Chapter 5 The Lure of Statistics: Data Mining Using Familiar Tools Note: Included in this Slide Set is a subset of Chapter 5 material and additional material from the instructor.

2 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

5 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

6 Population and Sample PopulationSample Use parameters to summarize features Use statistics to summarize features Inference on the population from the sample

7 Occam’s Razor – “Kiss” William of Occam, Franciscan monk, – 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!”

8 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?”

9 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%

11 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

12 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 the p-value for a day

14 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)

15 Different Shapes of Distributions

16 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)

17 Example: Sample Scores/Grades 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

18 Using MS Excel… B C D E F G H I

19 Using MS Excel…

20 End of Chapter 5