BUSA 3110 Statistics for Business Spring 2014 – Week 2 Kim I. Melton, Ph.D. Spring 2014

Homework Still posted at the public website… Faculty.ung.edu/kmelton/busa3110.html … but getting closer to moving to D2L for posting assignments.

Your List of Major Topics from Readings (Chapters 1 and 2.1)

Concepts from Chapters 1 and 2.1 Descriptive Statistics Measures of location (central tendency) Spread (variability) (and indirectly) shape Inferential Statistics Population and parameter Sample and statistic Confidence level and significance level [missing] Statistics for Analyzing Processes Chapter 2, Section 1 Levels of Measurement

Key Terms Population Parameter Sample Statistic Theory Hypothesis Significance (sufficient evidence) Stability Levels of Measurement (nominal, ordinal, interval, and ratio scale)

Underlying Concepts/Terms Variables Data Operational definitions Extending conclusions beyond the current dataset Theories and Hypotheses From sample to population Variability (and sources of variation) From current data to a different time or place

Data There is no such thing as “objective data.” Someone decides: What data to collect When to collect the data How to collect the data How to define the characteristic of interest Some data are more objective than other data. Examples: Write a one page paper describing _____. Count the f’s Count the pages What constitutes “most” of the time?

What vehicle is the “most stolen?” What does statistics have to do with answering this question? Hint: Look at four different lists that claim to provide an answer…

1 3 2 4 Ford F-250 crew 4WD Chevrolet Silverado 1500 crew Chevrolet Avalanche 1500 GMC Sierra 1500 crew Ford F-350 crew 4WD Cadillac Escalade 4WD Chevrolet Suburban 1500 GMC Sierra 1500 extended cab GMC Yukon Chevrolet Tahoe Toyota Camry/Solara Toyota Corolla Chevrolet Impala Dodge Charger Chevrolet Malibu Ford Fusion Nissan Altima Ford Focus Chevrolet Cobalt Honda Civic 1 3 1994 Honda Accord 1998 Honda Civic 2006 Ford Full Size Pickup 1991 Toyota Camry 2000 Dodge Caravan 1994 Acura Integra 1999 Chevrolet Full Size Pickup 2004 Dodge Full Size Pickup 2002 Ford Explorer 1994 Nissan Sentra Dodge Charger Pontiac G6 Chevrolet Impala CHRYSLER 300 Infiniti FX35 Mitsubishi Galant Chrysler Sebring Lexus SC Dodge Avenger Kia Rio 2 4

Most Stolen Cars Highway Loss Data Institute - Vehicles with the highest theft claim rates (2012) Based on reported claims from insurance (and do not distinguish between contents and vehicle thefts) http://www.bizjournals.com/nashville/morning_call/2013/07/car-thieves-top-10-favorites-least.html National Insurance Crime Bureau – Most stolen vehicles (2011) Based on vehicle thefts reported to law enforcement https://www.nicb.org/newsroom/nicb_campaigns/hot%E2%80%93wheels National Highway Traffic Safety Administration – Most stolen vehicles (2010) Based on FBI data on reported vehicle thefts http://www.nhtsa.gov/apps/jsp/theft/index.htm Based on FBI data on reported vehicle thefts per 1000 produced

Operational Definitions Tells what to measure How to measure When to measure How to interpret the result Relating to the stolen car example: Counting “thefts” of “cars” When is something a theft? What is a car? How will we identify “thefts” and at what level of detail? Over what period of time (for the thefts) and when will we collect the data Are we looking at raw counts or some kind of relative measure?

Three uses for statistics (Traditional) Describe (Descriptive Statistics) Summarizes data Graphically Through formulas and tables Infer (Inferential Statistics) Use data from a small number of observations to draw conclusions about the larger group Improvement (Process Studies) Use data from past experience to help predict expected outcomes at a different time or place or to direct action to influence future outcomes

Three uses for statistics (Evolving) Descriptive Includes current descriptive and inferential statistics Looks at past and current performance to “describe” Predictive Looks at past and current performance with a goal of predicting future performance (i.e., to be able to “explain”) Addresses what “if questions” Prescriptive Uses quantitative models to assess how to operate in order to achieve some objective within constraints (and may include deterministic and probabilistic aspects)

Descriptive Statistics Summary measures for some situation May be meant to provide general information about that situation May be intended (under appropriate conditions) to be used to generalize to some larger group. Occasionally (and inappropriately), used to say something about what to expect in some other time or place.

