Ch1 Larson/Farber 1 1 Elementary Statistics Larson Farber Introduction to Statistics As you view these slides be sure to have paper, pencil, a calculator and your text handy. Click to advance to the slide show.

An Overview of Statistics Section 1.1 After you see the slides for each section, do the Try It Yourself problems in your text for that section to see if you understood the material. Then, do the assigned problems for that section.

What is Statistics? Statistics is the science of collecting, organizing, analyzing, and interpreting data in order to make decisions.

Ch1 Larson/Farber 4 Important Terms Population The collection of all responses, measurements, or counts that are of interest. Sample A portion or subset of the population. x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x xx x x x x x x x x x x x x x x x x x x x x x x xx x x x x x x x x x x x x x x x x x x x x x x x x x x

Ch1 Larson/Farber 5 Important Terms Parameter: A number that describes a population characteristic. Statistic: A number that describes a sample characteristic. Average gross income of all people in the United States in gross income of people from a sample of three states.

Ch1 Larson/Farber 6 Inferential Statistics Involves using sample data to draw conclusions about a population. Two Branches of Statistics Descriptive Statistics Involves organizing, summarizing, and displaying data.

Data Classification Section 1.2

Ch1 Larson/Farber 8 Data Classification 1. Nominal2. Ordinal 3. Interval4. Ratio A data set can be classified according to the type and the level of measurement: There are two types of data: 1- Categorical data 2- Quantitative data There are four levels of measurement:

Ch1 Larson/Farber 9 Type of Data Categorical data consist of attributes, labels, or non-numerical entries. Quantitative data consist of numerical measurements or counts Examples: The color of shirts, the type of car, the condition of a patient. Examples: Age of students, Number of books in the book bag

Ch1 Larson/Farber 10 Levels of Measurement 1. Nominal 2. Ordinal 3. Interval 4. Ratio A data set can be classified according to the highest level of measurement that applies. The four levels of measurement, listed from lowest to highest are:

Ch1 Larson/Farber 11 Levels of Measurement Categories, names, labels, or qualities. Cannot perform mathematical operations on this data. Data can be arranged in order. You can say one data entry is greater than another. 1. Nominal : Ex: type of car you drive, your major 2. Ordinal : Ex: TV ratings, condition of patient in hospital. 1st place

Ch1 Larson/Farber 12 Levels of Measurement There is an inherent zero. Data can be ordered, differences can be found, and a ratio can be formed so you can say one data value is a multiple of another. 3. Interval : 4. Ratio: Ex. Height, weight, age Data can be ordered and differences between 2 entries can be calculated. There is no inherent zero (a zero that means “none”.) Ex: Temperature, year of birth

Ch1 Larson/Farber 13 Summary Ratio Between data can be found Nominal Ordinal Interval Ratio Difference between data can be found Data can be ordered Categorical Or Quantitative Level of measurement Categorical ×× × ×× × Quantitative

Experimental Design Section 1.3

xx x x x Random Sample : Each member of the population has an equal chance of being selected. Simple Random Sample: All samples of the same size are equally likely. x x x x x x x x x x x x xx x x x x x xx x x x x x x xx x x x x x x xx x x x x x xx x x x x x x x x x x x x x x xx x x x x x xx x x x x x xx x x x x x x xx x x x x x xx x x x x x x xx x x x x x x x Assign a number to each member of the population. Random numbers can be generated by a random number table, software program or a calculator. Data from members of the population that correspond to these numbers become members of the sample.

Ch1 Larson/Farber 16 Stratified Random Samples Divide the population into groups (strata) and select a random sample from each group. Strata could be age groups, genders or levels of education, for example. Sample

Ch1 Larson/Farber 17 Cluster Samples Divide the population into individual units or groups and randomly select one or more units. The sample consists of all members from selected unit(s). Cluster Sample:

Ch1 Larson/Farber 18 Systematic Samples x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x Choose a starting value at random. Then choose sample members at regular intervals. We say we choose every kth member. In this example, k = 5. Every 5 th member of the population is selected.

Ch1 Larson/Farber 19 Other Samples Convenience Sample : Choose readily available members of the population for your sample.

Ch1 Larson/Farber 20 Data Collection A count or measure of part of the population. Experiment: Apply a treatment to a part of the group. Simulation: Use a mathematical model (often with a computer) to reproduce condition. Census: A count or measure of the entire population Sampling: