Statistics with Matlab

1
Statistics with Matlab

• Engineering Experimental Design
• Winter 2003

2
Outline Matlab as a Tool for . . .

• Summarizing data
• Fitting data
• Hypothesis testing

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Some Matlab Tidbits

• Matlab saves dates as a number, but not the same
  number as Excel
• In Matlab, 1 Jan 1 0000
• exceldates caldata(,1)
• matlabdates datenum('30-Dec-1899')
  exceldates
• datestr(matlabdates,2)

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Exercise Construct a Histogram

• Load the file calibration.xls from
  http//132.235.16.144/ChE408/ and save
• Read the file into Matlab
• caldata, headertext xlsread('calibration.xls',
  'Data')
• Define the bins
• edges 46 47 48 49 50 51 52 53 54 55 56 57
• Count the number of entries in each bin
• calfactors caldata(,2)
• frequency histc(calfactors,edges)
• Calculate the fraction of entries in each bin
• total sum(frequency)
• fraction frequency/total

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Exercise Construct a Histogram

• Make the bar charts
• bar((edges0.5),frequency)
• xlim(min(edge) max(edge))
• figure
• bar((edges0.5),fraction)
• xlim(min(edge) max(edge))

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How can I summarize my data?

• Plots
• plot command for y vs. x (to investigate
  correlations)
• bar command (to make histogram)
• Descriptive Statistics
• Measures of location
• Measures of variability

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Descriptive Statistics Location

• Mean (average)
• Strongly affected by unusual points
• mean_resp mean(calfactors)
• Median (50 of data higher, 50 of data lower)
• Seldom strongly affected by unusual points
• median_resp median(calfactors)

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Descriptive Statistics Variability

• Standard Deviation
• std_dev_resp std(calfactors)
• A measure of the precision of a technique to
  compare with another technique
• A measure of the range of observed data
• Strongly affected by unusual points
• Relative Standard Deviation
• rsd_resp std(calfactors) / mean(calfactors)
• Usually given as percentage
• Variance
• variance (std(calfactors))2

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Descriptive Statistics Variability

• Interquartile range, IQR
• A measure of the range of measurements
• Seldom strongly affected by unusual points
• IQR q0.75 q0.25
• q0.75 75 of data is lower, p75
  prctile(calfactors,.75)
• q0.25 25 of data is lower, p25
  prctile(calfactors,.25)
• Range
• A measure of the spread of measurements
• range max(calfactors)-min(calfactors)
• Strongly affected by unusual points

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Exercise Summarizing Data

• Add to your histogram m-file to summarize the
  location and variability of the cal factor

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Fitting Data Hypothesis Testing

• I havent finished figuring this out yet
• I will update these files when I do
• Meantime, use Excel