What is Meant by Statistics? Statistics is the science of collecting, organizing, presenting, analyzing, and interpreting numerical data to assist in making more effective decisions. COPAID What is Meant by Statistics?

Origin John Graunt published an article in 1662. He studied the obituary sections in a weekly London church publication. They contained information on the cause of death. Based on the ‘sample data’ collected in one locality, he reached broad conclusions about the impact of diseases in the general population. His analysis and interpretation of data gave birth to the field of Statistics.

Why study Statistics? A. Numerical data is everywhere (you can create your own instruments to measure data) B. Statistics is used in making decision that affect our lives (traffic improvements) C. You will find yourself faced with decisions where an understanding of data analysis is helpful [say, you want to open a new car dealership] In order to make an informed decision, you must know how to: 1. Determine whether the existing information is adequate or additional information is required. 2. Gather additional information, if it is needed, in such a way that it leads to good results. 3. Analyze and draw inferences/conclusions. 4. Summarize the information in an informative manner. Collecting and selling data is a business by itself; eg. Credit, Priceline, Dow Jones, Standard&Poor,…

Example Applications of Statistics Recommending which stocks to buy & sell Quality of production Economic data to predict future trends Law enforcement Evaluating a new drug

Descriptive Statistics Inferential Statistics Types of Statistics Descriptive Statistics Inferential Statistics

Presenting data* in an informative way. Descriptive Statistics deals with methods of Organizing, Summarizing, & Presenting data* in an informative way. Typically, descriptive statistics include Mean, Mode, Median, Variance, Deviation, Skewness, Charts – histogram, bar, pie (we will see these in later chapters) * past/current data but not estimated future data

Excel Example Output of Descriptive Statistics

Sample – part of the population of interest Inferential Statistics: methods used to determine something about a population on the basis of a sample. Population – all possible individuals, objects. Sample – part of the population of interest

Inferential Statistics Example 1: TV networks constantly monitor the popularity of their programs by hiring Nielsen and other organizations to sample the preferences of TV viewers. Example 2: The accounting department of a large firm will select a sample of the invoices to check for accuracy for all the invoices of the company. (Sarbanes-Oxley Act)

Time & cost are prohibitive Why sample? Time & cost are prohibitive Physical impossibility of checking all items in population (eg. Checking quality of product if they are made in the millions) Destructive nature of some tests Sample results are adequate for decision-making

Types of Variables

Types of Variables For a Qualitative or Attribute Variable the characteristic being studied is non-numeric. It can only be labeled. (sometimes also called Categorical variable)

In a Quantitative Variable information is reported numerically. Types of Variables In a Quantitative Variable information is reported numerically. Balance in your checking account Minutes remaining in class Number of children in a family

Types of Quantitative Variables Quantitative variables can be classified as either Discrete or Continuous. Discrete Variables: can only assume certain values -there are usually “gaps” between values - usually “counted” Example: the number of bedrooms in a house, or the number of hammers sold at the local Home Depot (1,2,3,…,etc).

A Continuous Variable can assume any value within a specified range (“no gaps”). The pressure in a tire The height or weight of students in a class.

Chart to remember

Levels of Measurement Nominal Ordinal Interval Ratio The level of measurement dictates the kind of calculations you can do on the data. Eg. If one student’s major is Accounting and another’s IS, we cannot calculate the average major. On the other hand, we can average their heights, weights, etc.

Nominal level Data that is classified into categories. Can be arranged in any order. Measurement consists only of counts.

In this example, Country or Region is Nominal Level data Other examples: religion, major, gender, ethnicity, …

Mutually exclusive Exhaustive Nominal level data must be: An individual, object, or measurement is included in only one category. Exhaustive Each individual, object, or measurement must appear in one of the categories.

Ordinal level - involves data arranged in some order - magnitude of differences between data values cannot be determined. During a taste test of 4 soft drinks, Coca Cola was ranked number 1, Dr. Pepper number 2, Pepsi number 3, and Root Beer number 4.

Example of an Ordinal level variable Also, see the example table in page 12 (Homeland Security Advisory System)

Interval level - similar to the ordinal level - amounts of differences between data values is of equal size - there is no natural zero point. Eg. Temperature on the Fahrenheit scale. Difference between 10°F - 15°F is same as between 50°F& - 55°F 0° does not represent absence of temperature

Ratio level (“highest” level of measurement) - zero value means “absence” - differences and ratios are meaningful for this level of measurement (A person with $2Million is twice as rich as another with $1Million) Monthly income ‘0’ means did not make any money Traveled ‘0’ miles means did not travel at all

N-O-I-R ( Nerd Of India Rocks! )

Statistics can be used to mislead decision makers Don’t do it! Ethical Considerations Statistics can be used to mislead decision makers Don’t do it! Keep taking different samples until you get the result you want Quote ‘average’ to hide wide range of data values Misleading graphical outputs Make unwarranted conclusions on variable relationships

Ethical Considerations The cost/year doubled in 5 years. But the graph appears to depict more than that.

Ethical Considerations By changing the x-y scale, the rate of change in unemployment appears different.

Ethical Considerations Also, a statistical association between two variables does not automatically imply ‘causation’. More in Chapter 13. Eg. Consumption of peanuts is correlated with aspirin consumption (eating peanuts gives headaches)