Statistics in the present times is a subject that has lots of takers in different fields. Knowledge of statistics is used for taking important decisions in companies and how things should run. It is also used for predicting the future course that is taken by people for betterment. With the help of time series analysis, for example, one can make predictions in fields of econometrics as well as weather forecasting. Hence the usage associated with statistics is really vast. There are certain parts of statistics which students might find a little difficult to handle. These aspects will be discussed in details here.
Time Series Analysis
Tools associated with time series analysis, is used by different statisticians to draw certain conclusions and take up strategies according to it. Some methods, by which time series is studied, include linearity, parametric-non parametric method as well as univariate or multivariate analysis. Going by the parametric methods, a basic stationary process is initiated and depicted by use of few parameters. In non-parametric methodology, covariance associated with a procedure gets appraised without putting any structure to such procedures.
Why analysis is done?
The tool associated with time series analysis is a favorite among statisticians and other strategic managers. Using such analysis, future course of action taken by a company gets decided. A link is established between different past and future activities. A pattern gets emerged soon and that helps in studying. Different requirements are met properly by use of this analysis type. You have to ensure that a pattern exists between past and future before starting off with this kind of analysis. It is checked here whether constant variance in data is taking place.
Applications of Analysis
Descriptive analysis is used for determining trends or patterns in time series. All trends as well as changes in the cycle are observed, making analysis quite easy. When spectral analysis is done, a different periodic component in series gets separated. Business changes are therefore studied with the help of this. Various upcoming possibilities are forecasted and thus losses are prevented to a great extent. This tool is widely used in businesses and students always get these cases as a part of their assignments. By intervention analysis, it is determined whether occurrence of a particular event may lead to changes in a particular series. If explanative analysis is done, then relationship between two-time series’ gets established. Weak and strong areas of businesses are identified in this manner.
There are numerous ways in which correlation can be calculated. In graphical methods, pictorials are used for calculations; there are scatter diagrams as well as simple graphs. In mathematical methods, you have correlation methods of Pearson, Spearman as well as concurrent deviation method.
Using graphical method
Picture diagrams are used for checking out correlation here. Linear relationship is not maintained here, but it is easier to get a clear picture. Variables are seen to get plotted on graphs by use of scatter diagrams. Relationships existing among variables are not properly established here. Different data points are plotted on the rectangular axis. If a positive correlation happens, then points are observed to move from upper left to lower right. If points are too much scattered, then there is no clear relationship between variables.
Calculating Pearson’s coefficient
Students are usually given problems based on Pearson’s coefficient in their assignments. It is considered to be one of the best methods for correlating linear variables. It has mostly been deemed to be a ration of covariance between two variables and product of standard deviation between two variables. Similarly, Spearman’s coefficient of rank is used for getting comparing a pair of variables.
Properties that students must know
Students have to realize that correlation does not have any unit of measurement. Relation existing between two variables is expressed with its help. This relationship is without units or any other measurement. Degree of existing variation is made very clear by correlation. This coefficient of correlation is not seen to fluctuate with change in scale. Correlation values always stay within the range of 1 and -1. Values will not go outside this range, no matter what.
There are many direct applications associated with correlation. Students must know about all of them, because in real life, these methods will be used for different works of firms. Correlation is used for drawing relations that help in assessment of variables and predict about data that follows suit. With application of correlation, it becomes possible to know whether a given set of data is reliable in nature or not. Even different reliability tests are performed for this. Proofs to different theories are determined by use of correlation.
It helps researchers to investigate about different matters by use of correlation method. One is able to analyze data and pinpoint those areas where fluctuations are seen to occur. Relationship between data and its reliability gets tested by correlation, after which a researcher can go back to his works.
Dealing with econometrics
The very name of econometrics can usher in sleepless nights for lots of students. With use of this discipline, some form of practical content is provided to different economic relationships. Many researchers have defined this as application of mathematics and statistics into data obtained from economics. Everything is done for purpose of testing out hypotheses and forecasting trends for future. Analysis of actual economy takes place here, different theories and observations are consequently obtained. For example, if price of a product is reduced, then how its increase in demand will be.
Some definitions for students
In econometrics, quantitative analysis of different economic phenomenon based on simultaneous development of theory as well as observation takes place. Here you will find application of various statistical as well as mathematical methods in economics to test out different economic theories as well as find solutions to economic problems. Different mathematical models are setup in econometrics which describes various economic relationships. Validity of these hypotheses is checked out using econometrics. Consequently, influences of certain factors on various independent variables are also obtained. For example, it is found whether quantity of a good is positively or negatively dependent on price. One assumption that you need to make here, is that, the model you are using is correct.
