case study: use SAS to perform fundamental descriptive statistics (Original EN)

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Data: givingindex2015_ver2.sas7bdat.zip (4.41 KB, 需要: 5 个论坛币) 本附件包括：

• givingindex2015_ver2.sas7bdat

2019-8-4 08:28:53 上传

data set for case study
需要: 5 个论坛币  [购买]

Background:

The World Giving Index is published every year by the Charities Aid Foundation (CAF) www.cafonline.org. The index aims to provide insight into the scale and nature of giving around the world. The World Giving Index 2015 presents giving data from 145 countries from across the globe, based on questionnaires completed by a representative sample of individuals living across each country. Index scores have been calculated from responses to the following questions:

Have you done any of the following in the past month?

Donated money to a charity?

Helped a stranger, or someone you didn’t know who needed help?

Volunteered your time to an organization?

Variable	Description
Country_name	Name of country
Country_Code	Abbreviation for country name
Region	Africa, Asia, Europe, Middle East, North & Central America, Oceania, South America
Donating	Donating money score for each country, percent of population
Helping	Helping a stranger score for each country, percent of population
Volunteering	Volunteering score for each country, percent of population
Economy	Three levels of economic development

/**************************************************************************************************************************************/

Study the distributions of donating, helping and volunteering scores.

The values in Donating, Helping and Volunteering columns are calculated scores (percentage of population), numerial variables.

Location measures

Firstly, location measures, mean, median and mode, are used to observe data central tendency.

[td]

Variable	N	N Miss	Mode	Mean	Median
Helping	145	0	50.000	49.228	50.000
Donating	145	0	10.000	31.510	28.000
Volunteering	145	0	9.000	21.069	20.000

codes using the MEANS procedure:

1. proc means data=mydata.givingindex2015_ver2
   
2.    n nmiss mode mean median maxdec=3;
   
3.    var helping donating volunteering;
   
4. run;

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From the central tendency measures table, 2 patterns can be quickly found regarding variable 'Helping'.

• it has almost same mode, mean and median values, which means that it is very close to a normal distribution, where mode=mean=median. This indicates that regarding 'Helping' score, the 145 countries will have a near-symmetric distribution without outliers, with majority countries' scores close up to around 50 and minority of them have very low scores and equally minority have very high socres.

• it has the highest scores on all of the 3 measures, comparing with other 2 variables 'Donating' and 'Volunteering'.

  
  

As a result of this observation, mean can be used to represent the central of variable 'Helping'.

Regarding variables 'Donating' and 'Volunteering', both of them have their median values lower than their mean values, i.e. means on the right hand side of medians, which indicates their distributions will be right-skewed.

• 'Donating' has median value of 28, which means 50% of the countries socred 28 and lower, and another 50% scored higher than 28. Whereas its average socre across the 145 countries is 31.51, higher than the very middle value 28. Mean value has been carried away by some extreme values (could be very high scores or could be outliers) in this variable's range that contribute to the rise of the mean, therefore mean value has lost its representation.

• 'Volunteering' has the same tendency but with just a slight difference between mean and median, which is still right-skewed but skewness will be less than 'Donating'. The possibility of having outliers need to be examined through the analysis of distribution spread.

  
  

As a result of the observation, median can be used to represent the central of 'Donating' and 'Volunteering'.

Dispersion measures

Then, to discover what factors are affecting the spread of the distribuitons, measures like variance, standard deviation, range, quartiles, and interquartile range are used to observe data's dispersion.

[td]

Variable	N	Variance	Std Dev	Minimum	Lower Quartile	Upper Quartile	Maximum	Quartile Range	Range
Helping  Donating  Volunteering	145  145  145	193.149  379.210  130.315	13.898  19.473  11.416	16.000  3.000  3.000	38.000  16.000  11.000	59.000  44.000  29.000	79.000  92.000  50.000	21.000  28.000  18.000	63.000  89.000  47.000

codes using the MEANS procedure:

1. proc means data=mydata.givingindex2015_ver2
   
2.    n var std min q1 q3 max qrange range maxdec=3;
   
3.    var helping donating volunteering;
   
4. run;

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Variance and Standard Deviation - 'Donating' has higher variance 379.21 and std deviation score 19.473 than other 2 variables, which indicates bigger sample data fluctuation. 'Donating' samples take values (scores) in a much bigger range than the other 2 variables, that caused the bigger variation, i.e. more variaty, more information.

For 'Donating', q3+1.5xIQR = 86, the whisker will stop at this top limit 86, any values larger than this will be outliers. From above table, can see Maximum is 92, which already is an outlier. q1-1.5xIQR = -26, bottom limit stops at -26, while Minimum 3 falls above it, so no outliers at the lower end of the data.

For 'Volunteering', q3+1.5xIQR = 56. Top limit of the whisker is 56. Maximum 50 is within this limit, no outliers at the higher end. q1-1.5xIQR = -16, while Minimum 3 falls within this limit, so no outliers at the lower end either.

Skewness and Kurtosis

Next, measures skewness and kurtosis are printed to observe skewness level and peak distributions.

[td]

Variable	Skewness	Kurtosis
Helping	0.106	-0.686
Donating	0.807	0.050
Volunteering	0.528	-0.622

codes using the MEANS procedure:[LaTex]

1. proc means data=MYDATA.GIVINGINDEX2015_VER2
   
2.    skewness kurtosis maxdec=3;
   
3.    var Helping Donating Volunteering;

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'Helping' has smallest skewness 0.106 and 'Donating' has highest skewness 0.807 with 'Volunteering' 0.528 in the middle. All of them are not at significant skewness level. Regarding Kurtosis, both 'Helping' and 'Volunteering' are around -0.6, which distributions will be slightly flatter with shorter tails than 'Donating' (Kurtosis=0.05).

Summary

Finally, statistical description can be summed up:

for 'Helping', nearly symmetric distribution with no outliers, mean can be used to represent centre (central tendency) and Standard Deviation can be used to represent dispersion;

for 'Donating', right-skewed distribution with outliers, median to be used for centre and IQR to be used for dispersion;

for 'Volunteering', right-skewed distribution with no outliers, median to be used for centre and IQR to be used for dispersion

Alternative method - Summary Statistics

To obtain the central tendency and dispersion measure results, instead of coding, use Tasks and Utilities/Tasks/Statistics/Summary Statistics with 'Donating', 'Helping' and 'Volunteering' as Analysis variables, no Classification variables. Tick select measures in OPTIONS tab.

/**************************************************************************************************/

Basic knowledge and practice sharing for beginners. Please do not comment if not interested.

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关键词：Fundamental descriptive Fundamenta Case study Statistics Statistics SAS

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