fall 2008. where i’m from: about me… my “kids”… about me…

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Elementary Statistics Fall 2008

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  • Slide 1
  • Fall 2008
  • Slide 2
  • Where Im from: About Me
  • Slide 3
  • My kids About Me
  • Slide 4
  • My personality About Me
  • Slide 5
  • Webpage http://web.missouri.edu/~dls6w4 Syllabus Calendar Practice Materials Homework Exam Information
  • Slide 6
  • Make sure you have access to Blackboard You must either: Activate your stlcc email account Update Blackboard to different email Otherwise, you will not receive emails You are still responsible for all emails sent regardless of receipt When/if you send me an email, please put Stats Night in the subject line If you do not, I wont answer it Blackboard
  • Slide 7
  • Homework Long and painful Absences will not excuse you from completing homework All will be posted on the webpage Youll need to have a strong understanding of the material Group work I will take your top 5 scores I do not know how many we will have
  • Slide 8
  • Exams 4 exams Final is cumulative I will drop your lowest exam score of the first three The final exam counts You will be allowed a notecard for formulas and a non- programmable calculator
  • Slide 9
  • Project Paper, no minimum page requirement Do something that interests you Check webpage for details/deadlines Failure to complete the paper as required will result in the loss of an additional letter grade
  • Slide 10
  • Attendance Attendance includes being present, but it also includes: Not disrupting class Being attentive Not excessively talking Not doing anything I deem annoying This will cost you attendance credit If you come in after roll call, it is your job to notify me in person that day
  • Slide 11
  • Point Breakdown Exams: 60% Three Midterm exams: 100 points each Final Exam (cumulative): 100 points Homework: 30% Each homework worth fifty points each Ill count the top 5 Project: 10% Attendance: Loss of 3%
  • Slide 12
  • Introductory Material
  • Slide 13
  • Some Basics Descriptive Statistics Allow us to get a sense of things Inferential Tools Allow us to reach some conclusion Estimation, Hypothesis Testing
  • Slide 14
  • Where does data come from? Experiments Process generating outcomes Design is important Surveys Closed-end Questions Open-end Questions Demographics Interviews/Observation
  • Slide 15
  • Stop and Think What kinds of things can go wrong with surveys?
  • Slide 16
  • What can go wrong? Potential Problems Interviewer Bias Non-response Bias Selection Bias Observer Bias Measurement Error Validity Internal Eliminating useless info External Results beyond original
  • Slide 17
  • Key Terms Population All possible observations Sample A portion of the population Is error (sample) worth the lower cost (population)?
  • Slide 18
  • Sampling Techniques Statistical Sampling Based on chance Nonstatistical Sampling Not on chance Simple Random Sampling All possible Stratified Random Sampling Into levels Systematic Random Sampling Every kth Cluster Sampling Break into groups
  • Slide 19
  • Types of Data Quantitative v. Qualitative Quantitative Numerical Qualitative Categorical Time-series v. Cross-Section Time-series one value, many times Cross-section many values, one time
  • Slide 20
  • What level are the data? Nominal Simplest form, no rank implied Ordinal Rank data Interval Difference measure, no true zero Ratio Consistent, true zero
  • Slide 21
  • Describing Data Frequency Distribution Reports how often values occur Classifies observations by class Relative Frequency How often one value occurs compared to sample Usually expressed in percentage RF = (f i )/(n)
  • Slide 22
  • Describing Data Grouped Frequency Distribution Classifies data into groups Groups must be: Mutually Exclusive All-Inclusive Equal-Width Free of empty classes (if possible)
  • Slide 23
  • Describing Data Grouped Frequency Distribution How to determine groups Determine number of groups (2 k n) Establish width of classes Determine boundaries for classes Count values in each class Both types can be built into a histogram Also can construct Cumulative Frequency Distribution and build an ogive
  • Slide 24
  • Describing Data Other methods Bar Chart Pie Chart Stem-and-Leaf Diagram Line Chart (Time graph) Scatter Plot Can see relationship between X and Y Demand/Supply curves (Economics)
  • Slide 25
  • Describing Data May want to examine two variables Use Joint Frequency Distribution How? Get data containing two responses Build table Find joint occurrences Sum rows and columns for marginal frequencies
  • Slide 26
  • Numerical Measures Weve done some simple measures Now lets actually do some calculations Before we start: Parameter-based on population Statistic-based on sample
  • Slide 27
  • Center and Location Population Mean () A.k.a. average For population, sum of deviations=0 Sample Mean (x-bar) Based on a selected sample All means subject to distortion by extrema
  • Slide 28
  • Center and Location Median Middle value of the data Odd-numbered sample=find middle Even-numbered sample=find middle of middle two
  • Slide 29
  • Center and Location Taken together, the mean and median show skewness of data Median>Mean = Left Skewed Median
  • Slide 30
  • Center and Location Mode Value occuring most often Occasionally, a set of data has no mode
  • Slide 31
  • Center and Location Weighted Mean Same idea as mean, just unequal weights on observations Percentiles Describes where a particular value is located in data i = (p/100)*(n) If i is integer average (i, i + 1) If i is not integer round up Quartiles Dividing the data into four equal parts Qua implies four (quarter, quart, etc.)
  • Slide 32
  • Be careful! These not always useful for qualitative data masquerading as quantitative Need further assumptions/theory to hold
  • Slide 33
  • Measures of Variation Variation The spread of the data Range = Maximum minimum Sensitive to extrema Considered weak Interquartile Range = Third Q First Q Softens dependence on extrema
  • Slide 34
  • Measures of Variation Variance ( 2 ) Measure of dispersion or spread Equation Shortcut Standard Deviation () VAR Sample (s 2, s) and Population calculated in similar fashion Use n-1 instead of N in denominator
  • Slide 35
  • Combining and Coefficient of Variation (CV) Relative variation with different means (/)*(100%) for population Replace with sample measures for sample CV Empirical Rule (with bell-shape) 68% within 95% within 2 All within 3
  • Slide 36
  • Standardizing Values Allows us to compare different data effectively Z-value (population) = (x ) / X is value of interest Based on a standard normal distribution Mean = 0, Variance = 1 This will be important from now until the end
  • Slide 37
  • Probability The chance that something will happen Sample Space all possible events Event Element(s) of sample space Mutually Exclusive Independence v. Dependence Ways to determine Classical Relative Frequency Subjective
  • Slide 38
  • Probability Some rules to know All probabilities are between 0 and 1 (incl.) The sum of all probabilities is 1 Complement Rule Probability of X = 1 Probability of all others Addition Rule Probability of X or Y = Pr(X) + Pr(Y) Pr(X and Y) If events mutually exclusive = Pr(X) + Pr(Y)
  • Slide 39
  • Probability Some simple examples Probability of tails on fair coin? Probability of rolling a 1 or 6 on fair die? Probability of drawing a heart from standard deck?
  • Slide 40
  • Probability Conditional Probability The probability that one event occurs when you know something else has happened Pr(X|Y) = Pr(X and Y)/Pr(Y) If the events are independent, =Pr(X) Multiplication Rule Pr(X and Y) = Pr(X)(Pr(Y|X)) Independent = Pr(X)Pr(Y)