The Logic of Hypothesis Testing
Abstract
This case study will aim to provide a through description of hypothesis, hypothesis testing, and the logic behind the hypothesis testing. In addition an attempt will be made to analyze the steps to hypothesis testing and evaluate: when (in what situation) it will be appropriate to implement a specific test.
1. The Logic of Hypothesis Testing
Cooper & Schindler (2008) firmly emphasis the importance of recollecting the fact that difference among induction and deduction is fundamental in the process of testing hypothesis (p. 468). The accuracy of the hypothesis is evaluated by determining the statistical like hood that the data reveal true differences- not random sampling error. From the two approaches to hypothesis testing: {a). classical statistics, b).Bayesian statistics} the more established one seems to be the classical /sampling approach where he hypothesis are accepted or rejected on the bases of sampling information alone (Cooper & Schindler, 2008, p. 468).
There are two hypotheses used in classical test of significance:
1. Null hypothesis, 2. Alternative hypothesis
Null hypothesis (H0)
Null hypothesis (H0) states that there is no difference between the parameter and the statistic being compared to it. The evidence demonstrate that Null hypothesis cannot be tested definitively (findings that are consistent with null hypothesis might be consistent with other hypothesis too, so they do not demonstrate the truth of the given hypothesis) (Cooper & Schindler, 2008, p. 470).
Example (H0)
Situation: the management would like to evaluate the satisfaction level of tenants .Last year company used a survey and asked 200 tenants if they are content with their apartments’ condition 105 tenants were happy and 95 tenants were Not happy
Null hypothesis (H0): There has been no change on the level of satisfaction
Alternative hypothesis (HA)
The alternative hypothesis (HA) {also called experimental/ research hypothesis Elsevier’s Dictionary of Psychological theories, 2006)} is seen as the logical opposite of the null hypotheses. Consequently, while the research hypothesis/alternative hypothesis claims the existence of a relationship between variables is due to an actual relationship between the variables, the null hypothesis says that any relationship which may seem to exist is purely the result of sampling error and not because of a true relationship (The world of sociology, 2001). The alternative hypothesis (HA) may take a number of forms which will depend on the objective of the researchers (for instance: the alternative hypothesis (HA) maybe presented in form of: “not the same”, “greater than”, “less than” (Cooper & Schindler, 2008, p. 470)..
Example (HA)
Using the tenants instance as depicted above:
The alternative hypothesis (HA):
*The level of tenants’ satisfaction has changed
*The level of tenants’ satisfaction has increased
*The level of tenants’ satisfaction has decreased
Steps followed in Hypothesis Testing
First step (state the null hypothesis)
First step in hypothesis testing involves: specifying the null hypothesis (H0) and the alternative hypothesis (HA). Generally the researcher’s concerns is whether one method leads to better recognition than another, therefore the null hypothesis would most likely be that there is no difference between methods (H0: μ1 - μ2 = 0). On the other hand, the alternative hypothesis would be HA: μ1 ≠ μ2 (Cooper & Schindler, 2008, p. 477).
Second step (choose the statistical test)
Second step in hypothesis testing involves: choosing the appropriate statistical test, since there are many tests to choose from (Cooper & Schindler, 2008, p. 477).
Third step (select the desired level of significance)
Third step in hypothesis testing involves: choosing a preferred significance level and the choice must be made before the data is collected. Typically the 0.05 is the most commonly used followed by the 0.01 level. The level is mostly determined by the amount of risk the researcher is willing to take (Cooper & Schindler, 2008, p. 477).
Forth step (compute the calculated difference values)
Forth step in hypothesis testing involves: calculating the probability value (the possibility of obtaining a statistic as different as the statistics calculated from data collected (Cooper & Schindler, 2008, p. 477).
Fifth step (obtain the critical test value)
Fifth step in hypothesis testing involves: looking up the critical value in the appropriate tables for that distribution in order to define the region of rejection and /or the region of acceptance (Cooper & Schindler, 2008, p. 478).
Sixth step (interpret the test)
Sixth and last step in hypothesis testing involves: interpreting the test. If the calculated value is larger than the critical value, than the null hypothesis is rejected, and conclude that the alternative hypothesis (HA) is supported. But, if the critical value is larger we conclude we have failed to reject the null (Cooper & Schindler, 2008, p. 478).
Two – tailed tests/ non- directional test
During a two-tailed test, no matter what the direction of the relationship is , the possibility of the relationship in both directions is what interests the researcher. Bruin, (2006) illustrates the two tailed tests with the example depicted below:
“Researcher wants to compare the mean of a sample to a given value x by using a t-test. The null hypothesis is that the mean is equal to x. A two-tailed test will test both if the mean is significantly greater than x and if the mean significantly less than x. The mean is considered significantly different from x if the test statistic is in the top 2.5% or bottom 2.5% of its probability distribution, resulting in a p-value less than 0.05.”
One – tailed tests/ directional test
Throughout a one-tailed test, the possibility of the relationship in one direction is been tested, completely disregarding the possibility of a relationship in the other direction.
Bruin, (2006) illustrates the two tailed tests with the example depicted below:
“Let's return to our example comparing the mean of a sample to a given value x using a t-test. Our null hypothesis is that the mean is equal to x. A one-tailed test will test either if the mean is significantly greater than x or if the mean is significantly less than x, but not both. Then, depending on the chosen tail, the mean is significantly greater than or less than x if the test statistic is in the top 5% of its probability distribution or bottom 5% of its probability distribution, resulting in a p-value less than 0.05.”
Conclusion
Concluding this case study is extremely significant to be emphasized the imperative role of hypothesis and hypothesis testing process in business research field. Furthermore is similarly imperative to obtain knowledge on hypothesis and their testing process as well as in appropriateness of their application.
References
Cooper, R. D., & Schindler, S. P. (2008). Business Research Methods.
(10th Edition) New York: McGray-Hill/Irwin.
Bruin, J. (2006). Command to compute new test. Academic Technology Services,
Statistical Consulting Group. Retreived June 16, 2010, from:
(N.D.). (2006). Null Hypothesis. Elsevier’s Dictionary of Psychological theories.
Retrieved via LIRN/Gale.
(N.D.). (2001). Null Hypothesis. World of Sociology,
Retrieved via LIRN/Gale
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