Quantile Quantile Plot qq plot
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A qqplot is a graphical method for comparing two probability distributions by plotting their quantiles against each other. To construct a qqplot, the quantiles of each dataset are calculated and then plotted against each other. When the datasets have different sizes, interpolated quantile estimates are used. Quantiles divide a dataset so that a given percentage of values lie below a particular quantile. Qqplots are useful for comparing samples and revealing differences in location, spread, and shape between distributions.
Quantile Quantile Plot qq plot
- 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. November 8, 2014 2
- 3. Sample qqplot November 8, 2014 3
- 4. Qqplot November 8, 2014 4
- 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 November 8, 2014 5
- 6. Construction for different size Asimplecaseiswhereonehastwodatasetsofthesamesize. Inthatcase,tomaketheQ–Qplot,oneorderseachsetinincreasingorder,thenpairsoffandplotsthecorrespondingvalues. Amorecomplicatedconstructionisthecasewheretwodatasetsofdifferentsizesarebeingcompared. ToconstructtheQ–Qplotinthiscase,itisnecessarytouseaninterpolatedquantileestimatesothatquantilescorrespondingtothesameunderlyingprobabilitycanbeconstructed. November 8, 2014 6
- 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. November 8, 2014 7
- 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. November 8, 20148
- 9. DefiningQuantiles November 8, 2014 9
- 10. Defining Quantiles November 8, 2014 10
- 11. Draw November 8, 2014 11
- 12. Comparing Two Samples November 8, 201412
- 13. Comparing two data set November 8, 2014 13 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 15
- 14. Comparing two data set November 8, 2014 14
- 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. November 8, 201415
- 16. Thank you November 8, 2014 16