what is quantitative techniques: The techniques discussed in this section are classical statistical methods as opposed to EDA techniques. EDA and classical techniques are not mutually exclusive and can be used in a complementary fashion. For example, the analysis can start with some simple graphical techniques such as the 4-plot followed by the classical confirmatory methods discussed herein to provide more rigorous statements about the conclusions. If the classical methods yield different conclusions than the graphical analysis, then some effort should be invested to explain why. Often this is an indication that some of the assumptions of the classical techniques are violated.
quantitative techniques:
Many of the quantitative techniques fall into two broad categories:
1. Interval estimation
2. Hypothesis tests
1. Interval Estimates
It is common in statistics to estimate a parameter from a sample of data. The value of the parameter using all of the possible data, not just the sample data, is called the population parameter or true value of the parameter. An estimate of the true parameter value is made using the sample data. This is called a point estimate or a sample estimate.
For example, the most commonly used measure of location is the mean. The population, or true, mean is the sum of all the members of the given population divided by the number of members in the population. As it is typically impractical to measure every member of the population, a random sample is drawn from the population. The sample mean is calculated by summing the values in the sample and dividing by the number of values in the sample. This sample mean is then used as the point estimate of the population mean.
Interval estimates expand on point estimates by incorporating the uncertainty of the point estimate. In the example for the mean above, different samples from the same population will generate different values for the sample mean. An interval estimate quantifies this uncertainty in the sample estimate by computing lower and upper values of an interval which will, with a given level of confidence (i.e., probability), contain the population parameter.
2. Hypothesis Tests
Hypothesis tests also address the uncertainty of the sample estimate. However, instead of providing an interval, a hypothesis test attempts to refute a specific claim about a population parameter based on the sample data. For example, the hypothesis might be one of the following:
• the population mean is equal to 10
• the population standard deviation is equal to 5
• the means from two populations are equal
• the standard deviations from 5 populations are equal
To reject a hypothesis is to conclude that it is false. However, to accept a hypothesis does not mean that it is true, only that we do not have evidence to believe otherwise. Thus hypothesis tests are usually stated in terms of both a condition that is doubted (null hypothesis) and a condition that is believed (alternative hypothesis).
A common format for a hypothesis test is:
H0: A statement of the null hypothesis, e.g., two population means are equal.
Ha: A statement of the alternative hypothesis, e.g., two population means are not equal.
Test Statistic: The test statistic is based on the specific hypothesis test.
Significance Level: The significance level, , defines the sensitivity of the test. A value of = 0.05 means that we inadvertently reject the null hypothesis 5% of the time when it is in fact true. This is also called the type I error. The choice of is somewhat arbitrary, although in practice values of 0.1, 0.05, and 0.01 are commonly used.
The probability of rejecting the null hypothesis when it is in fact false is called the power of the test and is denoted by 1 - . Its complement, the probability of accepting the null hypothesis when the alternative hypothesis is, in fact, true (type II error), is called and can only be computed for a specific alternative hypothesis.
Critical Region:
The critical region encompasses those values of the test statistic that lead to a rejection of the null hypothesis. Based on the distribution of the test statistic and the significance level, a cut-off value for the test statistic is computed. Values either above or below or both (depending on the direction of the test) this cut-off define the critical region. Answer 2.Quantitative techniques attempts to provide a systematic & rational approach to the fundamental problems involved in the control of system by making decisions, a sense achieve the best results considering all the information that can be profitably used. Thus it is scientific method employed for problem solving & decision making by the management. Quantitative analysis is now extended & several alias of business operation & responsibilities probably the most effective approach to handling of some types of decision problems. A significant benefit of attaining some degree of profiency with quantitative methods is exhibited in the way problems are formulated. A problem has to well defined before it can be formulated in a well structure framework for solution. The 2 different divisions of quantitative techniques are:-
1) Business statistics
2) Operative Research
BUSINESS STATISTICS Statistical data & statistical method are of immense helping the proper understanding of the economic problem & in the formulations of economic policies as well as evaluating of their effect for example in order to check the overgrowing population, if emphasis has been placed on family planning methods one can ascertain statistically the efficiency of such methods in attaining the desired goals.
OPERATION RESEARCH It is the application of scientific methods, technique & tools to problems involving the operation of system. So as to provide these in control of operation & optimum solution to the problem.
The modus of operandi of each are:-
1. formulate the problem
2. analyse the data & collection of data
3. analyse the data
a. central tendency
i) mean
ii) median
iii) mode b. Dispersion
i) Standard deviation
ii) Mean deviation
iii) Skewness
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WHAT IS QUANTITATIVE TECHNIQUE
