1_1_First Class_F2023.pptx statistics course
- 2. Information: • Lectures: Tue., Thu. 13:30-14:50 • Lecture Hall: Audubon 0104 • Labs: Thu. 15:00-16:50, Fr. 12:30-14:20, 44 Woodin Hall • Office: 53 Woodin Hall • Office Hours: Tue. 3:00-4:00, Thu. 11:00-12:00 or by appointment (through ZOOM) • Email: agentimis1@lsu.edu • Moodle: Check it often! • Book: “Statistical Methods” Freund, Wilson, Mohr, 3rd edition
- 3. Thematic Units Covered: • Graphical and numerical Summary of Data • Elements of Probability • Random Variables • Basic Distributions • Confidence Intervals • Inference and t-tests • Two sample inference • Proportions tests • ANOVA • Linear Regression • Categorical Data Analysis (Maybe?)
- 4. Grades Breakdown: Assignment Points Total number Count Available Points: Lab Assignments 5 12 8 5x8=40 Exams 20 2 2 2x20=40 Project 20 1 1 1x20=20 Total 40+40+20=100 Letter Grade Points Letter Grade Points A+ x ≥ 99 C+ 80 > x ≥ 78 A 99 > x ≥ 92 C 78 > x ≥ 72 A- 92 > x ≥ 90 C- 72 > x ≥ 70 B+ 90 > x ≥ 88 D+ 70 > x ≥ 68 B 88 > x ≥ 82 D 68> x ≥ 62 B- 82 > x ≥ 80 F 62>X
- 5. What is Statistics? How is it used? • Data Collection: • Design Experiments • Sampling • Data Description: • Summary Statistics • Graphs • Probability: • Randomness • Uncertainty • Statistical Inference: • Conclusions from Data • Hypothesis testing “The science of collecting, analyzing and interpreting data.”
- 6. What time do my colleagues come to work? • Underlying Phenomenon: “My colleagues come to work around a certain time” • Observations: “The common doorway is locked if they have not arrived or is unlocked if they have” • Data: “A collection of times with the characterization U(unlocked) and L(locked)”
- 7. Generalities about data: • A data set is composed of information from a set of units. • Information from a unit is known as an observation. • An observation consists of one or more pieces of information about the unit; these are called variables.
- 8. Types of variables: • What is the time variable in this example? DISCRETE! • Definition 1.4: A discrete variable can assume only a countable number of values. • Typically, discrete variables are frequencies of observations having specific characteristics, but all discrete variables are not necessarily frequencies. • Definition 1.5: A continuous variable is one that can take any one of an uncountable number of values in an interval. • Continuous variables are usually measured on a scale and, although they may appear discrete due to imprecise measurement, they can conceptually take any value in an interval and cannot therefore be enumerated.
- 9. Types of variables: • Why should I care? Various statistical programs, R, SAS, STATA, etc. are very picky about the type of variables you are using! Lots of errors can occur if they are not defined properly! • The status variable is also called a categorical variable. • The two possibilities Locked and Unlocked are called names or levels or types. • We say that the STATUS variable follows a nominal scale. weakest type to do statistics with • The time variable is called Quantitative • The status variable is called Qualitative
- 10. Now what? Time in Status Time in Status 8:45 L 9:10 U 8:34 L 8:50 U 8:43 L 8:45 U 9:40 L 9:05 U 9:40 L 9:10 U 8:45 L 9:05 U 16:00 L 8:45 U 9:10 L 8:44 U 8:58 L 10:20 U 8:39 L 11:30 U 8:48 L 12:15 U 8:33 L 10:00 U 11:15 L 9:41 U 8:48 L 9:10 U 8:33 L 10:54 U 8:50 U 9:29 U 10:40 U 11:20 U 9:30 U 8:45 U 9:27 U 8:50 U 8:45 U 9:42 U • To give an answer to our problem we need to employ some Numerical Descriptive Statistics. • First though we need to “clean up” our data set. “In projects, cleaning up datasets is 80% of the work. Statistics is 20%. Convincing people about them is 20%. Revising is 80%. You need to give 200% every time!”
- 11. Transformations: Status Time Status Time L 45 U 70 L 43 U 50 L 100 U 45 L 195 U 65 L 48 U 70 L 33 U 65 L 34 U 45 L 45 U 44 L 480 U 140 L 70 U 210 L 58 U 255 L 39 U 120 L 100 U 101 L 48 U 70 L 33 U 174 U 50 U 89 U 160 U 200 U 90 U 45 U 87 U 50 U 45 U 102 • It is difficult to do descriptive statistics with “absolute time” • Much easier to change to “minutes after …” • What we are doing is called “change of scale” (useful technique) and it is a form of “transformation”! • Make sure you read about the different scales on page 10.
- 12. Ideas?? Locked Min 1st Q. Median Mean 3rd Q. Max 33 41 48 91.4 85 480 • We want to find the behavior “on average” • We can use the mean, or the median. • We can draw information from the quartiles. • We can draw information from the max and min. Unlocked Min 1st Q. Median Mean 3rd Q. Max 44 50 70 97.68 120 255
- 13. More Ideas? • We can use a boxplot Q1,Q3,median.
- 14. Outliers! Status Time Status Time L 45 U 70 L 43 U 50 L 48 U 45 L 34 U 65 L 45 U 70 L 70 U 65 L 58 U 45 L 39 U 44 L 48 U 101 U 70 U 50 U 89 U 90 U 45 U 87 U 50 U 45 U 102 • Due to errors • Due to abnormal situations • May skew our results • Whole branch of analytics “If you have no intelligent way to describe outliers, remove them and report that you are doing so.” • Here we removed everything above and below the Q1 and Q3
- 15. Review new data: Unlocked (clean) Min 1st Q. Median Mean 3rd Q. Max 44 46.25 65 65.72 82.75 102 • Notice now that the mean becomes more relevant. Perhaps even more informative than the median. • Page 37 has a nice review on outliers, make sure to check it. Locked (clean) Min 1st Q. Median Mean 3rd Q. Max 34 43 45 47.78 48 70
- 16. New Box Plot: • We can “infer” that people come between 47.78 and 65.72 minutes or some time between 8:47 and 9:06. • Or if we use the medians, between 8:45 and 9:05. “This corroborates with the anecdotal evidence that most professors and students come to work at 9:00 am.”
- 17. Improve the result: • Get More Data • Analyze variances • Do a survey • Install cameras
- 18. Comment • The idea of statistics is not “natural” for the human brain • It was developed WAY after Calculus, Algebra and Trigonometry If math is the language of science, statistics is the grammar!