1 Getting Started

2 Some stories to get us started “Smoking causes lung cancer.” You may have heard this before. Well, how the heck do they know this? Through careful study and observation, it has been established that smokers have a greater incidence of lung cancer than the rest of the population. Statistics, in general, is part of the careful study and observation I mentioned above. “Television advertising is better than newspaper ads when you want to reach the younger generation.” Again, who says? The answer, in part, comes from those who use the methods of statistics. Statistics are used to back up claims people make about the world (stats are used for other things as well, as we will see).

3 In statistics class we use certain “tools.” The tool kit looks an awful lot like math, with equations and graphs and tables and variables and the like. It is math. BUT, you can do this because for the most part all we do is add, subtract, multiply and divide. Occasionally we will take the square root of a number. Statistics is really about ideas. I am convinced that if you can work with the ideas, the math will follow. (Hey Parker, do you have statistics to back up your claim? NO, I have not done the study – but I am convinced!)

4 Data As we get started in this chapter say as a research project we want to learn more about faculty at WSC. Say we gather information from faculty about 1) what is their highest educational degree, 2) how often they cuss during the day, and 3) how long they have been in Wayne. The data that are collected for a particular study are referred to as a data set and some data collected from faculty might look like (note each row represents measurements on elements and each colum is variable): FacultyDegreeCussIn Wayne Person 1PhD022 Person 2EdD335 Person 3MFA015 Person 4PhD23716

5 Elements u Any data set provides information about some group of individual elements. u In my faculty example, faculty are the elements. u In other studies the elements can be people, states, organizations, objects, and many other things.

6 What is a variable? Each element in a data set may have 1 or more characteristics of interest. Each characteristic would be called a vaiable. For any variable in a study each element has to be assigned a valule. So each element has a “measurement” taken and the value is assigned. For the most part, in our class the measurements have already taken place. We tend to look at variables on subjects or elements in which we are interested. Each element has a value on each variable.

7 Qualitative or Categorical variable The variable Degree in our example is an example of a categorical variable. The data, or observed values, from the people on the variable just yield a categorical response. IN my example I have things like PhD, MFA, and EdD. Note that sometimes in a data set numbers may be used to express the values on the variable, but all we really have are categories of responses. For example, we could have 1 = EdD, 2 = PhD, 3 = MFA and in the data set all you would see are the numbers. But, the numbers really just represent a different category.

8 Quantitative or Numerical variable In our example the variables how often they cuss during the day and how long they have been in Wayne are numerical variables. The data, or observed values, from the people on the variables yield a numerical response.

9 Population Often in statistics we are interested in a group. The group may be large, or even huge! Plus we want to be able to make statements or draw conclusions about the group. A population is the set of all elements we want to study or know something about. So, the population is the main group we want to know about or draw conclusions about. A census is conducted if we have measurements on all the elements in a population. Remember, an element is a single entity of the population.

10 Sample Many times in a study all the elements of the population will not be observed, so a sample is said to have been taken. A sample is a subset of the elements of a population – just part of the population.

11 Descriptive Statistics Example: You are probably aware of the distribution of test scores from an exam. The instructor describes properties of the data. You see how many A’s, B’s and such were earned. You might be told the average grade. Why is this a big deal? Well, you want to know how you compare to others. Describing data is a big part of statistics. Descriptive statistics is the science of describing the important aspects of a set of measurements.

12 Inferential Statistics Inferential Statistics is a method used when only a sample from a population has been drawn, but we want to make statements about the larger population. Any cooks reading this? In order to tell if a pot of soup is ready to go, is taking a sample okay? Sure it is, but first make sure you have stirred the soup to mix in the ingredients. In statistics, we feel pretty good about samples as long as we have “mixed” things well.

13 Examples Say we want to study faculty salaries at WSC. Our research topic is faculty salaries. The population is WSC faculty. Elements are individual faculty. Parker is an element of the population, as is Lutt, Paxton, Nelson, and others. Another example might be we want to study the budgets of state governments. The population is all 50 states. The elements are the states. What are the elements? (Did you say something like Ohio, Nebraska, Iowa….?) Our interest may be people, companies, states, etc…

14 A note on data and our class During the term you will work on many problems in the book (hopefully more than just the ones I assign). You can assume the data in the problem has been collected properly. As you work a problem focus your attention on the concepts in the chapter and try not to get lost in the application to which the problem refers.