Inferential Statistics (in layman’s terms) You have: Large group of interest A small number of “representative” observations from that group You want: To draw some conclusion about a characteristic of the large group based on what you observe from the observations available You know: That your conclusion could be wrong, but you want to be “close.”

Inferential Statistics (with statistical terms) We have A population of interest A random sample of observations from the population You want: To draw some conclusion about a parameter of the population based on what you observe from the calculation of a statistic from the sample You recognize that there will be sampling error in your estimate and want to provide a level of confidence for any results that you state.

Populations and Parameters Samples and Statistics The collection of all items of interest OR more specifically: The measurements that would be obtained from evaluating all items of interest Parameter A summary measure obtained by using data from all elements of the population Usually identified with a Greek letter (m, s, p, b0) Sample A subset of the population (the items actually examined) OR more specifically: The measurements that are obtained from the subset of the population Statistic A summary measure obtained by using the data obtained from the sample Usually identified with traditional English letters ( , s, p, b0)

Parameters and Statistics Location Mean Median Mode  (read mu) no uniform symbol no uniform symbol (read X Bar) no uniform symbol no uniform symbol Spread Range Variance Standard Deviation R 2 (read sigma squared)  (read sigma) R s2 s Proportions p (read pi) or p (read p hat)

Statistics for Process Studies (we’ll come back to this later) Two issues arise: Changes can occur in an on-going process while you are collecting data—i.e., you don’t know if all of your data is coming from the same population Although describing past output may be useful, this is descriptive (history). You really want to be able to know what to expect in the future—i.e., you aren’t trying to make an inference about the process as it existed while you were collecting data.

Levels of Measurement Nominal – Qualitative; categorical; order has no meaning Ordinal – Qualitative; categorical; order has meaning; distance between categories does not Interval – Quantitative; distance has meaning; zero is “arbitrary” Ratio – Quantitative; distance has meaning; zero equates to “none of”

Examples Major Width of parking place Brand of soft drink preferred Year in school (Freshman,…, Senior) Year of birth Snowfall amount Time to complete an assignment Salary Grade (A,B,C,D,F) Grade on test (0 to 100) Level of agreement (strongly disagree, … strongly agree) Gender Job title Make of car

Calculations and Levels of Measurement For the results of addition, subtraction, multiplication, and division to have meaning, data needs to be at least interval in scale. For the results of calculations to be useful in prediction/estimation, certain conditions must exist in terms of how the data are collected.

Graphical Tools Bar charts Scatter diagrams Run charts Pie charts stacked unstacked Scatter diagrams Run charts Pie charts Histograms

Matching Methods to Data Bar Charts Typically for Nominal or Ordinal Data Pie Charts Nominal or Ordinal (but better for Nominal) Run Charts Interval or Ratio Histograms Interval or Ratio (but the order of the data is lost) Scatter diagrams Usually two Interval or Ratio scale variables

Scenario We need to “build a schedule.” One part of this is determining demand for courses Consider real data from NGCSU Variables: Headcount and credit hour production for the Dept/School of Business each Fall (01-12) Number of majors each Spring (07-13) Sample of student total earned hours for a single semester

Questions Building schedules involves forecasting demand. Can we use headcount (of majors) to estimate credit hours? Would we expect the same relationship between headcount and credit hours in the English Department? How is enrollment changing over time? Are we growing? What is happening to enrollment by campus? How are our students distributed across majors? How are students distributed across earned hours distributed?

Can we use headcount to estimate credit hours? Scatter Diagram Students Credit Hrs. 703 6167 751 6317 741 6779 719 6629 801 6777 837 6426 895 7017 925 7098 904 7002 891 7134 937 7341 987 8174

How is enrollment changing over time? Are we growing? Run Chart (aka Excel Line Chart)

Distortion of Graphical Display

What is happening with enrollment on each campus? Bar Chart (aka Excel Column Chart)

Would a Run Chart be easier to read?

How are our students distributed across majors? Pie Chart

How are our students distributed across majors? Pie Chart But would a Bar Chart be better?

Is a “Snap Shot” the best we can do?

How are earned hours distributed? Histogram (best made using Data Analysis Tools) Relative frequency histogram (Column chart)