2. Intro to Stats forIntro to Stats for
MuslimsMuslims
Unit 02: DescriptiveUnit 02: Descriptive
StatisticsStatistics
Lecture 2:Lecture 2:
Comparisons:Comparisons:
Sorting, Ranking, PercentilesSorting, Ranking, Percentiles
3. Comparisons: Always SubjectiveComparisons: Always Subjective
Sheikh Saadi: Story of boy who did not get newSheikh Saadi: Story of boy who did not get new
shoes for Eid.shoes for Eid.
What is the benchmark for comparisons?What is the benchmark for comparisons?
What is the criterion for comparisons?What is the criterion for comparisons?
Why are comparisons being made?Why are comparisons being made?
4. Numbers are clues to realityNumbers are clues to reality
Every fact about numbers provides someEvery fact about numbers provides some
information about the real world.information about the real world.
We must know the meaning of the numbersWe must know the meaning of the numbers
to understand what information is provided.to understand what information is provided.
Conventional statistics deals with numbersConventional statistics deals with numbers
onlyonly
IS deals with meanings of numbers – theIS deals with meanings of numbers – the
relation to the real world. It is this meaningrelation to the real world. It is this meaning
which allows us to make arguments/rhetoricwhich allows us to make arguments/rhetoric
5. GNP per capita: in PPP constantGNP per capita: in PPP constant
2000$2000$
If all market earnings in PKR wereIf all market earnings in PKR were
converted to USD at PPP exchange rates,converted to USD at PPP exchange rates,
and divided equally, everyone would haveand divided equally, everyone would have
USD 461 in inflation adjusted 2000 dollars.USD 461 in inflation adjusted 2000 dollars.
China was slightly behind Pakistan in 1990 inChina was slightly behind Pakistan in 1990 in
terms of this measure, but forgedterms of this measure, but forged
significantly ahead during the decade.significantly ahead during the decade.
Country GDP 1990 GDP 2000
China 391.65 949.18
Pakistan 461.40 531.00
6. Sorting the DataSorting the Data
Look atLook at
Spreadsheet.Spreadsheet.
UNSORTED data.UNSORTED data.
Rank of Pakistan?Rank of Pakistan?
Richest countries?Richest countries?
Poorest countries?Poorest countries?
After SORTING,After SORTING,
it becomes EASYit becomes EASY
to answer theseto answer these
questions just byquestions just by
looking at the list.
Country 2010
Algeria 2232
Bangladesh 558
Bermuda 63036
Chad 300
China 2427
Congo 106
Cuba 4495
Ethiopia 219
India 804
Indonesia 1145
LDC (UN class) 395
Morocco 1844
Pakistan 665
Saudi Arabia 9499
Spain 15419
Sri Lanka 1309
Turkey 5356
7. Spreadsheet ConceptsSpreadsheet Concepts
Lab Work [not covered in lecture]Lab Work [not covered in lecture]
Search for, find, download WDI Data SetSearch for, find, download WDI Data Set
Learn how to extract relevant information.Learn how to extract relevant information.
Create new spreadsheet with desired info.Create new spreadsheet with desired info.
SORT according to desired criterionSORT according to desired criterion
Lecture covers Use and Meaning.Lecture covers Use and Meaning.
TERMS: Maximum, Minimum, Rank, RangeTERMS: Maximum, Minimum, Rank, Range
8. Country Name 1980 1990 2000 2010
Congo, 779 631 260 316
Liberia 1263 355 344 488
Burundi 604 689 496 524
Niger 941 702 597 650
Cen African Rep 994 853 759 706
Malawi 691 572 670 780
Mozambique 435 396 501 823
United States 25510 31899 39545 42079
U A Emirates 123263 73502 69078 42353
Hong Kong 14118 24019 30290 42581
Brunei 80588 50393 48478 45507
Norway 26205 32362 43975 46906
Singapore 15116 25234 38063 52170
Luxembourg 27622 42707 61091 68679
MIN 435 355 260 316
MAX 123263 73502 69078 68679
RANGE 122828 73146 68818 68362
9. Outliers: Qatar, Kuwait, Brunei,UAEOutliers: Qatar, Kuwait, Brunei,UAE
0
2 0 0 0 0
4 0 0 0 0
6 0 0 0 0
8 0 0 0 0
1 0 0 0 0 0
1 2 0 0 0 0
1 4 0 0 0 0
1 9 7 5 1 9 8 0 1 9 8 5 1 9 9 0 1 9 9 5 2 0 0 0 2 0 0 5 2 0 1 0 2 0 1 5
R a n g e w it h o u t o u t lie r s
11. Comparing across groups
Group Size = N.
PERCENTILE: (N-Rank)/N
Example: 70, 75, 85, 95, 99 N=5
69: 0% 70 71: 20%
74: 20% 75 76: 40%
ALLOWS for comparisons across groups.
