Quantitative Analysis
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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A researcher with strong knowledge of statistical and quantitative skills conducts quantitative analysis to make a statistical inference about a particular sample of data drawn from a population. In other words, this analysis applies when one tries to make a statistical inference about the population after selecting a sample that represents the whole population. Quantitative analysis directly relates to statistical inference, and one can statistically infer data only after performing the analysis.
Quantitative analysis can be broadly classified into two categories: Estimation and Test of hypothesis.
In quantitative analysis, researchers use an estimator to estimate the data, focusing on the ideal properties of the estimator. The ideal estimator is the one that is unbiased, efficient, consistent and sufficient.
The unbiased estimator is the one that gives unbiased results. Here, an estimator achieves unbiasedness when the mean of its sampling distribution equals the parameter it estimates. So, while performing analysis, if an estimator gives a parameter along with some constant as an estimate, then that estimator is not unbiased. Similarly, an estimator qualifies as the best when it possesses additional desirable properties.
To obtain a sufficient estimator, one must apply the Fisher-Neyman Factorization theorem. This theorem 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.
Significant tests like the t-test, F-test, Z-test, and chi-square test serve as quantitative techniques in quantitative analysis. The researcher, while performing the Quantitative analysis, might commit errors. Quantitative analysis categorizes errors into two types: 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, it will be followed. For this case, it uses a right-tailed t-test. This test gets its name because the alternative hypothesis states that LRA > LRB. It calculates a t-test statistic and compares it to the tabulated value at a given significance level. If the calculated value exceeds the tabulated value, it rejects the null hypothesis. Otherwise it will be accepted.