COURSE: JUST 3900 INTRODUCTORY STATISTICS FOR CRIMINAL JUSTICE Chapter 1: Introduction to Statistics Peer Tutor Slides Instructor: Mr. Ethan W. Cooper, Lead Tutor © 2013 - - PLEASE DO NOT CITE, QUOTE, OR REPRODUCE WITHOUT THE WRITTEN PERMISSION OF THE AUTHOR. FOR PERMISSION OR QUESTIONS, PLEASE EMAIL MR. COOPER AT THE FOLLWING: firstname.lastname@example.org Learning statistics is like learning a foreign language: Make notecards to help you learn your key terms Population (p. 5) Sample (p. 6) Variable (p. 6) Parameter (p. 7) Statistic (p. 7) Descriptive Statistics (p. 8) Inferential Statistics (p. 9) Correlational Method (p. 13) Experimental Method (p.16) More Key Terms: Think Notecards Independent Variable (p. 16) Dependent Variable (p. 16) Control Condition (p. 16) Experimental Condition (p. 16) Nonexperimental Studies (p. 17) Quasi-independent Variable (p. 18) Constructs (p. 20) Operational Definition (p. 20) More Key Terms: Think Notecards Discrete Variable (p. 21) Continuous Variable (p. 21) Real limits (p. 22) Nominal Scale (p. 23) Ordinal Scale (p. 23) Interval Scale (p. 25) Ratio Scale (p. 25) Order of Operations (p. 27) Statistics, Population, and Samples Question1: If a researcher measures the number of text messages that each individual high school student sends each day and calculates the average number for the entire group of high school students, the average number would be an example of a ________. Statistics, Population, and Samples Question 1 Answer: Parameter. The researcher uses the entire population of college students. Statistics, Population, and Samples Question 2: A researcher is interested in how watching a reality TV show featuring fashion models influences the eating behavior of 13-year-old girls. a) b) A group of 30 13-year-old girls is selected to participate in a research study. The group of 30 13-year-old girls is an example of a ________. In the same study, the amount of food eaten in one day is measured for each girl and the researcher computes the average score for the 30 13-year-old girls. The average score is an example of a _________. Statistics, Population, and Samples Question 2 Answers: a) b) Sample Statistic Research Methods Question 3: Researchers have observed that high school students who watched educational television programs as young children tend to have higher grades than their peers who did not watch educational television. Is this study an example of an experiment? Why or why not? Research Methods Question 3: Answer: This study could be correlational or nonexperimental, but it is definitely not an example of a true experiment. The researcher is simply observing, not manipulating, the amount of educational television. Research Methods Question 4: What two elements are necessary for a research study to be an experiment? Research Methods Question 4 Answer: First, the researcher must manipulate one of the two variables being studied. Second, all other variables that might influence the results must be controlled. Research Methods Question 5: Loftus and Palmer (1974) conducted an experiment in which participants were shown a video of an automobile accident. After the video, some participants were asked to estimate the speed of the cars when they “smashed into” each other. Others were asked to estimate the speed when the cars “hit” each other. The “smashed into” group produced significantly higher estimates than the “hit” group. Identify the independent and dependent variables for this study. Research Methods Question 5 Answer: The independent variable is the phrasing of the question and the dependent variable is the speed estimated by each participant. Variables and Measurement Question 6: A survey asks people to identify their age, annual income, and marital status (single, married, divorced, etc.). For each of these three variables, identify the scale of measurement that is used and identify whether the variable is continuous or discrete. Variables and Measurement Question 6 Answer: Age and annual income are measured on ratio scales and are both continuous variables. Marital status is measured on a nominal scale and is a discrete variable. Variables and Measurement Question 7: An English professor uses letter grades (A, B, C, D, and F) to evaluate a set of student essays. What kind of scale is being used to measure the quality of the essays? Variables and Measurement Question 7 Answer: Ordinal Variables and Measurement Question 8: The teacher in a communications class asks students to identify their favorite reality television show. The different television shows make up what kind of scale? Variables and Measurement Question 8 Answer: Nominal Variables and Measurement Question 9: When measuring height to the nearest inch, what are the real limits for a value of 68 inches? Variables and Measurement Question 9 Answer: 67.5 and 68.5 67 68 67.5 69 68.5 Variables and Measurement Question 10: When measuring height to the nearest half inch, what are the real limits for a value of 68 inches? Variables