Southern New Hampshire University
MAT-133
Week 1 Notes
What is statistics?
Statistics is the science of collecting, organizing, analyzing, interpreting, and presenting data.
Some experts prefer to call statistics data science, a trilogy of tasks involving data modeling,
analysis, and decision-making. A statistic is a single measure, reported as a number, used to
summarize a sample data set. Statistics may be thought of as a collection of methodologies to
summarize, draw valid conclusions, and make predictions from empirical measurements.
Statistics help us organize and present information and extract meaning from raw data. Although
it is often associated with the sciences and medicine, statistics are now used in every academic
field and every area of business.
Plural or Singular?
Statistics- The science of collecting, organizing, analyzing, interpreting, and presenting data.
Statistic- A single measure, reported as a number, used to summarize a sample data set.
There are two primary kinds of statistics:
Descriptive statistics refers to the collection, organization, presentation, and summary of data
(either using charts and graphs or using a numerical summary).
Inferential statistics refers to generalizing from a sample to a population, estimating unknown
population parameters, drawing conclusions, and making decisions.
What is Business Analytics?
Analytics is a broad field that uses statistics, mathematics, and computational tools to extract
information from data. Analytics tools fall into three categories: descriptive, predictive, and
prescriptive. This terminology derived from the questions we are trying to answer.
What happened? Businesses use descriptive analytics tools to analyze historical data and help
them identify trends and patterns.
What is likely to happen next? Businesses use predictive analytics tools to predict probabilities
of future events and help them forecast consumer behavior.
What actions do we take to achieve our goals? Businesses use prescriptive analytics tools to
help them make decisions on how to achieve objectives within real-world constraints.
Why Study Statistics?
Communication
The language of statistics is widely used in science, social science, education, health care,
engineering, and even the humanities. In all areas of business (accounting, finance, human
resources, marketing, information systems, operations management), workers use statistical
jargon to facilitate communication.
Computer Skills
Specialists with advanced training design the databases and decision support systems, but you
must handle daily data problems without experts. You need to be able to analyze data, use
software with confidence, prepare your own charts, write your own reports, and make electronic
presentations on technical topics.
Information Management
Statistics can help you handle either too little or too much information. When insufficient data is
unavailable, statistical surveys and samples can be used to obtain the necessary market
information. But most large organizations are closer to drowning in data than starving for them.
Statistics can help summarize large amounts of data and reveal underlying relationships.
Technical Literacy
Marketing staff may work with engineers, scientists, and manufacturing experts as new products
and services are developed. Sales representatives must understand and explain technical products
like pharmaceuticals, medical equipment, and industrial tools to potential customers. Purchasing
managers must evaluate suppliers’ claims about the quality of raw materials, components,
software, or parts.
Process Improvement
Large manufacturing firms like Toyota and Boeing have formal systems for continuous quality
improvement. The same is true of insurance companies, financial service firms like Vanguard or
Fidelity, and the federal government. Statistics helps firms oversee their suppliers, monitor their
internal operations, and identify problems. Quality improvement goes far beyond statistics, but
every college graduate is expected to know enough statistics to understand its role in quality
improvement.
Applying Statistics in Business
Auditing
A large firm pays over 12,000 invoices to suppliers every month. The firm has learned that some
invoices are being paid incorrectly, but it doesn’t know how widespread the problem is. The
auditors lack the resources to check all the invoices, so they decided to take a sample to estimate
the proportion of incorrectly paid invoices. How large should the sample be for the auditors to be
confident that the estimate is close enough to the true proportion?
Marketing
Many companies use Customer Relationship Management (CRM) to analyze customer data from
multiple sources. With statistical and analytical tools such as correlation and data mining, they
identify specific needs of different customer groups, and this helps them market their products
and services more effectively.
