Displaying Data & Result Interpretation

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Displaying Data & Result Interpretation Dr. Nawaporn Wisitpongphan

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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 - PowerPoint PPT Presentation

Transcript of Displaying Data & Result Interpretation

Writing Technical Paper.. A-Z

Displaying Data & Result InterpretationDr. 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 PresentationGraphsType of graphs: Scatter, Line, Bar, Pie chart, 3D, heat mapAccuracy/Validity: Confidence IntervalScale of the graph: log-log plotTablesFlow ChartPseudo CodeDistribution Fitting

Result InterpretationExplain how to read the graph or tableExplain the overall trend of the results For exampleAs network load increases throughput dropsThe proposed method is 10 times better than the traditional approach..The accuracy of the XXX prediction is 90%Point out the interesting resultAre there any drawback? Tie the results with the other results you have presented earlier.Explain the cause of the misbehaved data

Scattered Plot: RAW DATA

Bar: Comparison

Cannot be compared directly if a certain dataset has different scale!Bar: Frequency or PDF

PIE Chart: Survey

HEAT MAP: Eye Tracking

Where else do we see heat map?

3D

Probability Distribution Function (PDF)

PDFProperties of pdf

Actual probability can be obtained by taking the integral of pdfE.g. the probability of X being between 0 and 1 is

12Confidence Interval: Definition

Example (8-1):

14Interpreting 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-).

Precision of ErrorThe length of a confidence interval is a measure of the precision of estimation.

Length of CI

Length of Interval?In the previous example with 95%, CI we have

If we are interested in 99% CI, then

CI is longer so thats why we have higher level of confidenceChoice of Sample Size

For Example

Sample Size vs. ErrorAs 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 .Large-Sample Confidence Interval: What if we dont 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

Example:

Solution:

CI on the mean of normal distribution:unknown mean, unknown varianceThe t-distribution

What if the sample size is small say n < 40? Assume: underlying distribution is normal true for many cases : Unknown mean and unknown varianceThe t DistributionFigure 8-4 Probability density functions of several t distributions.

K t Distribution Normal(0,1)The t DistributionFigure 8-5 Percentage points of the t distribution.

t Distribution has heavier tails than the normal; it has more probability in the tails than the normal distributionThe t Confidence Interval on

Example: t Distribution

Example of Data Presentation

Cumulative Distribution Function (CDF)

Cumulative Distribution Function Discrete RVs Continuous RVs

30Playing with Scale

For data with wide range

Playing with ScaleUse the scale that would best represent your data without cheating!!Remove outlier when possible

Flow Chart

Pseudo Code

Table

Misbehaved Data

How to interpret this data?

How do we interpret the result now?