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Displaying Data & Result Interpretation

Displaying Data & Result Interpretation . Dr. Nawaporn Wisitpongphan. What do you want to present depends on what you want to do!. What you want to do depends on what you want to present!!!. Result Presentation. Graphs Type of graphs: Scatter, Line, Bar, Pie chart, 3D, heat map

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Displaying Data & Result Interpretation

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  1. Displaying Data & Result Interpretation Dr. NawapornWisitpongphan

  2. What do you want to present depends on what you want to do! What you want to do depends on what you want to present!!!

  3. Result Presentation • Graphs • Type of graphs: Scatter, Line, Bar, Pie chart, 3D, heat map • Accuracy/Validity: Confidence Interval • Scale of the graph: log-log plot • Tables • Flow Chart • Pseudo Code • Distribution Fitting

  4. Result Interpretation • Explain how to read the graph or table • Explain the overall trend of the results For example… • “As network load increases throughput drops…” • “The proposed method is 10 times better than the traditional approach..” • “The accuracy of the XXX prediction is 90%” • Point out the interesting result • Are there any drawback? Tie the results with the other results you have presented earlier. • Explain the cause of the misbehaved data

  5. Scattered Plot: RAW DATA

  6. Bar: Comparison Cannot be compared directly if a certain dataset has different scale!

  7. Bar: Frequency or PDF

  8. PIE Chart: Survey

  9. HEAT MAP: Eye Tracking Where else do we see heat map?

  10. 3D

  11. Probability Distribution Function (PDF)

  12. PDF • Properties of pdf • Actual probability can be obtained by taking the integral of pdf • E.g. the probability of X being between 0 and 1 is

  13. Confidence Interval: Definition

  14. Example (8-1):

  15. Interpreting CI • The confidence interval is a random interval • The appropriate interpretation of a confidence interval (for example on ) is: The observed interval [l, u] brackets the true value of , with confidence 100(1-).

  16. Precision of Error • The length of a confidence interval is a measure of the precision of estimation. Length of CI

  17. Length of Interval? • In the previous example with 95%, CI we have… • If we are interested in 99% CI, then CI is longer so that’s why we have higher level of confidence

  18. Choice of Sample Size For Example

  19. Sample Size vs. Error • As the desired length of the interval 2E decreases, the required sample size n increases for a fixed value of  and specified confidence. • As  increases, the required sample size n increases for a fixed desired length 2E and specified confidence. • As the level of confidence increases, the required sample size n increases for a fixed desired length of 2E and standard deviation .

  20. Large-Sample Confidence Interval: • What if we don’t know ? • We can use central limit theorem: when sample size n is large, then • Hence, **This is true regardless of the shape of the population distribution

  21. Example:

  22. Solution:

  23. CI on the mean of normal distribution:unknown mean, unknown variance What if the sample size is small say n < 40? The t-distribution Assume: underlying distribution is normal  true for many cases : Unknown mean and unknown variance

  24. The t Distribution K   t Distribution Normal(0,1) Figure 8-4Probability density functions of several t distributions.

  25. The t Distribution t Distribution has heavier tails than the normal; it has more probability in the tails than the normal distribution Figure 8-5Percentage points of the t distribution.

  26. The t Confidence Interval on 

  27. Example: t Distribution

  28. Example of Data Presentation

  29. Cumulative Distribution Function (CDF)

  30. Cumulative Distribution Function • Discrete RVs • Continuous RVs

  31. Playing with Scale For data with wide range

  32. Playing with Scale • Use the scale that would best represent your data without cheating!! • Remove outlier when possible

  33. Flow Chart

  34. Pseudo Code

  35. Table

  36. Misbehaved Data

  37. How to interpret this data?

  38. How do we interpret the result now?

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