and Measurement Question 10 Answer: 67.75 and 68.25 67.5 68 67.75 68.5 68.25 Discrete or Continuous? Question 11: Foot length Height Time Number of students in JUST 3900 Weight Number of siblings Age Discrete or Continuous? Question 11 Answer: Foot length, height, weight, age, and time are all continuous because they are not limited to a fixed set of separate, individual categories. They can be divided into an infinite number of fractional parts. It is always possible to find a third point between any two points. Height and foot length, for instance, can be measured in meters, centimeters, and even millimeters. Time and age can be broken down into years, months, days, hours, seconds, or milliseconds. When two people say they each weigh 150 lbs., what they likely mean is that they each weigh about 150 lbs. There are an infinite number of possibilities between 149 lbs. and 150 lbs. and 150 lbs. and 151 lbs. that would more accurately describe their respective weights. Discrete or Continuous? Question 11 Answer: The number of students enrolled in JUST 3900 and the number of siblings one has are both discrete variables. They consist of separate, indivisible categories. Typically, discrete variables consist of whole, countable numbers. No values exist in between. For instance, there may be 100 students enrolled in JUST 3900 or one may have 7 siblings, but there cannot be 99.5 students or 7.5 siblings. Order of Operations Parentheses Exponents Multiplication/Division (in order from left to right) Summation Addition/Subtraction (in order from left to right) Order of Operations Question 12: Calculate each value requested for the following scores: 6,2,4,2. a) b) c) d) e) ΣX ΣX2 (ΣX)2 Σ(X-2) Σ(X-2)2 Order of Operations Question 12 Answers: a) b) c) d) e) = 6 + 2 + 4 + 2 = 14 2 = 62 + 22 + 42 + 22 = 36 + 4 + 16 + 4 = 60 2 = 6 + 2 + 4 + 2 2 = 142 = 196 −2 = 6−2 + 2−2 + 4−2 + 2−2 = 4+0+2+0=6 2 −2 = 6−2 2+ 2−2 2+ 4−2 2+ 2−2 42 + 02 + 22 + 02 = 16 + 0 + 4 + 0 = 20 2 = Summation Notation Question 13: Use summation notation to express each of the following. a) b) c) Add 4 points to each score and then add the resulting values. Add the scores and then square the total. Square each score, then add the squared values. Summation Notation Question 13 Answers: a) b) c) +4 2 2 Frequently Asked Questions FAQs How do I pass this class? 1) 2) 3) 4) 5) 6) 7) 8) Read the chapters before lectures. Complete Aplia tutorials/practice questions in preparation for in-class exercises. If needed finish in-class exercises at home. Come to tutoring (Workshops and Day time appointments). Review the answer key to the in-class exercises before completing the graded portion of Aplia. Never take a homework free holiday! (Towards the end of the semester this will make more sense) Finish Aplia within 24 hours of the last lecture! Always bring slides to class and take notes. Frequently Asked Questions FAQs What should I expect on the tests? a) b) c) d) Tests will consist of approximately 45 multiple choice questions. The final exam will consist of approximately 60 multiple choice questions. The material covered on the test will include knowledge of concepts, definitions, and formulas (know your terms). Strictly speaking, the tests are not cumulative. Each exam will only cover 3 chapters. e) However, statistics is a course that builds on the foundation that was laid in past chapters. If you do not understand chapters 1-3, you will not grasp chapters 4-6. “A small error in the beginning leads to a large error in the end.” Aristotle Any tables required for the test (e.g., the tables in the textbook’s appendices) will be provided by Dr. Kerbs. What is it Really Like to be a JUST3900 Student? Taking JUST3900 with Dr. Kerbs: FACT OR FICTION Taking JUST3900 with Dr. Kerbs is a demanding experience. FACT Dr. Kerbs does expect a great deal from his students -- he wants you to understand and preferably master the course material. However, he provides you with every resource to excel in his class: PowerPoint slides, in-class exercises with a detailed explanation of each problem, a great text book, office hours, and tutoring services. He gives you the tools to succeed in understanding and applying course content. That said, you need to do your part as well: Read before each class, attend each class and take notes, review your notes between classes, complete all homework assignments, ask questions, and study for each test. Getting extra help is difficult. FICTION Dr. Kerbs is very approachable on all levels. First, he wants students to ask questions in class and during office hours. If you’re asking questions, it means that you are trying to learn the material: This is a good thing! You can always expect that Dr. Kerbs will take your questions and requests for help seriously, and he will always treat you with respect and courtesy. Second, he holds office hours every week and is available by appointment. He is known for diligently helping students because he really does want you to succeed.