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所在平台: Udemy |
课程主页: https://www.udemy.com/course/tests-of-hypothesis-z-test-and-t-test/
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本课程“假设检验：z检验与t检验”旨在介绍假设检验的基本概念及其在统计分析中的应用，特别关注z检验和t检验这两种常用的统计方法。 **课程概述：** 假设是一个需要被验证的陈述，一旦被证明，它就成为事实。例如，在评估培训项目对员工的效果时，我们可以使用两种样本t检验或配对t检验来验证假设。在评估假设时，需要同时考虑样本的变异性和样本量大小。通过假设检验，我们可以判断观察到的差异是真实的还是仅仅由于偶然因素造成的。 课程将重点讲解z检验和t检验： * **z检验 (z-Test)：** 用于比较总体均值与样本均值。z检验衡量数据点距离数据集平均值的标准差数。它通常用于处理大样本（n > 30）且已知标准差的问题。 * **t检验 (t-Test)：** 也用于检验假设，特别适用于需要确定两独立样本组之间是否存在统计学意义上的显著差异。t检验旨在判断两组平均值之间的比较是否很可能源于随机机会。通常，t检验更适用于处理小样本（n < 30）的问题。 **假设检验的五个步骤：** 1. **明确原假设 (Null Hypothesis, H0)：** 陈述没有效应、关系或差异。研究者通常试图推翻原假设。 * 例如：两样本无差异；不同学院组的智商相同；疫苗接种与疾病治愈无关联。 2. **明确备择假设 (Alternative Hypothesis, H1)：** 陈述存在效应或差异，这是研究者通常希望证明的。备择假设可以是单侧（只规定方向，如“更低”）或双侧。 * 例如：学生的成功率因学校而异（双侧）；接种疫苗后疾病恢复时间更短（单侧）；运动技能与损伤类型有关联（双侧）。 3. **设定显著性水平 (Significance Level, α)：** 通常设定为0.05，即在原假设为真时，有5%的概率接受备择假设。显著性水平越小，拒绝原假设（支持备择假设）所需的证据就越充分。 4. **计算检验统计量和对应的p值 (Test Statistic and P-Value)：** 检验统计量用于比较组别或考察变量间的关联。p值表示在原假设为真的情况下，偶然获得当前样本统计量或更极端统计量的概率。p值的大小决定了是否拒绝原假设。 * 例如：p值=0.01，表示仅凭机会出现这种情况的概率为1%，不太可能由纯属偶然引起。p值=0.75，表示仅凭机会出现这种情况的概率为75%，很可能由纯属偶然引起。 5. **得出结论 (Drawing a Conclusion)：** * 如果检验统计量值小于显著性水平(α)，则不拒绝原假设，结论不具统计学意义。 * 无法绝对证明原假设，所以当没有找到反对原假设的证据时，我们“未能拒绝”原假设。当找到充分证据反对原假设时，则“拒绝”原假设。结论也应包含对备择假设的陈述，并提供描述性统计数据。 * 例如：H0：两样本生存率无差异。H1：两组生存率存在显著差异。 * 若p值 < α，则拒绝H0，接受H1，认为生存率确实存在显著差异。 * 若p值 ≥ α，则未能拒绝H0，认为没有足够的证据表明生存率存在显著差异。
IntroductionHypothesis is an assumption which needs to be proved and once proved then it becomes a fact. For example, you might want to check the effectivity of a training program on the employees and you can apply t test for 2 samples or paired t test to test the effectivity. When you are evaluating a hypothesis, you need to account for both the variability in your sample and how large your sample is. Based on this information, you'd like to make an assessment of whether any differences you see are meaningful, or if they are likely just due to chance. This is formally done through a process called hypothesis testing. There are 2 important tests in Hypothesis testing: z test and t test and this course gives a great insights on both z test and t test. Lets discuss them briefly:Z-TestZ-tests are the statistical tests that can be used to compare population averages to a sample's. The z-test will tell you how far, in standard deviations terms, a data point is from the average of a data set. A z-test will compare a sample to a defined population that is typically used for dealing with problems relating to large samples (i.e., n > 30) and are very useful when the standard deviation is known. T-TestT-tests are also statistical tests that can be used to test a hypothesis, but they are very useful when we need to determine if there is a statistically significant comparison between the 2 independent sample groups. In other words, a t-test asks whether the comparison between the averages of 2 groups is unlikely to have occurred due to random chance. Usually, t-tests are more appropriate when dealing with problems with a limited sample size (i.e., n < 30).Five Steps in Hypothesis Testing:Specify the Null HypothesisSpecify the Alternative HypothesisSet the Significance Level which generally is take as 5%Calculate the Test Statistic and Corresponding P-ValueDrawing a ConclusionStep 1: Specify the Null HypothesisThe null hypothesis (H0) is a statement of no effect, relationship, or difference between two or more groups or factors. In research studies, a researcher is usually interested in disproving the null hypothesis.Examples:There is no difference between the two samples.The inter college groups have the same IQ There is no association between the administration of vaccine and the disease cureStep 2: Specify the Alternative HypothesisThe alternative hypothesis (H1) is the statement that there is an effect or difference. This is usually the hypothesis the researcher is interested in proving. The alternative hypothesis can be one-sided (only provides one direction, e.g., lower) or two-sided. We often use two-sided tests even when our true hypothesis is one-sided because it requires more evidence against the null hypothesis to accept the alternative hypothesis.Examples:The success rate of the students differs with the school they are studying in (two-sided).The time to recover from a disease is lower due to the administration of the vaccine (one-sided).There is an association between injury type and the skills employed in the sports (two sided).Step 3: Set the Significance Level (a)The significance level (denoted by the Greek letter alpha) is generally set at 0.05. This means that there is a 5% chance that you will accept your alternative hypothesis when your null hypothesis is actually true. The smaller the significance level, the greater the burden of proof needed to reject the null hypothesis, or in other words, to support the alternative hypothesis.Step 4: Calculate the Test Statistic and Corresponding P-ValueIn another section we present some basic test statistics to evaluate a hypothesis. Hypothesis testing generally uses a test statistic that compares groups or examines associations between variables. When describing a single sample without establishing relationships between variables, a confidence interval is commonly used.The p-value describes the probability of obtaining a sample statistic as or more extreme by chance alone if your null hypothesis is true. This p-value is determined based on the result of your test statistic. Your conclusions about the hypothesis are based on your p-value and your significance level.Example:P-value = 0.01 This will happen 1 in 100 times by pure chance if your null hypothesis is true. Not likely to happen strictly by chance.Example:P-value = 0.75 This will happen 75 in 100 times by pure chance if your null hypothesis is true. Very likely to occur strictly by chance.Step 5: Drawing a ConclusionTest Statistic value significance level (a): reject your null hypothesis. Your result is not statistically significant.Hypothesis testing is not set up so that you can absolutely prove a null hypothesis. Therefore, when you do not find evidence against the null hypothesis, you fail to reject the null hypothesis. When you do find strong enough evidence against the null hypothesis, you reject the null hypothesis. Your conclusions also translate into a statement about your alternative hypothesis. When presenting the results of a hypothesis test, include the descriptive statistics in your conclusions as well. Example:H0: There is no difference in survival between the two samples.H1: There is a significant difference in survival between the two groups.
