One-Factor ANOVA Test Hypothesis Ho: ui=H2=p ●●● μc .All population means are equal No treatment effect (NO variation in means among groups HI: not all the k are equal .At least oNE population mean is different (Others may be the same!) There is treatment effect Does not mean that all the means are different 1≠μ2≠…≠μ
One-Factor ANOVA Test Hypothesis H0 : 1 = 2 = 3 = ... = c •All population means are equal •No treatment effect (NO variation in means among groups) H1 : not all the k are equal •At least ONE population mean is different (Others may be the same!) •There is treatment effect Does NOT mean that all the means are different: 1 2 ... c
3、[实例分析 三组销售不同包装饮料的商品的日均销售量 瓶装组罐装组袋装(老包装) 75 74 60 70 78 64 66 72 65 60 68 55 71 58 问题:三种包装的日平均销售量是否有显著差异?
3、[实例分析] 三组销售不同包装饮料的商品的日均销售量 瓶装组 罐装组 袋装（老包装） 75 74 60 70 78 64 66 72 65 69 68 55 71 63 58 问题：三种包装的日平均销售量是否有显著差异？
方差分析结果0:A1=/2=/3 anova for SALE SS df Mean Square F Sig Between 420.367 2 210.183 14.661.001 Within172.0331214.336 Total 592.40014 结论:P=0.001-0.05,可以认为不同包装下的饮 料平均销售量整体上表现出统计学意义上的 差。注意,要想知道是哪两种包装之间有差 异,尚须做两量两比较
方差分析结果 ANOVA for SALE SS df Mean Square F Sig. Between 420.367 2 210.183 14.661 .001 Within 172.033 12 14.336 Total 592.400 14 结论：P=0.001<0.05，可以认为不同包装下的饮 料平均销售量整体上表现出统计学意义上的 差。注意，要想知道是哪两种包装之间有差 异，尚须做两量两比较。 0 1 2 3 H : = =
One-Factor ANOVA No Treatment effect H0:p1=2=p3 请注意其含义 Hi: not all the pk are equal The null Hypothesis is True 1=12=13
One-Factor ANOVA: No Treatment Effect = = H0 : 1 = 2 = 3 = ... = c H1 : not all the k are equal The Null Hypothesis is True 请注意其含义
One factor ANOVa Treatment Effect Present H0:p1=2=3 Hr: not all the uk are equal The null Hypothesis is NOT True μ1=≠3
One Factor ANOVA: Treatment Effect Present = H0 : 1 = 2 = 3 = ... = c H1 : not all the k are equal The Null Hypothesis is NOT True