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ECON 1000
Frank Miller

Chapter 1: What is Statistics? - Way to get info from data - Descriptive statistics: deals with methods of organizing, summarizing and presenting data in convenient and informative way (ie. graphing techniques) - Use numerical techniques to summarize data; average - Average is a measure of central location - Range is measure of variability - Inferential Statistics: methods used to draw conclusions/inferences about characteristics of population based on sample data - Exit polls: random sample of votes exit the polling booth and asked for whom they voted; sample proportion of voters supported the candidates is computed Key Statistical Concepts - Population: group of all items of interest; very large; does not necessarily refer to group of people - Parameter: descriptive measure of a population; mean # of soft drinks consumer by all students at the university or proportion of 5 million who voted for Bush - Sample: set of data drawn from the studied population - Statistic: descriptive measure of a sample; used to make inferences about parameters - Statistical Inference: process of making an estimate/prediction/decision about a population based on sample data; measure of reliability - Confidence level: proportion of times that an estimating procedure will be correct - Significance level: measures how frequently conclusion will be wrong - Hw pg 39, 47, 57-62, 69-72, 195, 197, 202, 204, 91-94, 100-104, 110-112, 118-125 Chapter 2: Graphical Descriptive Techniques 1 Types of Data and Information - Variable: some characteristic of a population or sample (ie. prices of stocks varying daily) - Values: possible observations of the variable; integers between 0 - 100 of statistics exam(100 marks) - Data: observed values of a variable; midterm test marks of 10 students; datum refers to mark of one student  Interval data: real numbers; heights, weights, incomes, distances (quantitative or numerical)  Nominal data: values of nominal data are categories; responses to questions about marital status (qualitative/categorical); only calculations based on frequencies or percentages of occurrence are valid  Ordinal data: order of values has meaning; order of values of latter indicate higher rating; calculations based on ordering process are valid  Interval/differences between values of interval data are consistent and meaningful Calculation for Types of Data Interval Data: all calculations permitted; set of interval data described by using the average Nominal Data: calculations based on codes used to store this type of data are meaningless; compute percentages of occurrences of each category Ordinal Data: only permissible calculations should involve ranking process Describing Set of Nominal Data - Frequency distribution: presenting the categories and their counts; relative frequency distribution lsits categories and proportions with which each occurs - Bar graph shows frequencies, pie chart shows relative frequencies - Bars in bar graph arrange in ascending/descending ordinal values; pie chart wedges arrange clockwise in ascending/descending order for ordinal data Describing relationship between 2 nominal variables - Univariate: techniques applied to single sets of data - Bivariate: methods that depict relationship between variables - Cross-classification table: describes relationship between 2 nominal variables; lists frequency of each combination of values of the 2 variables - If two variables are unrelated, patterns exhibited in bar charts should approx.. be the same Comparing 2 or more nominal data sets - Consider the three occupations (newspaper example) as defining 3 populations; if differences exist between columns of frequency distributions (or between bar charts), then differences exist among the three populations Chapter 3: Graphical Descriptive Techniques 2 Graphing techniques to describe set of interval data - Create frequency distribution for interval data by counting number of observations that fall into each of a series of intervals; called classes, covering range of observations - Intervals should be equal; graphing and interpretation made easier - Histogram: created by drawing rectangles whose bases are intervals and heights are frequencies Determining number of class intervals - # of class intervals = 1 + 3.3 log(n) (Sturges’s formula) - Class interval width = (largest observation – smallest observation) / # of classes Shapes of histograms - Histogram is symmetric when we draw vertical lines down the centre and the two sides are identical in size and shape - Skewness: histogram with a long tail extending to either right or left - Modal class: class with the largest # of observations - Unimodal histogram: one with a single peak - Bimodal histogram: one with two peaks; no necessarily equal in height; indicate 2 different distributions are present - Bell shape: special symmetric, unimodal histogram - Stem-and-Leaf display: method that overcomes loss of information contained in actual experiment  Similar to histogram on its side; length of each line represents frequency in class interval defined by stems; actual observations can be seen - Relative frequency distribution: divide frequencies by # of observations - Cumulative frequency distribution: shows the proportion of observations that lie below each of the class limits - Ogive: graphical representation of cumulative relative frequencies Describing time-series data - Classify data according to whether observations are measured at same tie or whether they represent measurements at successive points in time - The former classed cross-sectional data (observations at same point in time); the latter called time series data (observations taken over time) - Line chart: plot of the variable over time; graphically depicts time series data Describing relationship between 2 interval variables - Scatter plot used to describe relationship between two interval variables Patterns of Scatter Plots - Linearity: linear relationship if most points fall close to the line - Direction: positive and negative relationships (CORRELATION IS NOT CAUSATION) Graphical Deception - Graph without a scale - Do not be influenced by graphs caption - Change scale on y-axis to make It more dramatic (greater slope; numerically same); add a break; shrink the x-axis - Show stability by stretching the x-axis; spreading points to increase distance thereby slope becomes less steep - Bar graphs with width proportional to height exaggerates the data Chapter 4: Numerical Descriptive Techniques - Parameter is a descriptive measurement about a population Ways to describe center of set of data - Mean: average;
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