Health Care
Health care is a major business (one-sixth of the U.S. GDP). Hospitals, clinics, and their
suppliers can save money by finding better ways to manage patient appointments, schedule
procedures, or rotate their staff. For example, an outpatient cognitive retraining clinic for victims
of closed-head injuries or stroke evaluates 56 incoming patients using a 42-item physical and
mental assessment questionnaire. Each patient is evaluated independently by two experienced
therapists. Are there statistically significant differences between the two therapists’ evaluations
of incoming patients’ functional status? Are some assessment questions redundant? Do the initial
assessment scores accurately predict the patients’ lengths of stay in the program?
Quality Improvement
A manufacturer of rolled copper tubing for radiators wishes to improve its product quality. It
initiates a triple inspection program, sets penalties for workers who produce poor-quality output,
and posts a slogan calling for “zero defects.” The approach fails. Why?
Purchasing
A food producer purchases plastic containers for packaging its product. Inspection of the most
recent shipment of 500 containers found that 3 of the containers were defective. The supplier’s
historical defect rate is .005. Has the defect rate really risen or is this simply a “bad” batch?
Medicine
An experimental drug to treat asthma was given to 75 patients, of whom 24 get better. A placebo
is given to a control group of 75 volunteers, of whom 12 get better. Is the new drug better than
the placebo, or is the difference within the realm of chance?
Operations Management
The Home Depot carries 50,000 different products. To manage this vast inventory, it needs a
weekly order forecasting system that can respond to developing patterns in consumer demand. Is
there a way to predict weekly demand and place orders from suppliers for every item without an
unreasonable commitment of staff time?
Product Warranty
A major automaker wants to know the average dollar cost of engine warranty claims on a new
hybrid vehicle. It has collected warranty cost data on 4,300 warranty claims during the first six
months after the engines are introduced. Using these warranty claims as an estimate of future
costs, what is the margin of error associated with this estimate?
New Frontiers
Machine learning refers to using observed data and algorithms to train computers to classify
events and predict outcomes in a useful way without task-specific rules. Statistics is a core
component of ML to code and clean large input data sets, perform data transformations, train and
test algorithms, and evaluate predictions. Programming skills are also essential to access data
warehouses, collect real-time information, and implement ML technology. Business subject
knowledge (e.g., accounting, financing, marketing) is essential to yield applicable results.
Artificial intelligence (AI) refers to an area of computer science that seeks to create intelligent
machines that can think and behave like humans to solve problems and act autonomously. While
it relies on machine learning, AI is a broader field of study involving high-order emulations of
human capabilities. AI also requires hardware and software for image recognition and natural
language processing (speech recognition, text translation, content extraction). AI seeks to equal
and improve outcomes in tasks that humans already perform. While AI might replace some
human jobs, new jobs are being created for individuals who design, test, and implement AI
algorithms.
Artificial neutral networks (ANN) or simply neutral nets are a key component of ML and AI.
These are “black boxes” whose internal connections mimic the human brain, learning to process
raw inputs and produce outputs or conclusions based on examples that are provided. Their node
structures assign weights randomly at first and then learn to modify these weights based on
training data. However, the weights used by the ANN are not easily interpreted and may even be
unknown. Such systems can keep learning as long as they are supplied with new data but in the
future may also self-learn using feedback about the accuracy of their own predictions. Statistics
will play a major role in oversight and management of such systems.
Statistical Challenges
Business professionals who use statistics are not mere number crunchers who are “good at
math.” The ideal data analyst
Is technically current (e.g., software-wise).
Communicates well.
Is proactive.
Has a broad outlook.
Is flexible.
Focuses on the main problem.
Meets deadlines.
Knows his or her limitations and is willing to ask for help.
Can deal with imperfect information.
Has professional integrity.
Imperfect Data and Practical Constraints
In mathematics, exact answers are expected. But statistics lies at the messy interface between
theory and reality. For instance, suppose a new airbag design is being tested. Is the new airbag
design safer for children? Test data indicate the design may be safer in some crash situations, but
the old design appears safer in others. The crash tests are expensive and time-consuming, so the
sample size is limited. A few observations are missing due to sensor failures in the crash
dummies. There may be random measurement errors. If you are the data analyst, what can you
do? Well, you can know and use generally accepted statistical methods, clearly state any
assumptions you are forced to make, and honestly point out the limitations of your analysis. You
can use statistical tests to detect unusual data points or to deal with missing data. You can give a
range of answers under varying assumptions. Occasionally, you need the courage to say, “No
useful answer can emerge from these data.”
