Business Statistics
The null hypothesis is important and continues to be used widely due to several reasons. First of all the null hypothesis is carried out in the context of a simple decision rule. The tests give a dichotomous outcome. Even though there are criticisms against the method, it enables scholars to progress in their theory testing. At the end of the day it gives a binary decision on whether two variables are related (Luce, McGill, & Peracchio, 2005).
There are several limitations of the hypothesis testing that scholars and experts have highlighted. First of all when the results reject the alternative hypothesis then it is assumed that the tests support the null hypothesis which may not be the case. It could be that there is no sufficient evidence against the null hypothesis or the sample size is too small. The hypothesis test results secondly do not give any information on the probabilities of the null or alternative hypothesis. These probabilities are known as significance levels.
There is a relationship between hypothesis testing and confidence levels. If one constructs a 95% confidence level, values within are considered to be possible values of the parameter being estimated however values outside the confidence level are rejected. In the null hypothesis, if the value of the parameter specified falls within the confidence level the null hypothesis is accepted. If it falls without it is rejected. However there are certain differences between the two methods. In hypothesis testing, tests are based on the assumptions on the null hypothesis while confidence levels are given based on the observed value.
Tests are usually carried out on dependent and independent samples. Independent samples refer to the samples obtained from the same population or different populations but they
have no effect on each other. Tests that can be carried out on independent samples are where one sample group acts as the treatment group while the other acts as a control group. Dependent or matched samples refer to where the same test is done twice on the samples after a treatment. For example athletes have their blood pressure measured before and after taking medication that addresses blood pressure.
A two sample hypothesis testing is done where the individual wants to compare the mean between two populations. The researcher may want to know whether there is a difference between the average salary of the female and male doctors in the New York City. Another test may be to know how the mean number of defective parts released by assembly plant O compares to the mean of defective parts that are released by assembly plant Q. One sample hypothesis test on the other hand is conducted when tests are only being carried out in one population. There is a specified mean value and the researcher gets the mean salary of the male doctors in New York to compare with the specified value.
Non-parametric tests are used to analyze populations that take on a ranked order for example movie rankings in the cinema. The tests are important for measuring data that has no numerical properties such as preferences. They are widely used as they have fewer assumptions so the tests are robust. Secondly the tests are simple for the researcher to use.
Variance is an important measure as it helps a researcher draw conclusions on how one or two independent variables affect the dependent variable. It helps tests whether two group means differ from each other thus supporting the null hypothesis. It also assists in calculating the probability of a type 1 error if the Null hypothesis is rejected (Sawyer, 2009)
References:
Luce, M., McGill, A. & Peracchio, L. (2005). On P-values. Journal of Consumer
Research, 32 (1). Retrieved from: http://ejcr.org/p-values.htm
Sawyer, S. (2009). Analysis of Variance: The Fundamental Concepts
The Journal of Manual & Manipulative Therapy, 17(2), 27-38.
