Week02. Statistics with R Part01

Coursera 2018.01

Exploring Numerical Data

1. visualizing numerical data

• scatterplots

  散点图

• evaluating the relationship

  • direction

    方向，正相关还是负相关

  • shape

    曲线形状

  • stength

    关系强弱

  • outliers

    离群点

    • naive approach

      直接讲这些离群点去除掉再处理数据

      这些outliers可能会包含一些很有趣的信息

  

• histogram

  In a histogram, data are binned into intervals and height of the bars represent the number of cases that fall into each interval.

  

• skewness

  倾斜度？

  

• modality

  形态

  • unimodal

  • bimodal

  • uniform

  • multimodal

  

  a distribution may be unimodal with prominent peak

• dotplot

• box plot

  

• intensity map

  

2. measures of center

• mean

• median

• mode

• skewness vs. measures of center

3. measures of spread

• range

  range: $(max - min)$

• variance

  deviation n. 偏差

  roughly the average squared deviation from the mean

  • samlpe variance $s^2$

  • population variance $\sigma^2$

  $$\begin{align*} s^2 = \frac{\sum_{i=1}^n(x-\bar{x})^2}{n-1} \end{align*}$$

  • 为什么是除以$(n-1)$呢？

  • Why do we square the differences?

    

• standard deviation

  

• variability vs. diversity

  Remember, distributions where more observations are clustered around the center, are less variable, versus distributions where more observations are away from the center, are more variable.

  

  

  diversity是指差异性，多样性；
  variability指偏离中心的程度。

• interquartile range

  

4.robust statistics

• we define robust statistics as measures on which extreme observations have little effect

  

  

  mean : consider the spread of the distribution

5.transforming data

Data transformations are useful tricks for making certain types of data easier to model.

• transformations

  • a transformation is a rescaling of the data using a function

  • when data are very strongly skewed, we sometimes transform them so they are easier to model

• (natural) log transformation

• other transformations

  

• goals of transformations

  • to see the data structure differently

  • to reduce skew assist in modeling

  • to straighten a nonlinear relationship in a scatterplot

Exploring Categorical Data and Introduction to Inference

1. Exploring Categorical Variables

• frequency table & bar plot

  • How are bar plots different than histograms?

    

• pie chart? No

  饼图？这是不科学的。信息量太少，当有很多level的时候不好用。

• contingency table

  

• relative frequencies

  

  相对频率，就是相对总数的占比。

• segmented bar plot

  • useful for visualizing conditional frequency distributions

  • compare relative frequencies to explore the relationship between the variables

    

  • relative frequency segmented bar plot

    

• mosaicplot

  

• side-by-side box plots

  

2. introduction to inference

• gender discrimination

  • data

    

  • two competing claims

    

  • 类比于法庭判决

    

    不能证明也也不能就肯定null hypothesis是正确的。

• recap: hypothesis testing framework

  

• simulation scheme

  用纸牌游戏来作模拟实验。

  non-face card 用来代表晋升了的人。 35张。
  face card 代表没有晋升的人。13张。

  

• summary