You will face constraints on the type and quantity of data you can collect. Automobile crash tests
can’t use human subjects (too risky). Telephone surveys can’t ask a female respondent whether
she has had an abortion (sensitive question). We can’t test everyone for HIV (the world is not a
laboratory). Survey respondents may not tell the truth or may not answer all the questions
(human behavior is unpredictable). Every analyst faces constraints of time and money (research
is not free).
Business Ethics
Upholding Ethical Standards
Know and follow accepted procedures.
Maintain data integrity.
Carry out accurate calculations.
Report procedures faithfully.
Protect confidential information.
Cite sources.
Acknowledge sources of financial support.
Because legal and ethical issues are intertwined, there are specific ethical guidelines for
statisticians concerning treatment of human and animal subjects, privacy protection, obtaining
informed consent, and guarding against inappropriate uses of data.
Ethical dilemmas for a non statistician are likely to involve conflicts of interest or competing
interpretations of the validity of a study and/or its implications. For example, suppose a market
research firm is hired to investigate a new corporate logo. The CEO lets you know that she
strongly favors a new logo, and it’s a big project that could earn you a promotion. Yet the market
data have a high error margin and could support either conclusion.
A perceived ethical problem may be just that – perceived. For example, it may appear that a
company promotes more men than women into management roles while, in reality, the
promotion rates for men and women are the same. The perceived inequity could be a result of
fewer female employees to begin with. In this situation, organizations might work hard to hire
more women, thus increasing the pool of women who are promotable. Statistics play a role in
sorting out ethical business dilemmas by using data to uncover real versus perceived differences,
identify root causes of problems, and gauge public attitudes toward organizational behavior.
Communicating with Numbers
Numbers have meaning only when communicated in the context of a certain situation. Tables
should be embedded in the narrative (not on a separate page) near the paragraph in which they
are cited. Each table should have a number and title. Graphs should also be embedded in the
narrative (not on a separate page) near the paragraph in which they are discussed. A graph may
make things clearer.
Critical Thinking
Statistics is an essential part of critical thinking because it allows us to test an idea against
empirical evidence. Random occurrences and chance variation inevitably lead to occasional
outcomes that could support one viewpoint or another. But the science of statistics tells us
whether the sample evidence is convincing.
“Critical thinking means being able to evaluate, to tell fact from opinion, to see holes in an
argument, to tell people whether cause and effect has been established, and to spot illogic.”
Source: Sharon Begley, “Science Journal: Critical Thinking / Part Skill, Part Mindset,” The Wall
Street Journal, October 22, 2006.
We use statistical tools to compare our prior ideas with empirical data (data collected through
observations and experiments). If the data does not support our theory, we can reject or revise
our theory. In The Wall Street Journal, in Money magazine, and on CNN, you see stock market
experts with theories to “explain” the current market (bull, bear, or pause). But each year brings
new experts and new theories, and the old ones vanish. Logical pitfalls abound in both the data
collection process and the reasoning process.
Chapter Summary
Statistics (or data science) is the science of collecting, organizing, analyzing, interpreting, and
presenting data. A statistician is an expert with a degree in mathematics or statistics, while a
data analyst is anyone who works with data. Descriptive statistics is the collection,
organization, presentation, and summary of data with charts or numerical summaries. Inferential
statistics refer to generalizing from a sample to a population, estimating unknown parameters,
drawing conclusions, and making decisions. Statistics is used in all branches of business.
Statistical challenges include imperfect data, practical constraints, and ethical dilemmas.
Statistical tools are used to test theories against empirical data. Pitfalls include non-random
samples, incorrect sample size, and lack of casual links. The field of statistics is relatively new
and continues to grow as new applications arise and technical frontiers expand.
