prediction so we have to assume that the research question is nondirectional. In this case the research question is that there will be a difference in the rate of people to get the flu depending on whether or not they get the nasal spray or the shot. In terms of the null and alternative hypotheses we could state them as:
H0: There will no difference in flu rates between groups that get the nasal spray and shot.
H1: There will be a difference between the groups in flu rates.
The Descriptions suggests the use of random assignment to the two different conditions of the study indicating that this is a variation of a true experiment (however there really is no control group). The results are significantly different as the alpha level was set at .05 and the obtained p value was .008. The results were statistically significant because there was a difference in the proportion of people who had the nasal spray getting the flu compared to the proportion of people who have the vaccination shot and got the flu. In other words based on the researchers' criteria for deciding what difference would actually be statistically significant difference found in the sample was deemed probably not due to chance factors. In this instance the researchers would reject the null hypothesis as the significance level from the obtained results is less than the stated alpha level.
However, there is another issue here regarding why the difference between the two groups may have been statistically significant. That difference has to do with the sample size and the particular type of test that was used in this particular research. Since there were only two groups (another issue) we can probably guess that the researchers used an independent t-test and with 500 subjects per group we would expect to achieve statistical significance in cases where the differences between the groups may actually not be that meaningful. Statistical significance simply means that the researcher can stay, within a certain level of confidence, that the findings from the particular research design/study are probably not due to chance factors and represent some type of real difference. However, the statistical significance and actual clinical or practical significance may not always be the same thing. The power of the statistical test is dependent on a number of issues that include the sample size and the magnitude of the difference between the means of the two (or however many there are) groups. If the sample size is rather large then magnitude of the difference between the two groups plays less of a factor in determining whether or not the findings are statistically significant, therefore it is possible to achieve statistical significance with what would be small differences between groups. Moreover, this particular design does not use a control group. This is an issue because we do not know if people who got no vaccination would get similar rates of the flu to both types of vaccinations (for example, how would the results would look if a control group who neither got nasal sprays or shots had significantly less flu outbreaks than both of the other two groups?). Thus, the findings of this particular study are limited by the methodology.
In revamping such a study one would want a true control group where the participants get nothing, a power analysis to figure out what is the optimal sample size for the effect one is predicting, and some other controls regarding the lifestyles of the particular participants. For example, even though there was random assignment, one group may have had higher risk factors for getting the flu such as working outside, drinking heavily, smoking heavily, etc. etc. There are a number of these factors at the researchers would want to control for directly in order to make the study tighter. Finally, we know nothing about how the participants were recruited and some type of sampling technique such as random sampling would make the results more generalizable.
There are always improvements that can be made to any study and follow research should look at the particular flaws in the study and try to replicate the results with different samples and a different approach that corrects for these issues.
2. The researchers found a strong positive correlation between IQ and GPA in the sample of students they studied. Typically obtained correlations over .7 are considered to be strong. What this means is that people with higher IQs tend to have higher GPAs (as well as the opposite condition, people lower IQs have lower GPAs). However, even though the correlation is strong it is not a perfect relationship and thus the researcher's findings regarding this relationship are not perfect; that is, not everyone in the sample demonstrated this relationship.
There are a number of issues with this type of research. The first issue to consider is the sampling method and the participants. In the case of a restricted range of participants where IQ levels are not measured across the full spectrum of IQ the resulting correlation may not adequately reflect the true relationship between the variables. We are given no information about the sample in this particular study.
Secondly, the assumptions in this particular study what appear to be that the only thing that can possibly affect GPA is IQ. Well, this does not make any sense whatsoever. In correlational studies of this nature there is always the "third variable problem" which states that perhaps there are other mediating variables involved that affect both IQ and GPA or just one of those variables. For instance, depending on the particular curriculum IQ alone may have very little bearing on GPA compared to such personal habits as the individual's study habits, prior course exposure, whether or not the individual works at job, has children, is on medication, etc. It is more realistic to think that there are other variables involved that affect GPA besides IQ (although certainly IQ has some effect on GPA). There are probably some fields of study were IQ has much less effect on GPA such as someone majoring in dance or social work compared to other fields such as theoretical physics. Besides the aforementioned factors that could affect the correlation in this study there are several others that affect the statistic including whether or not the relationship is linear or curvilinear (curvilinear relationships will tend to weaken the correlation) and the homogeneity of variance the group also decreases the magnitude of the correlation. Outliers in a data set will also affect the strength of the correlation depending on their particular value (e.g., outliers at the high-end of the distribution will tend to inflate the correlation and vice versa).
The old issue of "correlation does not imply causation" is one that is generally misunderstood. The correlation statistic, like any other statistic, is simply a tool that can calculate and specify a particular type of relationship between variables. The idea of causation is more dependent on the methodology used to collect the data that the statistic analyzes. Statistics analyze associations and relationships between data sets and variables, whereas the methodology used to collect and assigned participants to specific conditions of a study determine the types of inferences that the researcher can validly make. Thus, just because two things are associated with each other does not mean that one causes the other (for example the number of rapes and ice cream sales are positively associated, but how many people would endorse the assumption that eating ice cream causes people to commit rate?). Thus, the old saying "correlation does not imply causation" does not apply just to the correlation statistic but applies to the interpretation of any statistic. Statistical results need to be evaluated based on the methodology used to collect the data that the statistics analyze. Non-experimental research cannot make casual attributions no matter what type of statistical analysis is used.
If one looks at the literature one would find that IQ or scores on an intelligence test are pretty fair predictor variables for GPA as noted in most graduate school programs use of undergraduate GPA and several other predictor variables in a regression analysis to predict success (GPA) in graduate school. However, there are better tests that can be used to predict GPA such as multiple regression using additional criteria/variables that are also good predictors of GPA. Multiple regression allows the researcher to use a number of different predictors and determine the relative strength of the each predictor to the outcome variable. Of course multiple regression relies on the correlation coefficient in its prediction; however, as stated above there are multiple variables that contribute to GPA and regression analyses help can the researcher to determine the relative strengths of these predictor variables and how they contribute alone and together.
3. The group was separated into two groups of 10 based on the median value of the overall group (6.05). The descriptive statistics for the two groups follow: