1. 1 Introduction to Statistics Chapter 1 MSIS 111 Prof. Nick Dedeke

2. 2 Objectives Define statistics Differentiate between descriptive and inferential statistics Define statistical variables Classifying numbers

3. 3 What is Statistics? A general way to view statistics is as follows: it is a language and the set of rules that enables us to make sense of data about events, people, places and things.

4. 4 Valid Statistic?: Example 1 An online survey conducted recently led some to the conclusion that Apple’s iphone product will not succeed in the U.S. market. 75% of the men and 89% of the women surveyed answered “never” when asked the question: Would you buy an ipod?

5. 5 Valid Statistic?: Example 2 When you vote consider this information. A mail survey showed that in the years when Democrats controlled the Congress, U.S. had a higher number of destructive, level 5 hurricanes. In the years that the Republicans controlled Congress, the U.S. have more days with extremely cold and extremely hot days.

6. 6 Valid Statistic?: Example 3 If you are seeking to have a job quickly after you graduate, do not wear a clothing with a white color during your interview. A recent phone survey of fifty human resources managers at the top 10 retail firms in America revealed that only 2% of them wear white clothing to work.

7. 7 Facts There is such a thing as bad statistics Poor methods, sample, and/or interpretation You can always make bad statistics say anything you want it to say The cure for bad statistics is good statistics

8. 8 Do we really need statistics? Imagine a government never gathers data about population growth. Imagine a hospital that never stores data about patient data and care Imagine a car firm that never analyzes data about vehicle rollovers Imagine an insurance firm that never interprets the causes for the increases in health care costs

9. 9 Definition of statistics? Statistics is a science dealing with the collection, organization, analysis, interpretation and presentation of quantitative and qualitative data. Statistics is a means to an end. The objective is not statistics for its own sake, it is the effective use of statistics for decision-making that matters for firms.

10. 10 Challenge of statistics? Statistics has two primary challenges: Describing a group of entities using a segment of the group. For example, we have over 300 million U.S. citizens. I have the question to answer. How tall are Americans? This kind is called descriptive statistics. FOCUS – Present or Past Generating conclusions about future trends of a large group of data using smaller set from the same or related group. For example, I have the question: At which rate are we depleting fishes in our rivers? This kind is called inferential statistics. FOCUS – Present or Future

11. 11 Terminologies in statistics? Census: Gathering of data from every member of a group or population, e.g. all voters in a presidential election, all subscribers to cable TV Sample: A randomly sampled set of members of a population (fraction of the size of a census) Variable: Attribute of interest of each member of group Observation or measurement: The value of a variable for a member of a group (population or sample)

12. 12 Exercise 1: How many members are in this sample? Bill, Marty, Mary, Sue, Buba, Dub, Anne, Ali Baba, Jane, Phil, Don, Monki If I were interested in the physical attributes of the members, which two variables will I survey? If I were interested in the opinions of the sample which two variables will I survey? If I were interested in the identity of the members, which two variables will I survey?

13. 13 Exercise 1 Responses How many members are in this sample (data set)? 12 Physical attributes: height, weight, hair color, gender Opinion: political affiliation, political worldview, Identity: last name, nationality, ID number, Soc. Sec.No.

14. 14 Exercise 2 For each of the underlined variables write down an example of what the observation (responses to survey) would be when you survey a member of the population. Physical attributes: height, weight, hair color, gender Opinion: political affiliation, political worldview, Identity: last name, nationality, ID number, Soc. Sec.No.

15. 15 Exercise 2 Responses Weight: 200 pounds Gender: Female Politic. affiliation: Republican Political view: Liberal Nationality: Nigerian Soc.Sec: 123974 Numerical data Numerical data: Permit the use of arithmetical operations Categorical data Categorical data: Permit only the building of subgroups

16. 16 Data Measurement The question that one puts on a survey determines how a variable is measured. Consider the following questions: How much income do you make per year (in thousand $)? Do you make more than the US national average of $30,000 per year? [Yes] [No] How much income do you make per year? [Below $10k] [$10k to $30k] [$30k to $50k] [$50k to $70k] [above $70k]

17. 17 Data Measurement Many variables could be measured at different levels. Nominal level. Grouping only and ranking not advisable/ permissible Do you make more than the US national average of $30,000 per year? [Yes] [No] Nominal level. Grouping only and ranking not advisable/ permissible Ordinal level. Absolute zero not emphasized and ranking possible How much income do you make per year? [Below $10k] [$10k to $30k] [$30k to $50k] [$50k to $70k] [above $70k] Ordinal level. Absolute zero not emphasized and ranking possible Ratio level. Absolute zero and ratio of numbers are meaningful. Arithmetical operations possible How much income do you make per year (in thousand $)? Ratio level. Absolute zero and ratio of numbers are meaningful. Arithmetical operations possible

18. 18 Exercise 3: Data Measurement What is the level of measurements of the following observations: 1980: date of birth Social security number Temperature, e.g. 90 degrees Fahrenheit Age: 19 years old Rating of customer service: Excellent (7)

19. 19 Exercise 3: Responses What kind of level of measurements are the following observations: 1980: date of birth [ORDINAL] Social security number [NOMINAL] Temperature, e.g. 90 degrees Fahrenheit [INTERVAL] Age: 19 years old [RATIO] Rating of customer service: Excellent (7) [ORDINAL]

20. 20 Analyzing Data Nonparametric statistics [ORDINAL] Nonparametric statistics [NOMINAL] Parametric statistics [INTERVAL] Parametric statistics [RATIO]

21. 21 Data Measurement: Examples Two respondents: $20,000 and $ 40,000 income/yr. Many variables could be measured at different levels. Nominal level. Grouping only and ranking not advisable/ permissible. Analyses: Income class of B ranks higher than A. Difference in incomes = ??; ratio of income of class?? Not possible. Do you make more than the US national average of $30,000 per year? [Yes] [No] Nominal level. Grouping only and ranking not advisable/ permissible. Analyses: Income class of B ranks higher than A. Difference in incomes = ??; ratio of income of class?? Not possible. Ordinal level. Absolute zero not emphasized and ranking possible. Analyses: Income class of B ranks higher than A. Difference in income classes = ranges from $1-$40,000; ratio of income of class?? Not possible. How much income do you make per year? [Below $10k] [$10k to $30k] [$30k to $50k] [$50k to $70k] [above $70k] Ordinal level. Absolute zero not emphasized and ranking possible. Analyses: Income class of B ranks higher than A. Difference in income classes = ranges from $1-$40,000; ratio of income of class?? Not possible. If you divide your salary by $20,000 per year, what do you get? [¼] [½ ] [¾ ] [1] [1¼] [1½ ] 1¾ ] [2] [2¼] [2½ ] [2¾] Interval level. Absolute zero is convenient and ratio of numbers are meaningful. Analyses: Income B ranks higher than A. Difference between consecutive income classes =$5,000; ratio of income of B twice as high as A (2 divided by 1). Ratio level. Absolute zero and ratio of numbers are meaningful. Analyses: Income B ranks higher than A. Difference in income =$20,000; income of B twice as high as A (40,000/20,000). How much income do you make per year (in thousand $)? ___________ $ thousands Ratio level. Absolute zero and ratio of numbers are meaningful. Analyses: Income B ranks higher than A. Difference in income =$20,000; income of B twice as high as A (40,000/20,000).