Statistical Conclusion and Its Connection

Statistical conclusion and its connection to validity refer to consulting statistics to whether or not the independent and dependent variable covary and the extent to which they do so. Some of the threats to statistical reliability include low effect size, inaccurately calculated sample size, internal and external problems, and so forth (Cohen, R.J., & Swerdlik, M.E. (2004).

Problems with statistical conclusion can be seen in Criminal Justice research Designs when a population may be tested to see whether a certain intervention helps. The selected sample may be too small resulting in incorrect statistical conclusion.

Construct

This is when the main theme of the research or the primary variables is defined. They have to be definitively and thoroughly defined so that the research investigates the wanted objectives.

In connection to Criminal Justice: if research is done on certain criminals, operationalization of these criminals (age, gender, other characteristics) Have to be scrupulously carried out so that research investigates objectives of study.

Internal

Internal validity refers to constructs that ensure that the study is not distorted, such as that there is no interviewer bias, that control and experimental group are closely matched (if that design is used), that participants are not tired nor that they import factors that may bias the test, that the environment does not distract, and so forth.

In relation to the first example of intervention test on criminals, the researchers should be not subjectively involved with the test nor receive money for their testing. Various other conditions too should be incorporated to ensure that study remains as objective as possible.

External

External validity refers to the question of whether the results from this small group can be generalized to other groups. Repeatability. For instance, the study may be implemented on a certain sector of offenders who live in California. Can results of this study be extended to offenders from other jails?

2. The p-value refers to the probability value of the test.

The null hypothesis says that the expected hypothesis of the study will fail to occur. The p-(probability) value is the level of evidence against the null assertion. The smaller the p-value, the stronger the evidence. . Therefore, statistical results that show less than .1 probabilities are very strong indeed. Usually, less than .5 probability is the usual expectations (maximizing with . 10). If the p-value is below a certain predefined limit (set for that specific study according to sample), the results are considered "statistically significant"

The small p-value tells us that the chance of these results occurring is mathematically so small that we have to accept the results as significant. For instance, a p-value of < 0.05 tells us that the probability of occurrence is less than 5% (Greenfield et al. (1998).

Other factors however may lead to inaccuracy in p-value resulting in either a Type 1 error or in the less grievous Type 2 error. The Type 1 error refers to rejecting the null hypothesis when it is true. The Type 2 error is when one rejects the alternative hypothesis even though it is true.

3. Parametric and non-parametric tests

Parametric tests usually deal with samples that have a normal distribution and that are measured with means and standard deviations. T-tests and ANOVA are examples of this comparing one group against another. The Pearson would be used with correlation. Non-parametric tests, however deal with populations where there is no or vague assumptions about the shape or parameters of the population (for instance when one is dealing with a very small sample of offenders that cannot be measured with parametric instruments). Non-parametric tests include Wilcoxon rank-sum test and Kruskal-Wallis test as t-test / ANOVA contrast as well as Spearman's rank correlation instead of Pearson's. (Parametric and Nonparametric: Demystifying the Terms)

4. T-test and ANOVA

The t-test is used for 2 groups, control and experimental. The Anova is used for more than 2 groups. Both are parametric tests. The MANOVA is used for when many different components are expected to be involved in the study and researcher wants to study which one is likely to be most responsible for results. There are three types of t-test:

1. One-sample-t-test - Compares mean of sample with known population mean

2. The independent two-sample t-test is used to determine if the means of two independent samples are equal (for instance if interventions when applied to both show similar results).

3. Paired samples t-test - if the means of a paired sample is equal (for instance comparing the test scores of a group that received that same test on two different occasions).