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variables to see if there is a significant negative correlation between the two. If we do find this to be the case, then the hypotheses is substantiated. That is, giv- ing more training to pilots in handling crowded space in midair will reduce safety violations. If a significant negative correlation is not found, then the hypotheses would not have been substantiated. By convention in the social sciences, to call a relationship ―statistically significant,‖ we should be confident that 95 times out of 100 the observed relationship will hold true. There would be only a 5%
chance that the relationship would not be detected.
Statement of Hypotheses: Formats If–Then Statements
As already stated, a hypothesis is a testable statement of the relationship among variables. A hypothesis can also test whether there are differences between two groups (or among several groups) with respect to any variable or variables. To examine whether or not the conjectured relationships or differences exist, these hypotheses can be set either as propositions or in the form of if–then state- ments. The two formats can be seen in the following two examples.
Example 5.15 Employees who are more healthy will take sick leave less frequently.
Example 5.16 If employees are more healthy, then they will take sick leave less frequently.
Directional and Nondirectional Hypotheses
If, in stating the relationship between two variables or comparing two groups, terms such as positive, negative, more than, less than, and the like are used, then these hypotheses are directional because the direction of the relationship between the variables (positive/negative) is indicated, as in Example 5.17 below, or the nature of the difference between two groups on a variable (more than/less than) is postulated, as in example 5.18.
Example 5.17 The greater the stress experienced in the job, the lower the job satisfaction of employees.
Example 5.18 Women are more motivated than men.
On the other hand, nondirectional hypotheses are those that do postulate a relationship or difference, but offer no indication of the direction of these rela- tionships or differences. In other words, though it may be conjectured that there would be a significant relationship between two variables, we may not be able to say whether the relationship would be positive or negative, as in Example 5.19. Likewise, even if we can conjecture that there will be differences between two groups on a particular variable, we will not be able to say which group will be more and which less on that variable, as in Example 5.20.
HYPOTHESES DEVELOPMENT 105
Example 5.19 There is a relationship between age and job satisfaction.
Example 5.20 There is a difference between the work ethic values of American and Asian employees.
Nondirectional hypotheses are formulated either because the relationships or differences have never been previously explored and hence there is no basis for indicating the direction, or because there have been conflicting findings in previ- ous research studies on the variables. In some studies a positive relationship might have been found, while in others a negative relationship might have been traced. Hence, the current researcher might only be able to hypothesize that there would be a significant relationship, but the direction may not be clear. In such cases, the hypotheses could be stated nondirectionally. Note that in Example 5.19 there is no clue as to whether age and job satisfaction are positively or negatively correlated, and in Example 5.20 we do not know whether the work ethic values are stronger in Americans or in Asians. However, in Example 5.20, it would have been possible to state that age and job satisfaction are positively correlated, since previous research has indicated such a relationship. Whenever the direction of the relationship is known, it is better to develop directional hypotheses for reasons that will become clear in our discussions in a later chapter.
Null and Alternate Hypotheses
The null hypothesis is a proposition that states a definitive, exact relationship between two variables. That is, it states that the population correlation between two variables is equal to zero or that the difference in the means of two groups in the population is equal to zero (or some definite number). In general, the null statement is expressed as no (significant) relationship between two variables or no (significant) difference between two groups, as we will see in the various examples in this chapter. The alternate hypothesis, which is the opposite of the null, is a statement expressing a relationship between two variables or indicating differences between groups.
To explain it further, in setting up the null hypothesis, we are stating that there is no difference between what we might find in the population characteristics (i.e., the total group we are interested in knowing something about) and the sample we are studying (i.e., a limited number representative of the total population or group that we have chosen to study). Since we do not know the true state of affairs in the population, all we can do is to draw inferences based on what we find in our sample. What we imply through the null hypothesis is that any differ- ences found between two sample groups or any relationship found between two variables based on our sample is simply due to random sampling fluctuations and not due to any ―true‖ differences between the two population groups (say, men and women), or relationships between two variables (say, sales and profits). The null hypothesis is thus formulated so that it can be tested for possible rejection. If we reject the null hypothesis, then all permissible alternative hypotheses relating to the particular relationship tested could be supported. It is the theory that allows us to have faith in the alternative hypothesis that is generated in the particular
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research investigation. This is one more reason why the theoretical framework should be grounded on sound, defendable logic to start with. Otherwise, other researchers are likely to refute and postulate other defensible explanations through different alternative hypotheses.
The null hypothesis in respect of group differences stated in our Example 5.18 would be:
H 0: µM = µW or
H 0: µM – µW = 0
where H0 represents the null hypothesis, µM is the mean motivational level of the men, and µW is the mean motivational level of the women.
