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University of New South Wales

ECON1203 NotesCHAPTER 1 What is StatisticsStatistics is a way to get information from dataDescriptive statistics deals with methods of organising summarising and presenting data in a convenient and informative way o eg using graphical techniques visual allows easier extraction of info or numerical techniques finding the mean o The measure of central location is a value that attempts to describe a set of data by identifying the central position within that set of data eg the mean median mode etc o The measure of variability is a mathematical determination of how much the performance of the data set as a whole deviates from the mean or median eg the range standard deviation interquartile range variance etcInferential statistics is a body of methods used to draw conclusions or inferences about characteristics of populations based on sample datait involves three key concepts the population the sample and the statistical inference o A population is the group of all items of interest to a statistics practitionerthe group can be unlimited in size and doesnt necessarily refer to a group of people eg 100000 on campusA parameter is a descriptive measure of a populationin most applications of inferential statistics the parameter represents the information we need eg mean number of soda drunk by the 100000 o A sample is a set of data drawn from the studied population eg 1000 of the 100000 are interviewedA statistic is a descriptive measure of a sample eg the average number of soda drunk by the 1000We can then use statistics to make inferences about parameters eg using the sample mean to infer the value of the population mean which is the parameter of interest o Statistical inference is the process of making an estimate prediction or decision about a population based on sample data Necessary because populations can be unlimited in size and thus investigation would be impracticable and expensiveIn order to ensure conclusions and estimate are as accurate as possible a measure of reliability is built into the statistical inferencetwo such measuresThe confidence level is the proportion of times than an estimating procedure will be correct eg an estimate of the amount of sodas consumed by all 100000 has a confidence level of 95 meaning estimates based on this form of statistical inference will be correct 95 of the timeThe significance level measures how frequently the conclusion will be wrong CHAPTER 2 GraphicalDescriptive Techniques IA variable is some characteristic of a population or sample eg the mark on an exam since not all students achieve the same mark ie they will vary 1 Usually represented with uppercase letters such as X Y and ZThe values of the variable are the possible observations of the variables eg an exam marked out of 100 will have values as the integers between 0 and 100Data are the observed values of a variable eg 58100 100100 etc 1 Data is plural for datumthe mark of one student is a datum 1 There are three types of data 1 Interval data are real numbers eg height weight income distance etcAlso referred to as quantitative or numerical or ratio dataAll calculations are permitteda set of interval data are usually described by calculating the average 2 Nominal data are categories eg responses to questions about marital statusThe values of this variable are singled married divorced and widowed not numbers but words that describe the categoriesNominal data is often recorded with arbitrary assignments of numbers to each category eg single1 married50 divorced48 etcAlso referred to as qualitative or categorical dataSince the values are appointed arbitrary numbers calculations for nominal data using the numbers are meaninglessOnly calculations allowed involve counting or calculating the percentages of the occurrences of each category and reporting the frequency 3 Ordinal data is similar to nominal in appearance but the difference is that the order of the values for ordinal types of data indicate a higher rating thus when assigning codes to the values the order must be maintained eg poor1fair2 good3 very good4 excellent5Magnitude of values arent important only the order is ie poor1 fair50 good51 very good100 excellent6310 implies the same meaning as the previous exampleThe only permissible calculations are those involving a ranking process eg placing all the data in order and selecting the value that lies in the middle the medianCritical difference between ordinal and interval data is that the intervals between values of interval data are consistent and meaningfulThe data types can be placed in order of the permissible calculations 1 Interval dataall calculations are allowed 2 Ordinal data 3 Nominal datano calculations other than determining frequencies are permittedHigherlevel data types may be treated as lowerlevel ones the viceversa is not possible eg in UNSW marks interval data are converted to letter grades ordinal o This leads to loss of information eg a 83 provides more information than a D since D implies a mark between 7085The variables whose observations constitute our data will be given the same name as the type of data eg interval data are the observations of an interval variableFor nominal data the only allowable calculation is to count the frequency or compute the percentage each value of the variable represents o This data can be summarised in a table presenting the categories and their counts called a frequency distribution o A relative frequency distribution lists the categories and the proportion with which each occursgraphical techniques are commonly used to depict a picture of the dataBar chart and the pie chartused because they are eyecatching and enhance individuals ability to grasp the substance of the dataA bar chart is often used to display frequencies 2 A pie chart graphically shows relative frequencies percentagesFor ordinal data there are no specific graphical techniquesto describe a set of ordinal data theyre treated as if they were nominal o The difference is thatIn bar charts the bars should be arranged in ascending or descending ordinal valuesIn pie charts the wedges are arranged clockwise in ascending or descending orderTechniques applied to single sets of data are called univariateWhen depicting the relationship between variables bivariate methods are requiredA crossclassification table also referred as a crosstabulation table is used to describe the relationship between two nominal variables o A variation of the bar chart is employed to graphically describe the relationshipthe same technique is used to compare two or more sets of nominal dataTo describe the relationship between two nominal variables only the frequency of the values can be determined since its nominaltherefore a crossclassification table that lists the frequency of each combination of the values of the two variables needs to be producedIf the two variables are unrelated then the patterns exhibited in the bar charts should be approximately the sameif some relationships exist then some bar charts will differ from others CHAPTER 3 Graphical Descriptive Techniques IIFor interval data the most common graphical method is the histogram o A histogram is created by drawing rectangles whose bases are the intervals and whose heights are the frequenciesthe frequency distributions provides information about how the numbers are distributedA frequency distribution for interval data is created by counting the number of observations that fall into each of a series of intervals calledclasses that cover the complete range of observationsThe number of class intervals selected depend on the number of observations in the data setthe more observations the larger the number of intervals to enable a useful histogramSturges formula which recommends that the number of class intervals be determined by the following Number of class intervals 133logn where n is the number of observations eg if theres 50 observations number of class intervals133log501331766 which is rounded to 7The width of the class intervals is determined by the formula class largest observationsmallest observation119630width eg numer of classes81495 which is rounded up to 15 thus the first class is defined as Greater than or equal to 0 but less than or equal to 15Sturges formula acts a guideline onlyits more important to choose classes that are easy to interpret eg marks of an exam out of 100 where the highest is 94 and the lowest is 48 would lead to 8 class 3
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