandR2010R语言.ppt

漫谈生物统计和R的应用 李欣海 中国科学院动物研究所 Contents of my class Statistical software R Hypothesis testing t-test using R Question Black Americans continue to experience considerable disadvantages in the labor market, even more than a quarter of a century after Congress enacted major legislation aimed at equalizing opportunity in the workplace. Research proposition: American blacks still have an earnings disadvantage Operational hypothesis: mean income for blacks is lower than for the population as a whole We draw a random sample of 166 blacks and calculate their mean income for 1990 Based on census information, we know the mean income for all Americans in 1990 By comparing the means, we are asking whether it is reasonable to consider the sample of black Americans a random sample that is representative of the population of full-time workers in the U.S. The black sample mean is $5,729 below the population mean, but is it enough below to warrant the conclusion that blacks are not a random sample of the population? What are the possibilities? The average earnings of the black population are about the same as the national average and this sample happens to show a really low mean difference=sampling variability The average earnings of the black population are indeed lower than average earnings nationallydifference=real How do we decide which explanation makes more sense? Answer - We use hypothesis tests Hypothesis tests: A decision making tool that enables us to evaluate hypotheses about population parameters on the basis of sample statistics One Sample Hypothesis Test A random sample of 166 blacks earned an average of $18,037 in 1990. The national average was $23,766 with a standard deviation of $16,101. Do blacks make significantly less than the population? Set ? = 0.05. Step One: Making Assumptions Hypothesis testing involves several assumptions that must be met for the results of the test to be valid For the one sample hypothesis test, we assume Step Two: Stating Hypoth