This study source was downloaded by 100000839564890 from CourseHero com on 06 10 2023 06 07 01 GMT 05 00 https www coursehero com file 172904216 ECON2271 Econometrics Lecture Notesdocx ECON2271 Econometrics Lecture NotesTypes of Data Data is categorised by the length and distinctiveness of the measurement scale1 Binary Categories 0 1 yes no2 Discrete Scale 0 1 2 3 only whole positive numbers 3 Continuous Scale can take any value Eg length of a piece of string4 Unlimited Scale is unbounded at either end5 Limited Scale scale is bounded at either or both ends Data is categorised by informational quality 1 Nominal ScaleoFor categorical dataoDoes not contain any information beyond distinctiveness such as order 2 Ordinal ScaleoFor ordered dataoContains information on distinctiveness and orderoDoes not contain information beyond order such as how much better higher each information is etc 3 Interval ScaleoContains information on distinctiveness order and also distance between values oEg temperatures in degrees calendar datesoLacks a non arbitrary definitive zero point means ratios have no meanings4 Ratio ScaleoFor fully cardinal dataoEg dollars measurements of length volume weight etc oContains information on distinctiveness order distance between values and distance from non arbitrary zero pointoData has complete informational quality meaning the ratios are meaningfulData Formats1 Cross sectional DataoA set of observations across units at a point in timeoEg GDP of a set of countries income of households in a suburboData has one dimension the unit of interest oCan observe variation across units2 Repeated Cross sectional DataoA set of observations across different units at different points in timeoEg marks for econs students across semestersoCan observe variation across units and compare characteristics of these data sets at different points in time This study source was downloaded by 100000839564890 from CourseHero com on 06 10 2023 06 07 01 GMT 05 00 https www coursehero com file 172904216 ECON2271 Econometrics Lecture Notesdocx 3 Time series DataoFollow the change of one unit across time oEg Australian GDPoData has one dimension time oObserve variation across time for a given unitoFrequencies of variation differ GDP quarterly cash rate set monthly etc 4 Panel DataoFollow a set of units across timeoData has two dimensions unit of observation and time oEg annual financial year incomes of a set of householdsData DistributionsProbability frequency Distributions Normal DistributionoA probability distribution maps the probabilities of observing particular random events which is ideally measured on a continuous scale between negative infinity and infinity but rarely case in real life Non normal distributionSampling Versus Populations A sample is a selection drawn from a population and we study the sample in order to make statistical inferences about the true nature of the population In general you need at least 30 observations to get results that are of any use The greater the sample size relative to the population size the more accurate will be thestatistical inferences The more representative a sample is of the general population the more accurate the statistical inferences will be If we are studying a population distribution we know all the data This study source was downloaded by 100000839564890 from CourseHero com on 06 10 2023 06 07 01 GMT 05 00 https www coursehero com file 172904216 ECON2271 Econometrics Lecture Notesdocx If we are studying a sample distribution we use statistical inference to provide the best possible guess about the population The sample mean and distribution hopefully reflect the population if the sample is sufficiently large and representative true random selection of the population As the sample size is larger and larger approaching the size of the population itself the sample mean will naturally approach the population mean Sample characteristics may or may not equal that of the true populationMeasures of Central TendencyMean The average observed value Sum of each observed value divided by the number of observationsMode The most frequently observed observationMedian The middle observation when all observations are ordered from lowest to highestMeasures of Dispersion Variation Minimum Maximum The smallest and largest observed valuesRange The difference between the largest and smallest observed valuesStandard Deviation The average distance away from the mean in the data The square root of the varianceStandard Deviation and the Probability Distribution 99 7 of observations lie within 3 standard deviations either side of the population mean 95 of observations lie within 2 standard deviations either side of the population mean 68 of observations lie within 1 standard deviation either side of the population mean This study source was downloaded by 100000839564890 from CourseHero com on 06 10 2023 06 07 01 GMT 05 00 https www coursehero com file 172904216 ECON2271 Econometrics Lecture Notesdocx Powered by TCPDF www tcpdf org Hypothesis Testing We can use samples to estimate tendencies and probabilities associations ie Relationship between factors and test hypothesis about populations Can articulate a null hypothesis H0 pattern observed due to randomness and test this against the alternative hypothesis H1 pattern observed not due to randomness oNull Hypothesis H0 mean1 mean2 oAlternative Hypothesis H1 mean1 mean2 We use sample means and standard deviations to evaluate the probability of being wrong in concluding the population mean is equal to a given value or different from a given value When comparing means we use standard error SE SE measures how far the sample mean of the data is likely to be from the true population means SE is always smaller than s Testing the sample mean If t value 1 96 for 95 then reject H0 If t value 1 96 for 95 then accept H0