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所在平台: Udemy |
课程主页: https://www.udemy.com/course/hypothesis-testing-f-testchi-square-non-parametric-tests/
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这是一门关于假设检验的课程，重点介绍了 F 检验、卡方检验和非参数检验。 **课程概述：** 假设是对事实的初步判断，需要通过检验来验证。课程将引导学员理解，在评估假设时，需要考虑样本的变异性和样本量大小，以判断观察到的差异是真实的还是偶然的。整个过程通过假设检验方法进行。 **课程将涵盖以下检验方法：** * F-Test * Chi Square Test * Run Test * Sign Test * Mann Whitney Test (U Test) * Kruskal Wallis Test ( H Test) * Rank Correlation test **假设检验的五个步骤：** 1. **设定原假设 (Null Hypothesis, H0)：** 原假设通常陈述两个或多个群体或因素之间没有效应、关系或差异。研究者通常旨在推翻原假设。 * 例如：“两个样本之间没有差异。”，“不同学院组的智商相同。”，“接种疫苗与疾病治愈之间没有关联。” 2. **设定备择假设 (Alternative Hypothesis, H1)：** 备择假设陈述存在效应或差异，通常是研究者希望证明的。备择假设可以是一个单侧检验（规定方向，如“较低”）或双侧检验（不规定方向）。 * 例如：“学生的成功率因其就读的学校而异（双侧）。”，“接种疫苗后，疾病恢复时间会缩短（单侧）。”，“运动损伤类型与所使用的技能之间存在关联（双侧）。” 3. **设定显著性水平 (Significance Level, α)：** 显著性水平通常设定为 0.05，意味着当原假设为真时，有 5% 的概率会接受备择假设。显著性水平越低，拒绝原假设（支持备择假设）所需的证据就越强。 4. **计算检验统计量和对应的 P 值：** 检验统计量用于比较群体或检验变量之间的关联。 * **P 值** 表示在原假设为真的情况下，仅凭偶然性获得当前样本统计量或更极端结果的概率。 * 例如：P 值 = 0.01 表示如果原假设为真，该事件仅有 1% 的几率是偶然发生的，不太可能是偶然事件。P 值 = 0.75 表示如果原假设为真，该事件有 75% 的几率是偶然发生的，很可能是偶然事件。 5. **得出结论：** * 如果检验统计量值小于显著性水平 (α)，则**不拒绝 (fail to reject)** 原假设，意味着结果不具统计显著性。 * 如果检验统计量值大于显著性水平 (α)，则**拒绝 (reject)** 原假设，意味着结果具有统计显著性。 需要注意的是，假设检验无法完全证明原假设。当没有找到足够证据反对原假设时，我们应“不拒绝”原假设。而当有足够证据反对原假设时，则“拒绝”原假设。结论也应转化为关于备择假设的陈述，并在报告结果时包含描述性统计数据。 * 例如：H0：两样本的生存率无差异。H1：两组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 sign test for 2 samples. 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. The Tests of Hypothesis discussed in this course are:F-TestChi Square TestRun TestSign TestMann Whitney Test (U Test)Kruskal Wallis Test ( H Test)Rank Correlation testFive 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.
