Statistical Analysis of Data

1
Statistical Analysis of Data

• Many procedures.
• Various levels of details.

2
The proc means procedure

• Provides a concise descriptive statistics of the
  data Average, Standard Deviation, Min, Max.
• Example
• proc means data tickets
• var amount
• title "Brief Summary of Speeding Ticket
  Data
• run

3
Output

• Brief Summary of Speeding Ticket Data run
  1
•  
• The MEANS Procedure
•  
• Analysis Variable amount
•  
• N Mean Std Dev Minimum
  Maximum
• 5 28.8000000 18.7169709
  12.5000000 60.0000000

4
The proc freq procedure

• Produces a Table of the Data, detailing frequency
  and percentage of each value observed.
• Example
• proc freq data tickets
• tables amount
• title "Frequency Table"
• run

5
Output

• Frequency Table
•  
• The FREQ Procedure
•  
• Cumulative Cumulative
• amount Frequency Percent Frequency
  Percent
• 12.5 1 20.00 1 20.00
• 20 2 40.00 3 60.00
• 31.5 1 20.00 4 80.00
• 60 1 20.00 5 100.00
•  
• Frequency
  Missing 1

6
Producing Histograms proc chart and proc gchart
procedures

• The histogram bars can be displayed vertically
  (using keyword vbar) or horizontally (keyword
  hbar)
• Horizontal display will also include some
  statistics in addition to the chart itself.

7

• Example
• proc chart data tickets
• vbar amount
• title "Bar Chart"
• run
•  

8
Or

• proc gchart data tickets
• vbar amount
• title "Bar Chart"
• run

9
Output (vertical chart)
10
Output (horizontal chart)
11
Adding options

• On one independent line
• Example
• pattern v solid color gray
• proc gchart data tickets
• vbar amount
• title "Bar Chart"
• run
• Or
• option nodate
• goptions device win

12

• Or at the end of a statement using /
• Example
• proc freq data tickets
• tables amount/ nocum
• title "frequency table"
• run

13
The proc univariate procedure

• Provides a comprehensive descriptive summary of
  the data Many statistical parameters will be
  computed.
• Often overkill but nicely powerful.

14

• Example
• proc univariate data tickets
• var amount
• title "Summary of Speeding Ticket Data"
• run

15
Output

• Summary of Speeding Ticket Data run
  1
•  
• The UNIVARIATE Procedure
• Variable amount
•  
• Moments
•  
• N 5 Sum Weights 5
• Mean 28.8 Sum Observations
  144
• Std Deviation 18.7169709 Variance
  350.325
• Skewness 1.56939365 Kurtosis
  2.49299031
• Uncorrected SS 5548.5 Corrected SS
  1401.3
• Coeff Variation 64.9894823 Std Error Mean
  8.37048386
•  
•  

16

• Basic Statistical
  Measures
•  
• Location Variability
•  
• Mean 28.80000 Std Deviation
  18.71697
• Median 20.00000 Variance
  350.32500
• Mode 20.00000 Range
  47.50000
• Interquartile Range 11.50000
• Tests for Location Mu00
•  
• Test -Statistic- -----p Value------
•  
• Student's t t 3.440661 Pr t 0.0263
• Sign M 2.5 Pr M 0.0625
• Signed Rank S 7.5 Pr S 0.0625

17

• Quantiles (Definition 5)
•  
• Quantile Estimate
•  
• 100 Max 60.0
• 99 60.0
• 95 60.0
• 90 60.0
• 75 Q3 31.5
• 50 Median 20.0
• 25 Q1 20.0
• 10 12.5
• 5 12.5
• 1 12.5
• 0 Min 12.5
•  
•  

18

• Summary of Speeding Ticket Data run
  2
•  
• The UNIVARIATE Procedure
• Variable amount
•  
•  
• Extreme Observations
•  
• ----------Lowest---------
  ---------Highest---------
•  
• Value state Obs Value state
  Obs
•  
• 12.5 ID 4 12.5 ID
  4
• 20.0 NM 5 20.0 IL
  3
• 20.0 IL 3 20.0 NM
  5
• 31.5 DE 2 31.5 DE
  2
• 60.0 AL 1 60.0 AL
  1
•  
•