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Why a Manager (or you) Needs to Know Some Basics about Statistics
• To know how to properly present
information
• To know how to draw conclusions about
populations based on sample information
• To know how to improve processes
• To know how to obtain reliable forecasts
3
Statistics vs Data Mining
• For statisticians, data mining has a negative connotation – one of searching for data to support preconceived ideas
• Statistics don’t lie but liars use statistics!
• Statistics developed as a discipline to help scientists make sense of observations and experiments, hence the scientific method
• Problem has often been too little data for statisticians
• DM is faced with too much data
• Many of the techniques & algorithms used are shared by both statisticians and data miners
4
Some Definitions
• Population (universe) is the collection of
things under consideration
• Sample is a portion of the population
selected for analysis
• Statistic is a summary measure computed
to describe a characteristic of the sample
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Some Definitions*
• Mean (average) is the sum of the values divided by the
number of values
• Median is the midpoint of the values (50% above; 50%
below) after they have been ordered from the smallest to
the largest, or the largest to the smallest
• Mode is the value among all the values observed that
appears most frequently
• Range is the difference between the smallest and
largest observation in the sample
* laymen’s
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Population and Sample
Population Sample
Use parameters to summarize features
Use statistics to summarize features
Inference on the population from the sample
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Occam’s Razor – “Kiss”
• William of Occam, Franciscan monk, 1280-1349 – prior to modern statistics, the Renaissance and the printing press.
• Influential philosopher, theologian, professor with a very simple idea:
– Latin: Entia non sunt multiplicanda sine necessitate
– English: The simpler explanation is the preferable one or “Keep it simple, stupid!”
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The Null Hypothesis
• The NH assumes that differences among observations are due simply to chance
• Bush vs Kerry – poll’s margin of error ~ 3% - 4%
• Layperson asks, “Are these %’s different?”
• Statistician asks, “What is the probability that these two values are really the same?”
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Skepticism
• Is good for both statisticians and DMiners
• Goal for both is to demonstrate results that work, hence discounting the null hypothesis
• The less reliance on chance, the better
10
P-Values and Q-Values
• The null hypothesis can be quantified
• The p-value is the probability that the null hypothesis is true
• When the null hypothesis is true, nothing is really happening; differences are due to chance
• Confidence, the reverse of a p-value, is called the q-value. p-value = 5% then the q-value (confidence) is 95%.
• Example: Bush/Kerry…p-value 60% or 5%
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Data Visualization
• Discrete data, such as products, channels, regions, and descriptions is the main focus of data mining
• Histogram – bars show number of times different values occur
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Data Visualization
• Histograms describe a single moment in time
• Data mining is often concerned with what is happening over time.
• Time Series Analysis – choosing an appropriate time frame to consider the data
13
Standardized Values
• Time Series charts are useful, but have limitations also; cannot tell whether the changes over time are expected or unexpected
• We could look at a segment of the data, say a day at a time asking: “Is it possible that the differences seen on each day are strictly due to chance?”(null hypothesis)
• Answer:calculate thep-value for a day
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Variance and Standard Deviation
• Variance is a measure of the dispersion of a sample (or how closely the observations cluster around the mean [average])
• Standard Deviation, the square root of the variance, is the measure of variation in the observed values (or variation in the clustering around the mean)
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Example: Sample Scores/Grades
• 84
• 65
• 74
• 72
• 85
• 65
• 96
• 30
1. Sort the data from highest to lowest and assign grades
2. Find the Mean, Median, Mode, and Standard Deviation
3. Create a histogram for the grades
• 78
• 72
• 85
• 64
• 65
• 96
• 15
• 72
• 73
• 85
.
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Using MS Excel…
Sorted
Raw Data Grade (Bx-I5)^2
96 A 630.57 Range 81
96 A 630.57 Mean 70.9
85 B 199.12 Median 72.5
85 B 199.12 Mode 85
85 B 199.12 Standard Deviation 19.8
84 B 171.90
78 C 50.57
74 C 9.68
73 C 4.46 A's 2
72 C 1.23 B's 4
72 C 1.23 C's 6
72 C 1.23 D's 4
65 D 34.68 F's 2
65 D 34.68 W's 0
65 D 34.68 Sum 18
64 D 47.46
30 F 1671.90
15 F 3123.57
B C D E F G H I
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Central Limit Theorem
• As more and more samples are taken from a population, the distribution of the averages of the samples follows the normal distribution. The average of the samples comes arbitrarily close to the average of the entire population.
• Normal distribution is described by the mean (average count) and the standard deviation (clustering around the mean)
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Central Limit TheoremThe probability density function for the normal distribution
The (cumulative) distribution function for the normal distribution
90% confidence → z-value > 1.64 95% confidence → z-value > 1.96 99% confidence → z-value > 2.58 99.5% confidence → z-value > 2.81 99.9% confidence → z-value > 3.29 99.99% confidence → z-value > 3.89
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Data Visualization
The signed confidence (q-values) of the observed value based on the average and standard deviation. This sign is positive when the observed value is too high, negative when it is too low.
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Cross-Tabulations
The number of new customers from counties in southeastern New York state by three channels: telemarketing, direct mail, and other.
26
Other (more important) Sources of Bias
• Examples of what not to do:
– Use customers in California for the challenger and everyone else for the champion.
– Use the 5 percent lowest and 5 percent highest value customers for the challenger, and everyone else for the champion.
– Use the 10 percent most recent customers for the challenger, and every one else for the champion.
– Use the customers with telephone numbers for the telemarketing campaign; everyone else for the direct mail campaign.
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RapidMiner Practice
• To see:
– Training Videos\01 - Ralf Klinkenberg –RapidMinerResources\4 - Data Pre-processing -
• -1- Data type transformation.mp4
• -3- Missing values - Basics.mp4
• -4- Outlier detection.mp4
• To practice:
– Do the exercises presented in the movies using the files “Iris.ioo” and “Labor-Negociations.ioo”.