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Applied Statistical

2023-11-13 06:06:49   0  举报

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161111 Applied Statistics 学习笔记

学校教育

Massey

在线教育

学习笔记

统计学

作者其他创作

大纲/内容

Exploring Data

Types of Data

Categorical Data

Table

Insert pivot table in Excel

Bar plot

Insert bar or colum graph in Excel

Numerical Data

Histogram
How to dicr histograms data)

Center (mode=tallest peak)
. What does the peak of the distibution tell us

Spread (range)
. What does the range tell us?

Shape(Skew? 1 peak?)
. Is the distibution symmetric or skew?
. Is there more than one peak?

Outliers (extreme values?)
. Are there any extreme values?

Boxplot
(Five Number Summery )

IQR(inter quartile range)

Minimum, Lower Quartile, Median, Upper Quartile, Maximum

. Minimum is the smallest value.
. Lower Quartile (LQ) is the 25% value.
. Median is the halfway value.
. Upper Quartile (UQ) is the 75% value.
. Maximum is the largest value.

boxplots

Bar Chart VS Pie Charts

子主题

key word

The mode

the most common group

Mean

Median

Maximum and Minimum

Standard deviation (SD)

measures how close the data are to the mean value

Shape

Sampling

Collecting Data

compare Censue and Sample

Censue: Collecting data from all individual s in the population.

Sampl: Collecting data from a subset of the individuals in the population

Parameter

Numerical summaries calculated from a population are called parameters.

Statistic

Numerical summaries calculasted from a sample are called statistics

Statistical Sampling Methods

Simple Random

Systematic

Stratified

Cluster

Sampling methods

Representative sample

Error

Sampling erreor

Non-sampling error

Coverage error

Some members of the population are not in the sampling frame.

Non-response error

People may refuse to answer some or all of the questions.

Measurement error

Badly worded or misleading questions.

Experiments and Observational studies

Experiment

Experiment unit

帮助理解纸飞机举例： In our paper plane example, the experimental units are the paper planes themselves.
• We try to keep the paper planes similar by making them the same size, with the same material, etc.

Response variable (反应变量）

帮助理解纸飞机举例： In our paper plane example, the response variable is the length of time the plane remains in flight.

Treatment variable

纸飞机举例： In our paper plane example, the treatment variable is the plane design; with two levels, simple and complex.

例子，帮助理解

Experimental Design

Replication

纸飞机举例：• In our paper plane example, we would build 30 planes of the simple design, and 30 planes of the complex design.

Randomisation

纸飞机举例： • In our paper plane example, we would randomise the order in which we throw the planes. This avoids potential bias due to fatigue in the thrower.

blinding

纸飞机举例： In our paper plane example, it is difficult to include blinding; Blinding would involve the thrower not knowing which plane design is being thrown

Pairing

举例巧克力棒配方测试

Observational study

• explain the difference between an experiment and an observational study.

• identify lurking variables and explain how to control for them in an experiment.

Experiment vs Observational study

子主题

Normality Distribution
(正态分布)

Properties of the normal curve

Shape: Symmetry, one peak, flat tails, no outliers.

mean=median=mode

例子

z score

The empircal rule

Sampling Distribution and Confidence

Sampling Distribution （抽样分布）

Sampling distribution from a normal population

Central limit theorem
中心极限定理

子主题

Standard error (SE). （标准误差）

两个举例的样版

Confidence inervals (置信区间 or 可信区间）

举例练习

CI = mean _+ 2 x SE (计算示例)

Conition for CI

Two conditions need to be satisfied for a CI to be for valid:
The sample is representative of the population.
The sampling distribution is normal.

If both conditions are satisfied, then we trust the CI.

Interpreting confidence intervals
解释置信区间
（利用本章节所有知识，解决实际问题）

95% chance of what?

There is a 95% chance that the CI contains the true population mean.
This is not the same as saying there is a 95% chance that the population mean lies within the CI.

Interpreting confidence intervals 陈述规则

关键例题，搞懂这个题，全章节就懂了

答案1

答案2

Hypotheses testing

Write the hypotheses

The null: The true mean weight of chocolate bars is 250g.
The alternative: The true mean weight of chocolate bars is not 250g.

Test statistic

子主题

Use p-value to make deciion

Write conclusionincontext

Check conditions