Lab 12

Hypothesis testing

    Hypothesis testing - the big picture view (more details will follow in future labs)

    Hypothesis testing is an inferential procedure that uses sample data to evaluate the credibility of a hypothesis about a population.

    Step 1: Develop a hypothesis  - A hypothesis is a prediction based on a theory about the effect of something on something else.

    Example
    Theory: Fear is an emotion designed to motivate us to avoid danger and focus on survival goals.
    Hypothesis: Inducing college students to think about their own mortality will cause them, temporarily at least, to be more favorably disposed to careers that guarantee a moderate, steady income but may be less intrinsically interesting than to careers that are higher paying and more interesting but involve high risk of failure.

    Part of developing a hypothesis is to state what is likely to happen if one's hypothesis is not true. That is, in order for a hypothesis to be considered scientific, it must be falsifiable . Falsifiable does not mean "false." It means "capable of being proved false." That is, we have to be able to imagine conditions that, if observed, would lead us to believe that our hypothesis is wrong. In the case of the example, we would have less confidence in the theory if we observed no change in career preferences after thinking about one's mortality. A condition that, if observed, would lead us to have less confidence in our theory, is called a null hypothesis. A null hypothesis is usually the opposite of our actual hypothesis, called the alternative hypothesis.

    Step 2: Design and run a study that tests the hypothesis.

    In the example above, one experiment that might test the hypothesis would be to randomly select individuals from the college student population

    The participants would be randomly assigned to one of two groups:
     
    1) One group would be asked to imagine all the things they could do to live a long, healthy life. This task would indirectly induce the students to think of ways in which their lives might end prematurely.
    2) One group would be asked to imagine all the things they could do to accomplish an important long-term goal.

    Afterward, the students from both groups would be asked to rate their interest in various careers considered to be either safe but dull or exciting but risky.
     

    Step 3: Compute a test statistic

    There are many different kinds of test statistics but all of them are designed to tell you how likely it is for your data to come out the way they did if the null hypothesis is true. 

    Step 4: Draw a conclusion

    If the test statistic says that your data are reasonably likely to occur if the null hypothesis is true, then the null hypothesis is retained. Remember, the null hypothesis is the opposite of what you, the researcher, hope to prove. Retaining the null hypothesis, although necessary to do when the data indicate it, is a sad thing for the researcher. On the other hand, if the test statistic says that your data are highly unlikely to occur if the null hypothesis is true, the null hypothesis is rejected. This is what the research hopes will happen. Notice, however, that rejecting the null hypothesis does not mean that the alternative hypothesis is true. In fact, the alternative is never directly tested. In science we rarely "prove" any hypothesis to be true. We merely try to cast doubt on or eliminate competing hypothesis until our confidence in our own hypotheses increases. Rejecting the null hypothesis merely means that the data are "consistent with" the alternative hypothesis or that the data "support" the alternative hypothesis. However, there might be a wide variety of other hypotheses that also could explain the phenomenon better than your particular alternative hypothesis. Thus, it is proper to be tentative in discussing whether the hypothesis is true or false.

    In this lab, we will focus just on stating hypotheses well. Let's review and then elaborate on what is meant by the null and alternative hypotheses.

    The standard logic that underlies hypothesis testing is that there are always (at least) two hypotheses: the null hypothesis and the alternative hypothesis

    The null hypothesis (H0) predicts that a particular variable has no effect on some dependent variable.

    The alternative hypothesis (H1) predicts that the variable will have an effect on the dependent variable.

    The hypothesis testing procedure assumes we are trying to reject the null hypothesis, not trying to prove the alternative hypothesis.

    Why? Generally, it is easier to show that something isn't true, than to prove that it is. This is especially true when we are dealing with samples. Remember that we aren't testing every individual in the population, only a subset.

    Think about it this way. Suppose we had a hypothesis that all dogs have 4 legs. To reject this hypothesis, we'd need to have a sample that includes 1 or more dogs with more or fewer than 4 legs. To accept it, we'd need to examine every dog in the population and count its legs. It's much easier to find a sample that suggests that a hypothesis is wrong than it is to test the whole population to show that the hypothesis is correct.

    Example 1: Suppose that we know that the approval rating of a presidential candidate is 30% among registered voters. We want to try to increase that number with an ad campaign. So we conduct the ad campaign before the election and then measure the approval rating of the candidate in a sample of registered voters.

    What will our hypotheses be in this case? We state our hypotheses like this:
    H0: The ad campaign has no effect on the candidate's approval rating. The population from which the new sample was selected has a mean of μ = 30%.
    H1: The ad campaign had an effect on the candidate's approval rating. The population from which the new sample was selected has a mean of μ ≠ 30%.

    Alternatively, we could make a specific alternative hypothesis if we chose. This would change our H0 too. Let's consider the specific case above where we expect that the ad campaign will INCREASE voters. This means that we expect higher voting rates for our sample than is in the population (30%). Here our H1 is that m > 30%. That means that our H0 is m <= 30%.

    Example 2: Suppose that on a questionnaire measuring symptoms of posttraumatic stress, most soldiers returning from Iraq score, on average, μ = 5 with σ = 2. A score of 5 is low, indicating that most soldiers do not develop severe symptoms. However, soldiers who have been exposed to extreme level of violence during their tour of duty score, on average , μ = 7 with σ = 3, indicating that these soldiers typically have mild to moderate levels of posttraumatic stress with a minority of soldiers experiencing severe symptoms. A new community reintegration project is implemented with returning soldiers who have been exposed to extreme levels of violence in an attempt to help returning soldiers in a variety of ways, including reducing the incidence of posttraumatic stress disorder in that population. The U.S. Army wishes to know if their community reintegration project has any effect on posttraumatic stress symptoms.

    Sometimes we are given more information than we need to state our hypotheses. It is important to be able to identify the right information and ignore the rest. First, think about what the population we are dealing with is. Although we were given information about soldiers in general, that is not the population that was studied. The population of interest was returning soldiers who have been exposed to extreme levels of violence during their tour of duty. Thus, our hypotheses can be stated like this:
    H0: The community reintegration project has no effect posttraumatic symptoms. The returning soldiers will have posttraumatic symptom levels of μ = 7.
    H1: The community reintegration project reduces posttraumatic symptoms such that their mean posttraumatic symptom levels will be μ < 7.

    Example 3: In the entire telemarketing sector, employees' satisfaction with the jobs is μ = 65 and σ = 10 on a questionnaire. DirectXYZ is a firm that believes that its policies are significantly better at keeping its telemarketers happy on the job. At DirectXYZ, a sample of 25 employees randomly selected scored a mean of 70 on the worker satisfaction questionnaire. Is DirectXYZ correct about their policies' effects on employee satisfaction?

    H0: Worker satisfaction at DirectXYZ is no different from other telemarketing firms. The mean worker satisfaction at DirectXYZ is μ = 65.
    H1: Worker satisfaction at DirectXYZ is higher than that of other telemarketing firms. The mean worker satisfaction at DirectXYZ is higher than μ = 65.

    We are going to do something we have not done in a while. You are going to submit all your answers by email to your GA.

    Download this worksheet and save it somewhere you will be able to find it again (e.g., your datastore).

    Each of the following situations calls for a significance test for a population mean m.

    Using the examples above as models, state the null hypothesis H0 and the alternative hypothesis H1 in each case.

    Save your worksheet (somewhere you can find it again) and email it to your GA:
    Chris Sorric (chrissoric@hotmail.com)
    Ying Ong (yyong@ilstu.edu)