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Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics.

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Presentation on theme: "Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics."— Presentation transcript:

1 Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics for Economist Chap 2. The Histogram 1.Arrange of Data 2.Examples of the Histogram 3.Drawing a Histogram 4.The Density Scale 5.Controlling for a variable

2 Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics STATISTICS 2/22 INDEX 1 Arrange of Data 2 Examples of the Histogram 3 Drawing a Histogram 4 The Density Scale 5 Controlling for a variable

3 Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics STATISTICS 3/22 1. Arrange of Data  We use plots to summarize data Data summary  time-series plot  stem-and-leaf plot  histogram  pie chart  box plot  scatter plot

4 Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics STATISTICS 4/22 0 10 20 30 40 50 60 70 192019211922192319241925192619271928192919301931193219331934 Babe Ruth ’ home runs by year 홈 런 수 Time-series plot For examining the changes over time or a trend 1. Arrange of Data

5 Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics STATISTICS 5/22 stemleaf 22 345 41166679 5449 60 stem-and-leaf plot Babe Ruth ’ home runs by year (except 1925) Stem ; 10 ’ place Leaf ; 1 ’ place Ex) 41-homeruns is twice: stem 4 has two 1 leaves 1. Arrange of Data

6 Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics STATISTICS 6/22 Number of leaves per stem 2030405060stem Outline of the leaves Outline the leaves of the stem- and-leaf plot. 90 degree counter clockwise rotation gives a histogram. 1. Arrange of Data

7 Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics STATISTICS 7/22 stem 2 2 2 9932 3 45 92 4 1166679 82 5 449 5 6 0 0 7 leaf Double-stem-and-leaf plot Home runs of Babe Ruth and Mark McGwire To eliminate the illusion by differences of size of data, one leaf of McGwire is larger than that of Babe by 14/11. 1. Arrange of Data

8 Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics STATISTICS 8/22 Babe Ruth ’ home runs by year 30~40 14.3% 40~50 50.0% 50~60 21.4% 20~30 7.1% 60~70 7.1% Market shares of the mobiles SKT 40.8% KT 11.7% KTF 19.7% LGT 14.7% SK 13.1% Pie Chart sizes of pieces = component ratio of data 1. Arrange of Data

9 Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics STATISTICS 9/22 INDEX 1 Arrange of Data 2 Examples of the Histogram 3 Drawing a Histogram 4 The Density Scale 5 Controlling for a variable

10 Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics STATISTICS 10/22 2. Examples of Histogram Distribution of families by income in 1998 0369121521273960  To find the ratio of families with incomes $15,000 ~$21,000 In that range, the size of the block is ¼. That is, 25% of all the families have earned between $15,000 and $21,000

11 Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics STATISTICS 11/22 INDEX 1 Arrange of Data 2 Examples of the Histogram 3 Drawing a Histogram 4 The Density Scale 5 Controlling for a variable

12 Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics STATISTICS 12/22 3. Drawing a Histogram  class interval  frequency  relative frequency Income levelpercent $0 ~ $3001 $300 ~ $6003 $600 ~ $9006 $900 ~ $1,20010 $1,200 ~ $1,50011 $1,500 ~ $2,10024 $2,100 ~ $2,70020 $2,700 ~ $3,90018 $3,900 ~ $6,0005 $6,000 and over1 Distribution

13 Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics STATISTICS 13/22 3. Drawing a Histogram 6036912152127390 Put down the horizontal axis  The horizontal axis should not like this with same intervals.  The horizontal axis should consider the real intervals of level. If we mark the levels with same intervals, we cannot put the actual difference of the levels into the histogram. 2127396091215036 Income($100)

14 Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics STATISTICS 14/22  Don ’ t make the heights equal to the percents in the table! Plotting percents makes the blocks over the longer class intervals too big. 0369121521273960 Drawing a block 0 4 8 12 16 20 24 3. Drawing a Histogram

15 Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics STATISTICS 15/22  To figure out the height of a block over a class interval, divide the percent by the length of the interval.  Then the ratio is the size of each block. 0369121521273960 Histogram 0 2 4 6 8 10 12 Horizontal axis : $100 vertical axis : %/$300 3. Drawing a Histogram

16 Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics STATISTICS 16/22 INDEX 1 Arrange of Data 2 Examples of the Histogram 3 Drawing a Histogram 4 The Density Scale 5 Controlling for a variable

17 Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics STATISTICS 17/22 4. The Density Scale In the previous histogram, the height of the vertical axis means a ratio of families that belong to one unit of horizontal axis $300 Such ‘ a ratio per horizontal axis ’ is density scale. In the histogram, since the vertical axis is the density scale, the area of each block in its level indicates the portion of data belonging to the level. So, total area of blocks is 1. The Density Scale In the histogram, the height of each block is drawn using the density scale. The size of the block is the ratio of the data in each level.

18 Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics STATISTICS 18/22 INDEX 1 Arrange of Data 2 Examples of the Histogram 3 Drawing a Histogram 4 The Density Scale 5 Controlling for a variable

19 Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics STATISTICS 19/22 5. Controlling for a Variable  We need to control the effect of confounding factors not to distort the result by them.  How?  Divide data into groups by confounding factors and analyze those sub-groups separately.  What if too many sub-groups? Consult multiple regression.

20 Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics STATISTICS 20/22 The effect of the pill. Systolic blood pressures of the users and non-users age 25-34 The effect of the pill. Systolic blood pressures of the users and non-users age 25-34 5. Controlling for a Variable

21 Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics STATISTICS 21/22 Control for age 5. Controlling for a Variable

22 Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics Statistics & Econometrics STATISTICS 22/22 A visual for the blood pressure distribution of pill users and non-users with age A visual for the blood pressure distribution of pill users and non-users with age 5. Controlling for a Variable

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