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Steven Gollmer Cedarville University

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Presentation on theme: "Steven Gollmer Cedarville University"— Presentation transcript:

1 Steven Gollmer Cedarville University
Big Data Steven Gollmer Cedarville University Picture from wikipedia - Dice

2 Working with Large Data
Accessing data Collection and calibration assumptions Selecting appropriate parameters Formatting Calculation Testing hypothesis

3 Hipparcos Space Astrometry
Main Page Data Catalogues Software Desktop - Search tool - Data Format Flexible Image Transport System (FITS) -

4 Sloan Digital Sky Survey
Main Page Data 9th Data Release - Archive Server - Software IDL -

5 Weather Data NOAA National Climatic Data Center
Popular Data - Environmental Modeling Center

6 TERRA/AQUA http://terra.nasa.gov http://aqua.nasa.gov Data Format
LARC DAAC - LAADS Web - Format NetCDF - HDF -

7 Other Topics of Interest
Extra-Solar Planets Asteroid Mapping and Near Earth Detection Earthquakes Agencies and Products NASA - ESA - USGS - GOES - Paleoclimatology -

8 Hypothesis Testing P-value T-test
Probability of a value being found assuming the null hypothesis. Usually reject the null hypothesis if p < 0.05 or (5% or 1%) May have more stringent criteria for rejection. T-test Assume a normal distribution One-sample test 𝑡= 𝑥 − 𝜇 0 𝑆/ 𝑛 Two-sample test 𝑡= 𝑀 𝑥 − 𝑀 𝑦 𝑆𝑥2 𝑛𝑥 + 𝑆𝑦2 𝑛𝑦 Check significance using T distribution table Compare t value and degrees of freedom 1 sample df = n sample df = n1 + n2 – 2 S – Estimate of standard deviation M – Estimate of the mean n – Number of samples

9 Example Hypothesis Statistics Result 2 tail rejection
Data is from a distribution with mean m = 2.5 Statistics X = 3.317 S = df = 5 Result T = 2.80 2 tail rejection p = 0.05 is 2.571 p = 0.02 is 3.365 Data 2.3 4.2 3.6 3.1 2.8 3.9

10 Z-Value Assume a normal random variable Z – Value
x ~ (m, s2) m – mean s – standard deviation Z – Value z ~ (0, 1) If number of samples is large, then z-test will work on one-sample test instead of a t-test. erf(x)= 2 𝜋 0 𝑥 𝑒 − 𝑢 2 𝑑𝑢 One Tail: p=1/2(1+erf(z/ 2 ) Two Tail: p=erf(z/ 2 ) 𝑓 𝑥 = 1 𝜎 2𝜋 𝑒 − (𝑥−𝜇) 2 2 𝜎 2 𝑧~ 𝑥−𝜇 𝜎


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