Probability and Statistics Chapter 1 Notes Probability and

Probability and Statistics Chapter 1 Notes

Probability and Statistics Chapter 1 Notes III. Section 1 -3 A. Design of a Statistical Study 1. Identify the variable(s) of interest (the focus) and the population of the study. 2. Develop a detailed plan for collecting data. 3. Collect the data. 4. Describe the data, using descriptive statistics techniques. 5. Interpret the data and make decisions about the population using inferential statistics. 6. Identify any possible errors. B. Data Collection 1. Do an Observational Study a. Observe and measure characteristics of interest of part of a population, but do NOT change existing conditions.

Probability and Statistics Chapter 1 Notes III. Section 1 -3 B. Data Collection 2. Do an Experiment a. Apply a treatment to part of a population and observe responses or results. b. Observe another part of the population as a control group. 1) May use a placebo in place of the treatment being tested.

Probability and Statistics Chapter 1 Notes III. Section 1 -3 B. Data Collection 3. Use a simulation a. Use a mathematical or physical model to reproduce the conditions of a situation or process. 1) Simulations allow us to study situations that are impractical or even dangerous to create in real life. a) Testing the effects of alcohol on a pilot’s ability to fly is best done in a flight simulator. b) Predicting how quickly and how far a disease may spread is also best done using a computer model. 2) Simulations often save time and/or money.

Probability and Statistics Chapter 1 Notes III. Section 1 -3 B. Data Collection 4. Use a survey (census) a. A survey is an investigation of one or more characteristics of a population. 1) Usually carried out on people by asking them to respond to questions. b. It’s important to word the questions so that they do not lead to biased results.

Probability and Statistics Chapter 1 Notes III. Section 1 -3 C. Experimental Design 1. Experiments must be carefully designed in order to produce meaningful, unbiased, results. a. The Hawthorne effect occurs in an experiment when subjects change their behavior simply because they know they are participating in an experiment. 2. Three key elements of a well-designed experiment are control, randomization, and replication. a. Control 1) It is important to control as many influential factors as possible in a study. 2) When an experimenter cannot tell the difference between the effects of different factors in an experiment, a confounding variable has occurred.

Probability and Statistics Chapter 1 Notes III. Section 1 -3 C. Experimental Design 3) Placebo effect occurs when a subject reacts favorably to a placebo when in fact they have been given no medical treatment at all. a) Blinding is a technique used in which the subject does not know whether he or she is receiving a real treatment or a placebo. b) Double-blind experiments occur when neither the subjects nor the experimenter know which individual subjects are receiving a treatment or a placebo. 1. The experimenter only finds out which subjects are which after all the data have been collected.

Probability and Statistics Chapter 1 Notes III. Section 1 -3 C. Experimental Design b. Randomization is a process of randomly assigning subjects to different treatment groups. 1) Randomized block design – Divide subjects with similar characteristics into blocks, and then randomly split each block up into different treatment groups. 2) Matched-pairs design – Subjects are paired up according to a similarity. a) One subject in each pair is randomly selected to receive one treatment, while the other one gets another, different treatment. c. Replication is the repetition of an experiment using a large group of subjects. 1) The larger the sample size, the better.

Probability and Statistics Chapter 1 Notes III. Section 1 -3 D. Sampling Techniques 1. Census – a count or measure of an entire population. a. Provides complete information, but is often too costly or difficult to perform. 2. Sampling – a count or measure of part of a population. a. Researcher must ensure that the sample is representative of the population. 1) This is necessary to ensure that inferences about a population are valid. a) Sampling error – the difference between the results of a sample and those of the population. b. Random sample – a sample in which every member of the population has an equal chance of being selected.

Probability and Statistics Chapter 1 Notes III. Section 1 -3 D. Sampling Techniques 1) Methods of sampling randomly a) Simple Random Sample – assign each member of the population a number and then randomly select the numbers that you will survey. 1. Random number table (Appendix B of the book) a. Randomly pick a starting point b. Count off digits in groups that match how many digits your population has. c. Record the numbers, ignoring those that are larger than the population size.

Probability and Statistics Chapter 1 Notes III. Section 1 -3 D. Sampling Techniques 2. Calculator a. Press Math, select PRB, press 5(rand. Int) b. Enter the number that you started with when assigning labels to your population, then a comma, then the last number you assigned, comma, and the sample size you wish to use. 1) The calculator will generate the requested quantity of random numbers. 3. If you do not want to have any member of the population included in the sample twice, the sampling process is said to be without replacement.

Probability and Statistics Chapter 1 Notes III. Section 1 -3 D. Sampling Techniques 4. If you don’t care if a member of the population is included twice, the sampling process is said to be with replacement. b) Stratified Sample 1. Separate population into two or more subsets, called strata, using some similar characteristic. a. Randomly select members of each strata to make up your sample.

Probability and Statistics Chapter 1 Notes III. Section 1 -3 D. Sampling Techniques c) Cluster Sample 1. When the population is already divided into subsets that are very similar to each other, you could randomly select a number of entire groups (not all the groups) and do your data collection on those groups. a. We call these groups clusters.

Probability and Statistics Chapter 1 Notes III. Section 1 -3 D. Sampling Techniques d) Systematic Sample 1) Each member of the population is assigned a number. a. Put the members of the population in order somehow. b. Randomly select a starting point. c. Randomly select an interval. d. Survey every nth member of the population from your starting point.

Probability and Statistics Chapter 1 Notes III. Section 1 -3 D. Sampling Techniques e) Convenience Sample 1) NOT RECOMMENDED!! a. Simply select those members of the readily available. population who are

Assignments: Classwork: Pages 25 -26, #5 -14 ALL, #15 -27 ODD Homework: Page 27 #29 -34 ALL