1. A t-test would be of help in comparing the two different groups' blood pressure average before and after being subjected to the drug. The difference will be meaningful and real if:
The responses are constantly close enough to the average value with a low standard deviation from the mean value.
The differences between the averages are large.
The t test effect size and the t test statistical significance are the two primary outputs of the t test. Statistical significance helps indicate whether the difference existing between sample averages represents actual differences between my populations (my two group before and after taking the drug). A two tailed t test would be appropriate because it will help determine if the drug has an effect on blood pressure-our null hypothesis Ho-or the drug does not have an effect on blood pressure- our alternative hypothesis H1. Ho will be rejected when the p- value is sufficiently extreme in relation to the sampling distribution of the test statistic’s and thus concluded to be unlikely to be the result of chance.
When required to compare several groups like age, gender, race, or by body type within one table, the ANOVA would be the best fit for this analysis. This is because a number of independent variables can be included using this method. One way ANOVA indicates that there is one independent variable in the model that can be divided into a given number of groups, but the case is different in t test that allows for an independent variable with just two groups.
2. The t test would not be the best way for this study. This is because the problem of multiple comparisons would arise. The more the number of groups, the more the number of tests required as all possible outcomes needs to be covered. The potential of type 1 error when statistical testing is done repeatedly with the same data does not remain the same but grows. It is also tedious. The use of multiple t tests is not a good option. One way ANOVA would be the best option. Three groups of the same size should be selected from the population to represent the three distributions- negative effect, no effect, or a positive effect. The drug effect is indicated by how the independent variable affects our dependent variable. The ultimate question would be whether, as a result of use of the drug, the samples still represent populations with the same mean, or whether they may represent populations with different means.
3. I would recommend the use of ANOVA for the analysis. This is because it can allow the division of the independent variables into a number of groups, unlike in the z-test and t-test. Type 1 errors resulting from repeated tests on the same data would be avoided. The problem of multiple comparisons would also not arise. Z tests focus on a single parameter treating all the other unknown parameters to be fixed at their true values. It is inappropriate to use the z statistic if the standard deviation is not known. It will also be inappropriate if the sample size is small. The t test is also limited to a given sample size. The null hypothesis would be that there was no effect on the blood pressure. Total variability from all sources can be easily computed. The F statistic is to be used, which is drug effect variance divided by the error variance. When the F ratio is small, it means the independent variable has not had enough impact to overcome error variability, and the differences between groups are not significant.
The hypothesis would be non-directional as the hypothesis will be two tailed. Manipulation the independent usually variable results to a change in the dependent variable thus hard to predict if this change is positive or negative.
Reference:
Tanner, D. (2011). Statistics for the behavioral & social sciences. San Diego, Ca: Bridgepoint Education, Retrieved from Inc. http://docs.statwing.com/examples-and-definitions/t-test.
Ellestad, M. (2003). Stress Testing: Principles and Practice. New York. Oxford University Press
