T-test on independent samples that have unequal variance. The problem here is determining sampling error in order to accurately determine whether two samples are or are not really different. This test is also used when the number of cases in each sample is different or when the number of cases in one or both the samples is small. Steps:

1. Hypothesis is formulated. Means and SD for groups are worked out

2. Standard error for each group is calculated as is overall standard error

3. The t-score for the difference of means is calculated

4. The t-score is looked up and probability result applied to hypothesis.

B. T-test for independent samples with equal variances.

Since you want to avoid a Type 1 error, it is important to ensure that both groups do indeed have equal variances. To do so, perform a Levene test. Alternately, test for unequal variances can be used, unless one is absolutely certain that both groups have equal variances.

The only difference in calculation here to that of unequal variances is that instead of standard error worked out for each group, an overall standard error is calculated. The t-score is then calculated and results assessed to investigate probability.

c. T-test with dependent samples

In this case, the items are paired (e.g. with a pre -- and post test) therefore the differences between the scores of each of the individuals in both pre- and post- are calculated. Mean, SD, and SE are then calculated one of each of the differences. The t-score is calculated and probability assessed in order to see, for instance, whether differences have been found between pre- and post test.

Proportions

The t-test can also be used to investigate whether there are differences between two sample proportions.

Steinberg (2007) discusses the importance of the cause and effect relationship in policy research and the great role that it plays particularly in developing policies and in the policy process. He then goes on to...

On the other hand, historical analysis is often confusing and more complex in its response showing -- as indeed is the case in real life -- that more than one explanation can be produced as explanation for causality. All of these factors may be necessary but none are exactly sufficient to describe the outcome response. Steinberg (2007) seeks to resolve the problem by suggesting that measurement criteria can be employed in order to rank the relative importance of the component causes. Nonetheless, when compared to linear regression, historical analyses is more complex in that it posts various factors as possible correlation. On the toehr hand, historical analyses seems more accurate in that it simulates reality by indicating that more than one element can be posited as explanatory factor for outcome.
The GAO case study paper in contrast focuses on qualitative, as opposed to quantitative research (thereby dramatically differing form Steinberg) and advises that GAO evaluators could better use caste methods in performing their works, proffering six applications of case study methods, explaining their similarities and differences, defining them, and determining their appropriateness.

The GAO case study, dealing with qualitative research, has little to do with the summary of research methods mentioned in this assignment. excepting the fact that it indicates that objective methodology could be used to reinforce the reliability, dependency, and consistency of results of the case studies. Taking this message to heart would lead one to employing some of the strategies mentioned in this assignment, and causing one to integrate quantitative with qualitative studies in that which is called triangulated experiments.