Presentation on Quantile Quantile Plot. Definition, Construction, Comparing Procedure, Drawing etc.

1. MdSaeedSiddik
IIT, University of Dhaka
qqPlot

2. What is qqplot ?
In statistics, a Q–Q plot ("Q" stands for quantile) is a probability plot, which is a graphical method for comparing two probability distributions by plotting their quantilesagainst each other.
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3. Sample qqplot
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4. Qqplot
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5. Constructing qqplot
The main step in constructing a Q–Q plot is calculating or estimating the quantilesto be plotted.
If one or both of the axes in a Q–Q plot is based on a theoretical distribution, all quantilesare uniquely defined
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6. Construction for different size
Asimplecaseiswhereonehastwodatasetsofthesamesize. Inthatcase,tomaketheQ–Qplot,oneorderseachsetinincreasingorder,thenpairsoffandplotsthecorrespondingvalues.
Amorecomplicatedconstructionisthecasewheretwodatasetsofdifferentsizesarebeingcompared.
ToconstructtheQ–Qplotinthiscase,itisnecessarytouseaninterpolatedquantileestimatesothatquantilescorrespondingtothesameunderlyingprobabilitycanbeconstructed.
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7. Percentiles and Quantiles
The k-thpercentile of a set of values divides them so that k% of the values lie below and (100−k)% of the values lie above.
• The 25th percentile is known as the lower quartile.
• The 50th percentile is known as the median.
• The 75th percentile is known as the upper quartile.
It is more common in statistics to refer to quantiles. These are the same as percentiles, but are indexed by sample fractions rather than by sample percentages.
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8. Some Difficulties
The previous definitionof quantilesand percentiles is not completely satisfactory.
For example, consider the six values:
3.7 2.7 3.31.3 2.2 3.1
What is the lower quartile of these values? There is no value which has 25% of these numbers below it and 75% above.
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9. DefiningQuantiles
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10. Defining Quantiles
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11. Draw November 8, 2014
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12. Comparing Two Samples
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13. Comparing two data set
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Data set 1
Dataset 2
Quartile
0
.25
.5
.75
1
0
.25
.5
.75
1
value
3
3
4
5
7
7
7
9
11
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14. Comparing two data set
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15. Summary
QQplotsare an excellent graphical tool for comparing two samples to each other, or one sample to a theoretical distribution like the Normal. They reveal differences in location, spread and shape more clearly than do density plots or histograms.
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16. Thank you
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