Chapter 1: Introduction to Statistics

1. Chapter 1: Introduction to Statistics Lesson 1.1: An Overview of Statistics

2. What is “Statistics”? • Statistics is the science of collecting, organizing, analyzing and interpreting data in order to make decisions. • There are two branches of statistics: • Descriptive Statistics: involves the organization, summarization, and display of data. • Inferential Statistics: involves using a sample to draw a conclusion about a population

3. Important Vocabulary • An individual is a person or object that is a member of the population being studied. • A population is the group of individuals to be studied. • A sample is a subject of the population being studied. • A parameter is a numerical summary of a population • A statistic is a numerical summary of a sample

4. Vocabulary Practice Example: A drug manufacturer is interested in the proportion of persons who have hypertension whose condition can be controlled by a new drug. A study involving 5000 individuals with hypertension is conducted, and it is found that 80% of the individuals are able to control their hypertension with the drug. • The individual is • The population is • The sample is • The parameter is • The statistic is • What can we infer?

5. Chapter 1: Introduction to Statistics Lesson 1.2: Data Classification

6. What is Data? • Datais a collection of values or measurements. (Numbers, words, measurements, descriptions, etc.) • Data can be qualitative or quantitative. • Qualitative data is descriptive information (words) • Quantitative data, is numerical information (numbers) • Quantitative data can also be discrete or continuous • Discrete data can only take on a finite or countable number of possible outcomes • Continuous data can take on an infinite number of possible outcomes, represented by an interval on the number line.

7. Data Type Practice • Determine if the data is Qualitative or Quantitative. • If it is Quantitative determine if it is discrete or continuous. • Type of wood used to build a kitchen table. • Number of times your phone rings today • Amount of time students do homework • Way of getting to school (walk, bus, drive) • Money you make at work each week • Shoe size • Social security number

8. Levels of Measurement • Nominal: Names, labels, or qualities. Cannot perform meaningful operations on this data. (Type of car, Eye Color, Zip codes) • Ordinal: Data can be arranged in order, but differences are not meaningful.(Hotel Ratings, poor/fair/good, low/medium/high) • Interval: Data can be ordered and differences can be calculated. There is no inherent zero. (Temperature, Year of birth) • Ratio: 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. (Height, weight, age)

9. Level of Measurement Practice State the Level of Measurement: • The average daily temperature (°F) in Dover, NH during the month of August. • The height, in centimeters, of an NFL player. • The hair color of every female in Dover High School. • How good a movie is: “bad”, “ok”, “good”, “great”

10. Chapter 1: Introduction to Statistics Lesson 1.3: Data Collection and Experimental Design (Part 1)

11. Methods of Data Collection • Observational Study: researcher observes characteristics of interest but does not change existing conditions. • Experiment: Apply a treatment to a part of the population and responses are observed • Simulation: Use a mathematical or physical model to reproduce conditions of a situation or process • Survey: An investigation of one or more characteristics of a population. This can be done by taking a census or a sample.

12. Identify Method of Collection Identify: Observational Study, Experiment, Simulation, or Survey (census or sample) • A study of the effect of changing flight patterns on the number of airplane accidents. • A study of the effects of aspirin on preventing heart attacks. • A study of how fourth grade students solve a problem • A study of the weights of all linemen in the National Football League. • A study of U.S. residents’ approval rating of the U.S. presidents.

13. Sampling Techniques • Random - Every member in the population has an equal chance of being selected. • Stratified - Divide the population into groups (strata) and select a random sample from each group. Strata could be age groups, genders or levels of education • Cluster - Divide the population into clusters (subgroups) and randomly select one or more clusters to sample. • Systematic - Choose a starting value at random. Then choose sample members at regular intervals. • Convenience - Choose readily available members of the population for your sample.

14. Sampling Practice • You select a class at random and question each student in the class. • You divide the student population with respect to majors and randomly select and question some students in each major • You assign each student a number and generate random numbers. You then question each student whose number is randomly selected.

15. Warning! Beware of Bias Biased samples are not representative of the population • Sampling Bias – the technique used to obtain the individuals to be in the sample tends to favor one part of the population. • Convenience Samples • Not drawing from a full list of the population • Example: The 1948 US Election • Nonresponse Bias – exists when individuals selected do not respond to the survey have different opinions from those who do respond. • Mail in surveys, phone calls, etc • Response Bias – exists when the answers do not reflect the true feelings of the respondent. • Wording of questions – written in a way that leads to biased answers. • Social Desirability – The respondent answers based on peer pressure

16. Chapter 1: Introduction to Statistics Lesson 1.3: Data Collection and Experimental Design (Part 2)

17. Observational Studies • In an observational study, researchers don’t assign choices. • Example: the relationship between music education and grades. • Researchers do not assign students to get music education and simply observed students “in the wild” • Observational studies are valuable for discovering trends and possible relationships. • It is not possible for observational studies to demonstrate cause and effect

18. Experiments • In an experiment, the experimenter must identify at least one explanatory variable (factor) to manipulate and at least one response variable to measure. • An experiment is a study design that allows us to prove a cause-and-effect relationship. • The three key elements of a well designed experiment are control, randomization, and replication.

19. Experiment Vocabulary • In general, the individuals on whom or which we experiment are called experimental units. • When humans are involved, they are commonly called subjects or participants. • The specific values that the experimenter chooses for a factor are called the levels of the factor. • A treatment is a combination of specific levels from all the factors that an experimental unit receives.

20. Placebos and Blinding • A “fake” treatment that looks just like the treatment being tested is called a placebo. • In order to avoid the bias that might result from knowing the treatment assigned, we use blinding. • Blinding is when the subjects do not know whether they are receiving a treatment or a placebo. • In a double-blind experiment neither the subjects nor the experiments know who is receiving the treatment or the placebo. • The placebo effect occurs when a subject reacts favorably to a placebo when they have been given no medical treatment.

21. Experiment Practice Is diet or exercise effective in combating insomnia? Forty volunteers suffering from insomnia agreed to participate in a month long study. Half were randomly assigned to a special no dessert diet and the other half ate dessert as usual. Half of the people in each group were randomly assigned to an exercise program, while the others did not exercise. Those who ate no desserts and engaged in exercise showed the most improvement. (a) What subjects were studied? (b) What are the factors in this experiment and how many levels are in each factor? (c) What is the number of treatments? (d) What is the response variable that is measured?

22. Types of Experiments • Completely Randomized Design: All experimental units have an equal chance of receiving any treatment. • Randomized Block Design: Randomization only occurs within blocks. • Matched Pairs Design: Used when there are 2 “treatments”. The pairs are created by some common variable, one person receives one treatment the pair received treatment 2.