HOWEVER, Quiz toughness, Student IQ and
other factors not considered.
15. Grouping according to PercentilesGrouping according to Percentiles
Top 10% countries.Top 10% countries.
Top Quarter = Third QuartileTop Quarter = Third Quartile
Top Half = Above Median.Top Half = Above Median.
Bottom Quarter = First Quartile.Bottom Quarter = First Quartile.
Qualitative labels like: poor, rich, middleQualitative labels like: poor, rich, middle
income are based on these, but subjective.income are based on these, but subjective.
16. Review of Technical TermsReview of Technical Terms
Minimum, Maximum, RangeMinimum, Maximum, Range
Ranks and PercentilesRanks and Percentiles
Median, Quartiles, QuintilesMedian, Quartiles, Quintiles
New Term: Inter-Quartile Range (IQR)New Term: Inter-Quartile Range (IQR)
Exercises will give you practice on use andExercises will give you practice on use and
calculation of these terms.calculation of these terms.
17. RhetoricRhetoric
Sorting and Ranking used for comparions.Sorting and Ranking used for comparions.
Data/facts Objective BUT actuallyData/facts Objective BUT actually
subjective:subjective:
Choose Group (take only African countries)Choose Group (take only African countries)
Choose Benchmark. BETTER than who?Choose Benchmark. BETTER than who?
Choose Criterion. HDI instead of GNPChoose Criterion. HDI instead of GNP
Happiness/Welfare instead of Wealth.Happiness/Welfare instead of Wealth.
Editor's Notes
Intentions:
Emulate Prophet who was asked to seek increase in knowledge.
Know that all knowledge belongs to Allah alone, and we cannot acquire any fragment of it except by his will
We do not seek knowledge for fame or for acquiring wealth, or for winning arguments.
We seek knowledge for self-purification, for recognition of the greatness of God, and for service of the Ummah of the prophet Mohammed SAW.
1: Comparisons are tricky & depend on meanings.
2: Conventional statistics dals with numbers alone, we deal simultaneously with numbers and their meaning.
3: This lecture will deal with some elementary techniques used in making comparison.
Sorting, ranking, percentiles. Using EXCEL.
Conventional Stats is based on separation between numerical facts and real world.
We must deal simultaneously with number facts and their real world interpretation.
To do this, we must know the sources of data, amount of imprecision, real world meaning attached to these numbers and the debates and controversies surrounding these.
Statistical analysis is PROFOUNDLY affected by the real world meaning and we CANNOT separate the technical analysis from the real world meanings.
Numerical Fact: 460>399:
Where the numbers come from, how accurately they are measured, adjustment for prices, currency, purchasing power, population. Size of non-market sectors in the two countries.
Then there is issue of whether GDP accurately reflects prosperity, on which there is huge current debate.
WDI Data Set has 246 Countries/Groupings
Eliminate All countries with missing data (sometimes due to PPP, sometimes War)
Eliminate All GROUPS
Remains: 130 Countries. SORT by 2010 GDP per capita in PPP terms Constant 2005 USD
Table shows Bottom 7 & Top 7, also MAX MIN and Range.
Convergence Hypothesis: If true, then range will shrink to zero.
Top Line: ALL countries in WDI data set. Convergence occurs from 1980 to 1990, after that range remains constant.
Bottom Line: After Eliminating SMALL Oil Producing Countries. Increasing Trend for Range.
PURE Numbers: TOP Line
With Meanings: Bottom Line.
After sorting, ranking is easy. Familiar to students. Countries are ranked from 1 to 130. Because sorted according to 2010, the ranks are in perfect order in 2010.
As we have seen, GDP comparisons require adjusting for population, prices, currencies, and other factors. All these adjustments require arbitrary decision. When learning to make arguments with data, we should know the places where fuzzy elements are introduced into hard facts.
Rank comparisons require adjustment for size of group. Simplest way to adjust is via percentile. Note that this does not adjust for composiition of the group, which remains subject to debate.
As we have seen, GDP comparisons require adjusting for population, prices, currencies, and other factors. All these adjustments require arbitrary decision. When learning to make arguments with data, we should know the places where fuzzy elements are introduced into hard facts.
Rank comparisons require adjustment for size of group. Simplest way to adjust is via percentile. Note that this does not adjust for composiition of the group, which remains subject to debate.
EXCEL Percentilerank assigns 0% to bottom score and 100% to top score. There are 129 steps from top to bottom,so each step adds 1/129.
Last column has every step of size 0.8% which is 1/129. Other columns are not in order.
Poorer countries have mostly slipped in percentile rank. Among the rich countries, we now see that UAE was the TOP country – this was not possible earlier because of the omitted countries in the middle. Singapore has gained a lot in ranking.
Here percentile rank is not so useful because group size remains the same.