Introductory Statistics

Introductory Statistics
Class 2 Chapter 1: Statistics (1) Ichiro Sugimoto

Contents of Today’s Class
(1) Review session (Confirm what we have studied such as leaning objectives, outcomes and key concepts.) (2) Q&A session (3) Explain new content: Chap (4) Conduct exercises and provide solutions (5) Assignment for Next Class

What Is Statistics? the universal language of the sciences
statistical methods  accurate information from data Mastering both the “science” and the “art” of using correct statistical methodology is essential.

Work One Watch presentation of Hans Rosling!
What were the three most significant things you learned ? Please write down

What Is Statistics? These methods include Defining the situation
(2) Gathering data (3) Accurately summarizing the data (4) Deriving [finding] and communicating meaningful conclusions. Statistics is the science of collecting, describing, and interpreting data.

What Is Statistics? Descriptive Statistics Inferential Statistics.
The field of statistics can be roughly subdivided into two areas: Descriptive Statistics Inferential Statistics.

What Is Statistics? Descriptive statistics is what most people think of when they hear the word statistics. It includes: the collection, presentation, description of sample data.

What Is Statistics? The term inferential statistics refers to:
the technique of interpreting the values resulting from the descriptive techniques and making decisions and drawing conclusions about the population.

What Is Statistics? Statistics is more than just numbers: it is data,
what is done to data, what is learned from the data, and the resulting conclusions.

Examples of Statistics in Everyday Life

From sports to politics to business, statistics are a near-daily presence in our lives. Where do you see statistics in your daily life?

Teenagers’ classroom and driving behavior Consider the information collected to formulate these graphics: cell phone status number of text messages per week number of text messages during class per week types of activities while driving How would the organizations responsible for the surveys use that collected information to come up with the 84% and 83% shown in the graphs? The percentages in the Busy Behind the Wheel graph add up to well over 100%, suggesting that respondents were allowed to select more than one answer. Always take note of the source for published statistics (and any other provided detail) In these cases, both are national organizations. Common Sense Media is a respected leader on children and media issues, and Allstate is a funding partner for the National Youth Health and Safety Coalition. These source details can give you information about the quality of the information.

Keep in mind that information may be biased or incomplete. Knowing the source and data collection method helps you recognize biases. One of the primary vehicles for delivering statistics is the media. Do you ever wonder how much of what we think is directly influenced by the information we read in these articles?

The graphic “What Employers Are Looking For” reports that 39% of employers look for a positive attitude and eagerness in seasonal employees.

Q: Where did this information come from? A: Note the source, SnagAJob.com. Q:How did the researchers collect the information? A: They conducted a survey of 1,043 hiring managers.

A margin of error is given at 3 percentage points. (Remember to check the small print, usually at the bottom of a statistical graph or chart.) Based on this additional detail, the margin of error, the 39% on the graph becomes: “between 36% and 42% of employers...”

Don’t believe statistics just because they are in newspapers or magazines or on TV or online. Be critical! Consider the source when reading a statistical report. Look at the complete picture.

Exposed: How Fox News Lies With Statistics

“[A little] statistics technique requires [a lot] of common sense for proper application (use).” （Example) International Shark Attack File (ISAF). surveyed by American Elasmobranch Society and the Florida Museum of Natural History

It is shown in the graph and chart below.

Using common sense while reviewing the shark attack graph, one would certainly stay away from the United States if he or she enjoys the ocean. Nearly two-fifths of the world’s shark attacks occur in the United States. U.S. waters must be full of sharks, and the sharks must be mad! Common sense—remember? Is the graph a bit misleading? What else could be influencing the statistics shown here? First, one must consider how much of a country’s or continent’s border comes in contact with an ocean. Second, who is tracking these attacks? In this case, it is stated at the top of the chart—The Florida Museum of Natural History, a museum in the United States. Apparently, the United States is trying to keep track of unprovoked shark attacks. What else is different about the United States compared with the other areas? Is the ocean a recreational area in the other places? What is the economy of these other areas, and/or who is keeping track of their shark attacks? Remember to consider the source when reading a statistical report. Be sure you are looking at the complete picture.

Where Statistics Are Used

The uses of statistics are unlimited. (Examples) education  test results science  data from experiments government  many kinds of data The U.S. government is probably the world’s greatest collector of statistical data. It is much harder to name a field in which statistics is not used than it is to name one in which statistics plays an integral part.

Very important parts of the statistical process are: (1) Study statistical results (2) Formulate appropriate conclusions (3) Share the findings with others

Statistics are being reported everywhere: Newspapers Magazines Radio Television Internet

The Language of Statistics

(*Keyword) *population all individuals or objects that are of interest to the sample collector The population to be studied must be carefully defined and is considered fully defined only when its membership list of elements is specified. To further continue our study of statistics, we need to “talk the talk.” Statistics has its own jargon, terms beyond descriptive statistics and inferential statistics, that needs to be defined and illustrated.

(Example) All students who have ever attended a U.S. college Often we think of a population of “people,” but a population can be anything.

Two kinds of populations: *finite (countable) When the membership of a population can be (or could be) physically listed, the population is said to be finite. *infinite (uncountable) When the membership is unlimited, the population is infinite. The books in your college library form a finite population; the OPAC (Online Public Access Catalog, the computerized card catalog) lists the exact membership. All the registered voters in the United States form a very large finite population; if necessary, a composite of all voter lists from all voting precincts across the United States could be compiled. On the other hand, the population of all people who might use aspirin and the population of all 40-watt light bulbs to be produced by General Electric are infinite.