Econometrics application for students
Everything about econometrics is based upon development of different statistical methods for finding out economic relationships. Mostly economic theories are tested out by using econometrics and then different government policies are evaluated for implementation. Students will get assignments related to some really important macroeconomic topics such as forecasting of GDP, inflation rates as well as interest rates. These forecasts are done quite commonly and are also published in different mediums. However, application of econometrics is also found in areas that have got nothing to do with forecasting. Examples include study of various political campaigns and how those expenditures are related to outcome of voting. Other than this, econometric is also used for forecast of different economic time series.
Students may be required to build economic models that contain mathematical equations. These equations, describe different relationships. Using these economic modeling is often considered the starting point of empirical analysis itself. It is also quite common to make use of this theory by not strictly adhering to conventions but also relying on intuition. For analysis, a model is firstly specified for use. After this, data is obtained and estimation of different parameters of economic models is done. Following this, hypothesis testing as well as forecasting is done. Finally, the econometric model is tested and then made ready to use for different policies.
Different from mathematical statistics
In econometrics, you will find intersection of different disciplines such as statistics, mathematics and economics. Empirical content is added to economic theories here and therefore these theories get ready for testing and eventually used for making forecasts. It has emerged as a discipline distinct from mathematical statistics, because it focuses solely on problems related to collection and analysis of non-experimental data. If econometric models are not specified properly, then a correlation emerges between two variables.
By statistical inference, characteristics of a population or a group of data, gets generalized by working with a sample data. Estimation is a process by which a person will be able to make statistical inferences about characteristics of a population. This done by using information obtained from one sample. In statistics, population refers to a collection of objects that get selected for conducting studies. Sample is referred to as a subset of a population. Parameters are numerical characteristics associated with a population that can be measured. Population based parameters are mostly unknown but are seen to be fixed constants. Estimation of population is given according to sample statistics.
It is known that value of population parameter is unknown. Sampling statistic can be inferred from a sample in an easy manner. You need to understand that population parameter can also be prone to errors. You require studying the entire population, to get exact values associated with parameters. These tasks are difficult for students to complete on their own; therefore they require taking help of online tutors and complete assignments. This particular value would be varying from one sample to another. In estimation, a formula is used for doing calculations related to certain population parameters.
In point estimate, a single value is provided as estimate associated with a one population parameter. An example of this would be sample mean. Sample standard deviation is used for getting point estimate of standard deviation related to the entire population. You can also find confidence interval estimate, where you find two numbers between which a particular population parameter lies. Probability of an interval estimate is also known as confidence interval. Confidence interval gets calculated by getting hold of confidence level. Students must know that interval estimates are always preferred over point estimates. This is because, width associated with a confidence interval tells you about accuracy of an estimate. It is observed that high confidence levels show narrow sized confidence interval.
Properties of good estimators
Good estimators are always unbiased in nature. An unbiased estimator is observed when expected value of estimator is equal to that parameter which gets estimated. An estimator is said to be consistent in nature if it goes towards population parameter as sample size gets slowly increased. When sample size tends towards infinity, then estimator will produce estimates that have small sized standard errors. If an estimator is seen to converge with population parameter, then also it is said to be consistent in nature.
By efficiency, variability of a sample becomes known. All unbiased estimators are said to be well efficient in nature. You will observe that it usually has the smallest value of standard error among other estimates of population parameter. Estimators therefore need to have minimum variance and also be unbiased in nature.
By sampling distribution, probability distribution of a given statistic gets known. It is based completely on a random sample. These distributions are very significant in statistics. In this way, statistical inference gets very simplified. If a sampling distribution is known from beforehand, then ability of sampling statistic for estimating population parameter gets ascertained easily.
Students are usually seen to face problems while dealing with descriptive and inferential statistics. Here you are required to collect as well as present data. It is one of the first steps of evaluation of data. A set of graphical data is defined and described out here. In inferential statistics, correct result of any statistical operation is deduced. While solving problems students may come across odd values of percentages, may require doing some manipulation of value and data. Al these things can be done properly with help of online tutors for completing assignments.
John Colby is a name quite popular among student circles these days. He is a savior for all those, struggling with statistics assignment. He has got his degree from Imperial College in London. He has been associated with online teaching for more than three years and loves to interact with students. He is a very good teacher of multiple disciplines of statistics, such as inferential and descriptive statistics.