Statistics for Decision Making STA 253

1. Dr. Ginner W. Hudson Covenant College Statistics forDecision MakingSTA 253

2. 1.1 Examining Distributions - Intro • A statistical analysis starts with a set of … Data • We construct a set of data by first deciding what cases or individuals that we want to study. • For each case/individual we record information about characteristics that we call variables.

3. Constructing Our Data Set Looking at data … Individuals, cases, records the WHO Observation Takes Place Variable – a characteristic of a case the WHAT

4. Important terms • Individuals (cases, records): Objects described by the data. • Ex: customers, cities, patients, cars • Variable: A characteristic of a case. • Ex: profit, duration of a service call, number of customers, gender • Different cases can have different values for the variables. • Some variables may be a labelto distinguish the different cases. • Distribution of a variable: the values the variable takes and how often it takes them.

5. To better understand a data set, ask: • Who? • What cases (individuals) do the data describe? • How many cases (individuals)? Think of an assembly line with the WHO passing by on the conveyor belt and the variables of interest being observed.

6. To better understand a data set, ask: • Who? • What cases do the data describe? • How many cases? • What? • How many variables? • What is the exact definition of each variable? • What is the unit of measurement for each variable? • Why? • What is the purpose of the data? • What questions are being asked? • Are the variables suitable?

7. Types of variables • Quantitative Variable: • Takes numerical values for which we can do arithmetic • Ex: credit card balance, number of employees, time until customer is served, age Discrete or continuous? • Categorical Variable: • Places a case into one of several groups or categories • Ex: gender, brand of credit card, own a home (yes/no)

8. Example: An iTunes playlist

9. Example: Grade book data for statistics course

10. Example: The FAA • The Federal Aviation Administration (FAA) monitors airlines for safety and customer service. For each flight the carrier must report the type of aircraft, number of passengers, whether or not the flights departed and arrived on schedule, and any mechanical problems. • Identify the WHO. • The FAA • The airline carriers • The passengers • The flights • None of the above

12. Example: The common cold • Scientists at a major pharmaceutical firm conducted an experiment to study the effectiveness of an herbal compound to treat the common cold. They exposed volunteers to a cold virus, then gave them either the herbal compound or a useless sugar solution. Several days later they assessed each patient’s condition using a cold severity scale ranging from 0-5. • Identify the WHO. • Scientists • Volunteers • The pharmaceutical firm • The herbal compound • None of the above

13. Don’t forget: You can copy-paste this slide into other presentations, and move or resize the poll.

14. Displaying distributions with graphs • Ways to chart categorical data • Bar/column graphs (called Pareto charts when ordered) • Pie charts • Ways to chart quantitativedata • Histograms • Stemplots • Time plots

15. Law firm example • A law firm studies the gender of their clients. They find 55% are males and 45% are females. • Cases: • Variable: • Distribution: • Values: Male, Female • How often: 55% and 45%, respectively Are the data (the variable) categorical or quantitative?

17. Credit card example A credit card company studies the spending behavior of their 21- to 25- year-old customers with a $1000 credit limit. They randomly select 100 of them and record the following variables for each person. For each item identify the type of variable. • Average balance on their card over the last year • Whether customer has ever made late payments • Which day of the week their card is used the most • Customer’s age (in years)

18. Credit card example For each item, give its possible values. • Average balance on their card over the last year • Quantitative: $0.00 through $1000.00 • Whether customer has ever made late payments • Categorical: Yes, No • Which day of the week their card is used the most • Categorical: Sunday, Monday, Tuesday, …, Saturday • Customer’s age (in years) • Quantitative: 21, 22, 23, 24, 25 years

19. Displaying categorical data Purpose: • Summarize the data so the reader can grasp the distribution quickly Process: • List the categories • Give either the count or the percent of cases that fall into each category Methods: • Tables, pie charts, bar/column graphs, Pareto charts

20. Ways to chart categorical data Because the variable is categorical, the data in the graph can be ordered any way we want (alphabetical, by increasing value, by year, by personal preference, etc.). • Bar graphsEach category is represented by a bar. • Pie chartsThe slices must represent the parts of one whole.

21. Automobile Accidents per day of the week Bar graph sorted by rank (Pareto Chart)  Easy to analyze Sorted chronologically  Much less useful

22. Ways to chart quantitative data • Histograms and stemplots These are summary graphs for a single variable. They are very useful to understand the pattern of variability in the data. • Line graphs: time plots Use when there is a meaningful sequence, like time. The line connecting the points helps emphasize any change over time.

23. Histograms The range of values that a variable can take is divided into equal size intervals. The histogram shows the number of individual data points that fall in each interval. Example: Histogram of the December 2004 unemployment rates in the 50 states and Puerto Rico.

24. How to create a histogram It is an iterative process – try and try again. What bin size should you use? • Not too many bins with either 0 or 1 counts • Not overly summarized that you loose all the information • Not so detailed that it is no longer summary  rule of thumb: start with 5 to10 bins Look at the distribution and refine your bins (There isn’t a unique or “perfect” solution)

25. Interpreting histograms When describing the distribution of a quantitative variable, we look for the overall pattern and for striking deviations from that pattern. We can describe the overall pattern of a histogram by its shape, center, and spread. Histogram with a smoothed curve highlighting the overall pattern of the distribution Histogram with a line connecting each column  too detailed

26. Common distribution patterns (shapes) • Symmetric • Left and right sides are mirror images of each other (or close)

27. Common distribution patterns (shapes) • Skewed left • Left side extends farther out than the right side

28. Common distribution patterns (shapes) • Skewed right • Right side extends farther out than the left side

29. Common distribution patterns (shapes) • Many shapes are bimodel or complex • Two peaks • First part symmetric; flat in the middle; increasing at the end

30. Outliers An important kind of deviation is an outlier. Outliersare observations that lie outside the overall pattern of a distribution. Always look for outliers and try to explain them.

31. Outliers The overall pattern is fairly symmetrical except for two states clearly not belonging to the main trend. Alaska and Florida have unusual representation of the elderly in their population. A large gap in the distribution is typically a sign of an outlier. Alaska Florida

32. IMPORTANT NOTE:Your data are the way they are. Do not try to force them into a particular shape. Example: US Female Population 1997

33. Example: Dry Days per Month 1995 Histogram of dry days in 1995 It is a common misconception that if you have a large enough data set, the data will eventually turn out nice and symmetrical.

34. Example: Customer Service Center Call Lengths

35. Example: Customer Service Center Call Lengths Why were there so many calls lasting 10 seconds or less?

36. Example: Customer Service Center Call Lengths The inappropriate actions by customer service reps were hidden in this histogram where the software chose the classes (bin intervals). Example: Customer Service Center Call Lengths

37. Example: Constructing a Histogram Class Exercise: GDP by Country

38. StatTutor • StatsPortal

39. Example: T-bill interest rates

40. What is this type of plot called?

41. What is a Time Series? • Time series -- observations collected over time • Time plot -- plot of the data over time

42. Identifying Trends in the Data • Trend - gradual increases or decreases over time Annual Sales – XYZ Company In millions Year

43. Other Common Components Of Time Series Seasonality Cycles Quarter Year

44. Line Graphs: Time Plots Retail Price of Fresh Oranges over Time Time is on the horizontal, x axis. The variable of interest—here “retail price of fresh oranges”— goes on the vertical, y axis. This time plot shows a regular pattern of yearly variations. These are seasonal variations in fresh orange pricing most likely due to similar seasonal variations in the production of fresh oranges. There is also an overall upward trend in pricing over time. It could simply be reflecting inflation trends or a more fundamental change in this industry.