1 …continued… Part III. Performing the Research 3 Initial Research 4Research Approaches 5 Hypotheses 6 Data Collection 7 Data Analysis

2 5 Hypotheses A hypothesis is an assertion, made about a problem, to be tested : the testing of the hypothesis will, hopefully, help corroborate or refute it the key word, however, is to “test” the hypothesis – we cannot really prove or disprove a hypothesis.

3 Remember, a hypothesis is not appropriate for all research: for projects where there is minimal theory and understanding of the area, a hypothesis will be difficult to formulate in such cases, you should not try to force the issue, otherwise you may end up testing something of little significance Also, remember, depending on the project, the hypothesis may result at: a very early stage in the research (for well defined subjects), in the middle of the research, as the result of a preliminary research (for less well defined subjects), or it may be the end product of the research (to be tested by someone else)

4 A hypothesis may be hard, that is, we are certain about what it is we want to test. Alternatively, a hypothesis may be soft, that is, we are willing to revise it as we progress with the research. The choice of hard, soft, (or somewhere between), should depend on how well we understand the problem area: hard hypotheses are generally best used for well defined problems, but they do not cater for unexpected results; soft hypothesis are best for poorly defined problems, but be careful in that this strategy can lead to shallow, meandering research.

5 There are three requirements for a hypothesis: it should be testable – so that it may be supported or refuted; it should be positive – concerning what is, not what ought to be or some other ideal; and it should be expressed in simple and clear language – so that it means the same thing to everyone.

6 Usually, testing of a hypothesis requires sampling from a population (see the section on experimental design for details): consequently it involves the use of statistical techniques a good reference for statistical testing of hypotheses is: –Hoel, P. G.; Port, S. C.; and Stone, C. J. "Testing Hypotheses." Ch. 3 in Introduction to Statistical Theory. New York: Houghton Mifflin, pp , 1971

7 –Consider hypothesis testing for a population mean. –For example, we may suspect graduates with master’s degrees do NOT earn the same on average as graduates with bachelor’s degrees, when taking-up employment as a project engineer: we know that the average salary of all new project engineers is $77k per year; the null hypothesis would be: H 0 : μ = $77k here, we are considering the chances that masters graduates, on average, earn the same as the entire population of new project engineers – if it is rejected, then we may assume the alternate hypothesis

8 the alternate hypothesis may take on one of three forms: H 1 : μ > $77k (right tailed test) here, we are considering the chances that masters graduates, on average, earn more than the entire population of new project engineers H 1 : μ < $77k (left tailed test) here, we are considering the chances that masters graduates, on average, earn less than the entire population of new project engineers H 1 : μ ≠ $77k (two tailed test) here, we are considering the chances that masters graduates do not, on average, earn the same as the entire population of new project engineers probability density z value eg: 2.5% of area under curve (right tail) z-value = 1.96

9 lets say we suspect that the masters salaries are higher: H 1 : μ > $77k now, we sample at random 50 masters graduates and find: – SM (sample mean) = $79k – SSD (sample standard deviation) = $5k – therefore the z-value is: z = (79-77) / (5 / √50) = 2.83 therefore p is almost = 99.77% this indicates that the probability of getting $79k or more due to sampling error is 100%-99.77% = 0.33% this is not very likely, so it is likely that something else is causing the difference,.. the masters students may actually be paid more on average! this indicates that the null hypothesis (H 0 : μ = $77k) is false and so we may accept the alternate hypothesis (H 0 : μ > $77k) that masters graduates start at a higher salary

10 however, we should first determine what is an acceptable level of significance: this depends on the problem, but lets say it is 2.5% for the right tail (ie: p <= 2.5% ) then we can formally reject the null hypothesis and conclude that the students earn more. What would we conclude if sampled data had indicated a probability of getting a salary of $79k or more was 4.3%, and the level of significance for the right tail was 2.5%? –we would NOT conclude that the null hypothesis was correct, but rather that there was not enough evidence to reject it –and therefore there was not enough evidence to support the alternative hypothesis In summary: –small p rejects the null hypothesis –large p fails to reject the null hypothesis