Introduction to Statistics

Lecture Notes Chapter 1: Introduction to Statistics. The term Statistics originally referred to " affairs of the state" (think "stateis-tics"), such as the number of people in a kingdom or the amount of tax revenue collected. A more modern definition of the term statistics would be "data-o-logy"so you should think of statistics as the science of data. What is Statistics? Statistics is the art and science of collecting, organizing, analyzing, and interpreting data in order to make decisions. Data consist of information coming from observations, counts, measurements, or responses. Data can be numerical, as in height, or they can be nonnumerical, as in gender. In either case, data describe characteristics of an individual. Quantitative data consist of numerical measurements or counts. Qualitative data consist of attributes, labels, or nonnumeric entries. There are two branches of Statistics: (Descriptive Statistics and Inferential Statistics) Descriptive Statistics: (The Building Blocks of Data Analysis) As a first step in data analysis, we use numbers (such as counts and percents) and graphics to describe the data set. Suppose we are collecting data about the patients in a particular hospital, including the diagnosis, length of stay, gender, and total cost. The sources of the information (the patients) are called the elements. the patients' characteristic (for example, diagnosis, length os stay) are called the variables. And the complete set of characteristics for a particular patient is called an observation. An element is a specific entity for which information is collected. A variable is a characteristic of an element, which can assume different values for different elements. An observation is the set of values the variables for a given element. A qualitative or categorical variable is a variable that does not have a numeric value but is classified into categories. A quantitative variable is a variable that takes numeric values, and it makes sense to say, for example, that one value is larger than another. For example, Alex's qualitative variables include his gender, ethnicity, marital status, and college. In contrast, Alex's grade point average is an example of a quantitative variable. Quantitative variables can be classified as either Discrete or Continuous. A Discrete variable can take either a finite or a countable number of values. Each value can be graphed as a separate point on a number line, with space between each point. A continuous variable can't take infinitely many values, forming an interval on the number line, with no space between the points. For example, the variable " the number of children" is discrete and the variable " GPA" is continuous. Since GPA can take an infinite number of possible values, for example interval 0.0 to 4.0. Inferential statistics is the branch of statistics that involves using a sample to draw conclusions about a population. A population is the complete collection of all elements (scores, people, measurement, and so on) to be studied. The collection is complete in the sense that it includes all subjects to be studied. A parameter is a characteristic of a population. A census is the collection of data from every element in a population. A sample is a sub collection of elements drawn from a population. A statistic is a characteristic of a sample Example 1: In a recent survey, 3002 American adults were asked if they read new on the Internet at least once a week. Responses of American adults (population) Responses of adults in survey (sample) Statistical inference consists of methods for estimating and drawing conclusion about population characteristics based on the information contained in a subset (sample) of that population. For example, the Pew Internet and American Life Project conducted a survey of 886 teenagers and found that 284 of them (32%) said they had been the targets of cyberbullying. At this point, the sociologist can make the inference that the proportion of all American teenagers who have been subjected to cyberbullying is 32%, because this is the proportion in the sample. In doing this, the sociologist is performing statistical inference.