[小学教育]统计学.ppt

Contents §1. z test z检验 §2. One-sample t test 单样本t检验 §3. Paired-samples t test 配对样本t检验 §4. Two independent-samples t test 两独立样本t检验 P值计算 双侧检验的P 值为检验统计量X 落在样本统计值C 为端点的尾部区域内的概率的2 倍: P = 2P{ X C} (当C 位于分布曲线的右端时) 或P = 2P{ X C} (当C 位于分布曲线的左端时) 。若X 服从正态分布和t 分布，其分布曲线是关于纵轴对称的，故其P 值可表示为P = P{| X| C}) 应用条件 单个样本变量来自随机、独立的正态分布总体，方差已知。- - 应用条件 Random and independent samples Normality 两组变量值分别来自随机、独立的正态分布总体 例5-4 研究正常人与高血压患者胆固醇含量(mg%)的资料如下,试比较两组血清胆固醇含量有无差别。 正常人组 高血压组 §2. One-sample t test单样本t检验 This test is used to check hypotheses about the fact that the mean of random variable X equals to given μ0. 适用于样本均数与已知总体均数μ0的比较。μ0一般为标准值、理论值或经大量观察得到的较稳定的指标值。 Testing sample X should be a sample of a normal random variable. 检验样本是来自正态总体的随机样本 If X is not normal, t will have an unknown distribution and, strictly speaking, the t-test is inapplicable. However, according to the central limit theorem, as the sample size increases, the distribution of t tends to be normal. Therefore, if the sample size is big, we can use the t-test even if X is not normal. But there is no way to find out what value is big enough. This value depends on how X deviates from the normal distribution. Some sources claim that n should be greater than 30, but sometimes even this size is not enough. Alternatively, we can use non-parametric test: Wilcoxon rank-sign test（非参数检验）。 应用条件 单个随机样本来自正态分布总体，方差未知。 例5-1 结果图示 Example μ0 = 0.25 t0.05/2,9 =2.26 t0.05,9 =1.83 Excel result SPSS计算方法 SPSS计算方法（续） SPSS result §3. Paired-samples t test 配对t检验 也叫Dependent t-test for paired samples 非独立样本t检验 This test is used when the samples are dependent; that is, when there is only one sample that has been tested twice (repeated measures) or when there are two samples that have been matched or “paired” 适用于非独立两样本的检验。如每一个个体被前后测量两次；或两组样本1：1配成对子（按每一对子的混杂因素（如年龄、性别）配对）。 The paired t-test assumes that the differences between pairs are normally distributed. If this