*sample Large populations are difficult to study; therefore, it is customary (usual) to select a sample, or a subset of a population, and study the data in that sample. A sample consists of the individuals, objects, or measurements selected from the population by the sample collector.

*variable Statisticians are interested in particular variables of a sample or a population. one or more characteristics of interest about each member of a population or sample. age hair color height weight

*data value Each variable associated with one member of a population or sample has a value. That value, called the data value, may be a number, word, or symbol.

(Example) Bill Jones entered college at age “23,” his hair was “brown,” he was “71 inches” tall, and he weighed “183 pounds.” These four data values are the values for the four variables as applied to Bill Jones. *data The set of values collected from the variable from each of the elements that belong to the sample.

*experiment To collect a set of data, a statistician would conduct an experiment, which is a planned activity whose results yield a set of data. An experiment includes the activities for: selecting the elements obtaining the data values

*parameter The “average” age at time of admission for all students who have ever attended our college and the “proportion” of students who were older than 21 years of age when they entered college are examples of two population parameters. A parameter is a numerical value that summarizes the entire population.

For every parameter there is a　corresponding sample statistic. *statistic The statistic is a numerical value summarizing the sample data and describing the sample the same way the parameter describes the population. Often a Greek letter is used to symbolize the name of a parameter.

The “average” height, found by using the set of 25 heights, is an example of a sample statistic. A statistic is a value that describes a sample. Most sample statistics are found with the aid of formulas and are typically assigned symbolic names that are letters of the English alphabet (for example, , s, and r).

Kinds of Variables

Kinds of Variables There are basically two kinds of variables:
qualitative variables result in information that describes or categorizes an element of a population (2) quantitative variables result in information that quantifies an element of a population.

Kinds of Variables A sample of four hair-salon customers was surveyed for their “hair color,” “hometown,” and “level of satisfaction” with the results of their salon treatment. All three variables are examples of qualitative (attribute) variables because they describe some characteristic of the person, and all people with the same attribute belong to the same category.

Kinds of Variables The data collected were {blonde, brown, black, brown}, {Brighton, Columbus, Albany, Jacksonville}, and {very satisfied, satisfied, somewhat satisfied, dissatisfied}. By contrast, the “total cost” of textbooks purchased by each student for this semester’s classes is an example of a quantitative (numerical) variable.

Kinds of Variables A sample resulted in the following data:
$238.87, $94.57, $ [To find the “average cost,” simply add the three numbers　and divide by 3: ( ) ÷ 3 = $ ] As you can see, arithmetic operations, such as addition and averaging, are meaningful for data that result from a quantitative variable (and would be useless in examining qualitative variables).

Kinds of Variables Each of these types of variables (qualitative and quantitative) can be further subdivided as illustrated in the following diagram.

Kinds of Variables Qualitative variables may be characterized as nominal or ordinal. A nominal variable is a qualitative variable that characterizes (or describes, or names) an element of a population. For example, (blonde + brown + black + brown) ÷ 4 is undefined. Not only are arithmetic operations not meaningful for data that result from a nominal variable, but an order cannot be assigned to the categories. In the survey of four hair-salon customers, two of the variables, “hair color” and “hometown,” are examples of nominal variables because both name some characteristic of the person, and it would be meaningless to find the sample average by adding and dividing by 4.

Kinds of Variables An ordinal variable is a qualitative variable that incorporates an ordered position, or ranking. (example) In the survey of four hair-salon customers, the variable “level of satisfaction” is an example of an ordinal variable. Very satisfied Satisfied Somewhat satisfied

Kinds of Variables Quantitative or numerical variables can also be subdivided into two classifications: discrete variables and continuous variables. (Discrete variables) A discrete variable is a quantitative variable that can assume a countable number of values. The discrete variable can assume any values corresponding to isolated points along a line interval. That is, there is a gap between any two values.

Kinds of Variables (Continuous Variables)
Continuous variable is a quantitative variable that can assume an uncountable number of values. The continuous variable can assume any value along a line interval, including every possible value between any two values. The variable “number of courses for which you are currently registered” is an example of a discrete variable; the values of the variable may be found by counting the courses. (When we count, fractional values cannot occur; thus, there are gaps between the values.) The variable “weight of books and supplies you are carrying as you attend class today” is an example of a continuous random variable; the values of the variable may be found by measuring the weight. (When we measure, any fractional value can occur; thus, every value along the number line is possible.)

Within a set of measurement data, we always expect variation. If little or no variation is found, we would guess that the measuring device is not calibrated with a small enough unit.

(Example) If we weigh 24 chocolate bars, we may observe that each of the candy bars weighs 100 grams. (Question) Does this mean that the bars are all identical (same) in weight?

(Answer) Not really! Suppose we were to weigh them on an analytical balance that weighs to the nearest milligram. Now the 24 weights will most likely show variability. It does not matter what the response variable is; there will most likely be variability in the data if the tool of measurement is precise enough.

One of the primary objectives of statistical analysis is measuring variability. For example, in the study of quality control, measuring variability is absolutely essential. *variability The extent (amount) to which data values for a particular variable differ from each other.

Assignment for Next Class
Please read Chapter 1: Section Problem Set 1 (Practice) By using Aplia

Introductory Statistics

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