Quantitative analysis involves the quantifying of data with the help of some form of statistical analysis. Quantitative analysis generally involves statistical techniques like significance testing, regression analysis, multivariate analysis, etc.
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Quantitative analysis is done by a researcher who has a strong knowledge of statistical and quantitative skills, in order to make a statistical inference about a particular sample of data drawn from a population. In other words, this type of analysis is applied in those cases, where one is trying to make a statistical inference about the population after selecting the sample which represents the population as a whole. Quantitative analysis is directly related to the statistical inference and data can be statistically inferred only after analysis of that data has been preformed.
Quantitative analysis can be broadly classified into two categories: Estimation and Test of hypothesis.
In quantitative analysis, estimation generally involves the ideal properties of an estimator, which is used to estimate the data. In quantitative analysis the ideal estimator is the one that is unbiased, efficient, consistent and sufficient.
The unbiased estimator is the one that gives unbiased results. In other words, one can say that an estimator in quantitative analysis is unbiased only if the mean of the sampling distribution of that statistic is equal to the parameter that is being estimated. So, while performing analysis, if an estimator gives a parameter along with some constant as an estimate, then that estimator is not unbiased. Similarly, if the estimator in quantitative analysis has other properties as well, then it is considered to be the best estimator.
In order to obtain a sufficient estimator, there is one criterion called the Fisher-Neyman Factorization theorem. This theorem in quantitative analysis provides a convenient characterization of the sufficient estimator.
The second category of quantitative analysis is the test of the hypothesis. A test of hypothesis generally involves testing of the null and the alternative hypothesis. Null hypothesis is the one that states that the two samples are statistically significant. On the other hand, the alternative hypothesis in quantitative analysis is the complement of the null hypothesis.
There are significant tests, like t-test, f-test, z-test, chi square test, etc. that are referred to as quantitative techniques in quantitative analysis. The researcher, while performing the Quantitative analysis, might commit errors. The errors in quantitative analysis are basically categorized into two categories, namely Type I error and Type II error.
Type I error is the one that involves the researcher rejecting a correct sample during quantitative analysis. On the other hand, Type II error is the one that involves the researcher accepting an incorrect or false sample.
In the field of medicine and nursing, committing a Type II error is extremely dangerous. According to the definition of Type II error in quantitative analysis, if the researcher accepts a defective drug, then it can pose a serious health hazard problem.
In the field of psychology, quantitative techniques of the statistically significant tests like the t-test, f-test, z-test, chi square test, etc. are used. Suppose one wants to compare the literacy rate in region A and region B. After conducting a primary research over a given sample drawn from the region, the quantitative analysis will be followed. For this case, quantitative analysis will be performed in the form of a right tailed t-test. This is called a right tailed test because in this case, the alternative hypothesis is LRA>LRB in quantitative analysis. A t-test statistic in quantitative analysis will be obtained and if the calculated value is more than the tabulated value at the given level of significance, then the null hypothesis will be rejected. Otherwise it will be accepted.