The alternate for the above example would statistically be set as follows:
HA: µM < µW
which is the same as
HA: µW > µM
where HA represents the alternate hypothesis and µM and µW are the mean moti- vation levels of men and women, respectively. For the nondirectional hypoth- esis of mean group differences in work ethic values in Example 5.20, the null hypothesis would be:
H 0: µAM = µAS
or
H 0: µAM – µAS = 0
where H0 represents the null hypothesis, µAM is the mean work ethic value of Americans and µAS is the mean work ethic value of Asians.
The alternate hypothesis for the above example would statistically be set as:
HA: µAM ≠ µAS
where HA represents the alternate hypothesis and µAM and µAS are the mean work ethic values of Americans and Asians, respectively.
The null hypothesis for the relationship between the two variables in Example 5.17 would be
H 0: There is no relationship between stress experienced on the job and the job satisfaction of employees.
This would be statistically expressed by H 0: ρ = 0
HYPOTHESES DEVELOPMENT 107 where ρ represents the correlation between stress and job satisfaction, which in this case is equal to 0 (i.e., no correlation).
The alternate hypotheses for the above null, which has been expressed direc- tionally in Example 5.17, can be statistically expressed as
HA: ρ < 0 (The correlation is negative.)
For Example 5.19, which has been stated nondirectionally, while the null hypoth- esis would be statistically expressed as:
H 0: ρ = 0 The alternate hypothesis would be expressed as:
HA: ρ ≠ 0
Having thus formulated the null and alternate hypotheses, the appropriate sta- tistical tests (t tests, F tests) can then be applied, which would indicate whether or not support has been found for the alternate—that is, that there is a signifi- cant difference between groups or that there is a significant relationship between variables as hypothesized.
The steps to be followed in hypothesis testing are:
1. State the null and the alternate hypotheses.
2. Choose the appropriate statistical test depending on whether the data col- lected are parametric or nonparametric (discussed in a later chapter).
3. Determine the level of significance desired (p = .05, or more, or less).
4. See if the output results from computer analysis indicate that the significance level is met. If, as in the case of Pearson correlation analysis in Excel software, the significance level is not indicated in the printout, look up the critical val- ues that define the regions of acceptance on the appropriate table [(t, F, χ2)—
see tables at the end of the book]. This critical value demarcates the region of rejection from that of acceptance of the null hypothesis.
5. When the resultant value is larger than the critical value, the null hypothesis is rejected, and the alternate accepted. If the calculated value is less than the critical value, the null is accepted and the alternate rejected.
Now do Exercises 5.12, 5.13, and 5.14
Exercise 5.12
For the theoretical framework developed for the Haines Company in Exer- cise 5.9, develop five different hypotheses.
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Exercise 5.13
A production manager is concerned about the low output levels of his employees. The articles that he read on job performance frequently mentioned four variables as important to job performance: skill required for the job, rewards, motivation, and satisfaction. In several of the articles it was also indicated that only if the rewards were valent (attractive) to the recipients did motivation, satisfaction, and job per- formance increase, not otherwise.
Given the above situation, do the following:
1. Define the problem.
2. Evolve a theoretical framework.
3. Develop at least six hypotheses.
Exercise 5.14
Retention of minority women at the workplace is becoming more and more difficult. Not finding an influential mentor in the system who is willing to help them, lack of an informal network with influential col- leagues, lack of role models, and the dearth of high-visibility projects result in dissatisfaction experienced at work and the minority women ultimately decide to leave the organization. Of course, not all minor- ity women quit the system. Only those who have the wherewithal (for example, resources and self-confidence) to start their own business leave the organization.
For the above situation, define the problem, develop a theoretical frame- work, and formulate six hypotheses.
Before concluding the discussion on hypotheses, it has to be reiterated that hypotheses generation and testing can be done both through deduction and induction. In deduction, the theoretical model is first developed, testable hypotheses are then formulated, data collected, and then the hypotheses are tested. In the inductive process, new hypotheses are formulated based on what is known from the data already collected, which are then tested. Recall from our discussions in Chapter 2, the example of the Hawthorne experiments, where new hypotheses were developed after the data already collected did not substantiate any of the original hypotheses.
In sum, new hypotheses not originally thought of or which have been pre- viously untested might be developed after data are collected. Creative insights might compel researchers to test a new hypothesis from existing data, which, if substantiated, would add new knowledge and help theory building. Through the enlargement of our understanding of the dynamics operating in different