假设检验相关知识简介

4. 在这种情况下，决定可能是主观的. 5. 我们采用正统假设检验以客观地判断是否存在差別。
数据帮助每个人作出同样的决定。
18
Nature of Hypotheses
Null Hypothesis (Ho):
Usually describes a status quo
The one you assume unless otherwise shown
2
1
2
X
R is k
R is k
11
可信区间和特征值的估计
可信区间 确定了总体参数中样
本统计可能的数值范围. 它们 可以是单边也可是双边。
▪ 样本均值、样本标准偏差、样本 方异和其它样本统计被称为特征 值评估者。因为它们是用以代表 总体参数的单一数值。
2
1
2
X
R is k
R is k
12
Data helps everyone makes the same decision.
17
为何要做假设检验?
1. 为了改进过程，我们需要确定影响均值和标准偏差的因素.
2. 一旦确定了这些因素并对改进措施进行了调整，我们就需 要验证其在过程中的切实效果。
3. 若过程中存在统计上的重大差别，有时我们就不能利用图 表或算得的统计数据（样本均值和样本标准偏差）作出决 策.
Or
Its either Null (same) or Alternative (Different)
19
假设的种类
虚无性假设 通常用以描述现状 除非其它方面有所说明，否
则就是人为设想的。 在Minitab中用“=”表示
选择性假设 (Ha ): 通常用以描述差別
以证据为基础接受或拒绝的类型
In America we assume innocence until proven guilty.
Innocence corresponds to the null hypothesis.
It requires strong evidence, “beyond a reasonable doubt,” to convict the defendant. Returning a guilty verdict corresponds to rejecting the null hypothesis and accepting the alternative hypothesis.
15
统计假设
对于一个或多个总体里的参数的肯定或推断
▪ 为了判断它的正误，我们必须检查总体的全部。这是不可能 的！！
▪ 我们应使用随机样本，观察其是否能支持该假设. ▪ 从而该结论是建立在统计学意义的基础之上的. ▪ 必须记住该有关总体的结论是由样本推测出的.
16
Why Do Hypothesis Testing?
Confidence intervals identify a
range of plausible values for a sample statistic of a population parameter. They can be either one-sided or two-sided.
3. Sometimes we cannot decide graphically or by using calculated statistics (sample mean and standard deviation) if there is a statistically significant difference between processes.
sample based “chance” variation and a true process difference?
9
怎样使用样本？
样本 A 样本 B
所有的过程都有差异.
我们怎样区分随机变化的样本和真
来源于给定过程的样本也可能是多样 实总体的差别呢?
化的.
10
Confidence Intervals and Point Estimates
Why should we take a sample?
Population: The Universe
Data or information that defines the entire set Parameters(m, s) may, or may not be known.
Is it possible to have sampling error?
Using a sample reduces time and cost Capturing data on the entire population may be very difficult, if
not impossible.
When to use a sample
We use samples to Baseline a process Use samples to evaluate the results of a controlled change to a
13
假设检验
对参数特征值估计和可信区间的诠释都是得出样本数据推 论的路径.
假设检验是用以帮助我们在需要的可信度上对真实的总体 数值进行推论的。
我们将用可信区间和样本均值、样本差异及样本标准偏差测验来
研究使用数据的差別和因果关系。
假设检验有助于判断一个明显的差别是否真实存在还是偶然的， 而且还可以提高差异真实性的可信度.
We will use confidence intervals and tests of sample means, variances and sample standard deviation to investigate difference and cause/ effect relationships using data.
如何获取样本?
请看第五部分.
8
How can we depend on a sample?
Sample A Sample B
All processes have variation.
How can we differentiate between
Samples from a given process may vary.
1. To improve processes, we need to identify factors which impact the
mean or standard deviation.
2. Once we have identified these factors and made adjustments for improvement, we need to validate actual improvements in our processes.
14
A Statistical Hypothesis
An assertion or conjecture about one or more
▪ parameters of the population To determine whether it is true or false, we must examine the entire population. This is impossible!! ▪ Instead use a random sample to provide evidence that either supports or does not support the hypothesis. ▪ The conclusion is then based upon statistical significance. ▪ It is important to remember that this conclusion is an inference about the population determined from the sample data.
4. In such cases the decision will be subjective.
5. We perform a formal statistical hypothesis test to decide objectively whether there is a difference.
为何要选取样本？
总体: 统计总体
用以定义所有可知或不可知参数(m, s) 的数据或信息
可能出现取样 错误吗？
应取多少样本？
样本需要随机抽取吗？
我们以样本为基础做出总体决策
6
Samples? Why Use Them?
Why use a sample instead of a population?
Signs used in Minitab: =
Alternative Hypothesis (Ha ):
Usually describes a difference
The one you accept or reject based upon evidence
Signs used in Minitab: not =or < or >
▪ Sample Means, Sample Standard
deviation, Sample Variances and other sample statistics are known
as Point Estimators because
they are single values used to represent population parameters
Hypothesis Testing
1
假设检验
2
Populations and Samples
Sample: A subset data or
information that possesses the same characteristics as that of the population. We can calculate statistics (X Bar, s).
process.
How should the sample be taken?
See section 5.
7
样本? 为何使用样本?
为何采用样本而非总体?
采用样本可减少时间和成本消耗 即使可能，获取总体数据也是非常困难的.
何时采用样本？
我们利用样本定流程基线 利用样本对过程的可控变化结果进行评估.
Hypothesis Tests help determine if an apparent difference is real or could be due to chance. By using data and hypothesis testing, we can quantify our level of confidence that the difference is real.
How many samples should be taken?
Should the sample be random?
We make decisions about the population based on the sample
5
总体和样本
样品: 总体中具有共同特征的子集。
可以计算其形成的统计表（X）.
在Minitab中用“not =or < or >”表 示
Or
不是全பைடு நூலகம்性假设（相同）就是选择性假设（相区别的）
20
Hypothesis Testing Guilty vs. Innocent Example
The American justice system can be used to illustrate the concept of hypothesis testing.
Hypothesis Tests
Point Estimates of parameters and Confidence Interval Interpretation are both means for making inferences about sample data.
Hypothesis tests are designed to help us make an inference about the true population value at the desired level of confidence.