# Statistical Methodologies In Criminal Justice

| June 19, 2015

For this assignment find an academic article that uses one a statistical methodologies. The article should be related to some criminal justice issue. Explain how the authors made use of the particular methodology in answering their research question.

Be sure to include the website, journal, or periodical where the article can be found.

There are two basic types of statistics: descriptive and inferential. Descriptive statistics are intended to summarize, describe, or show relationships between data; inferential statistics infer or generalize sample findings to larger populations. Basic descriptive techniques such as measures of central tendency (mean, median, and mode) were illustrated, as were measures of dispersion such as the range and standard deviation. Z scores, or standard deviation scores, are quite useful in assessing probability so long as we can assume the data are normally distributed. Chi-square was presented as an inferential technique (test of independence) appropriate for nominal level data. As with other tests of significance, a calculated value is compared at appropriate degrees of freedom with a calculated table of expected values. If a calculated value exceeds the expected value at the .05 probability level, this means that in fewer than five of one hundred trials could such a result be caused by sampling error. Chi-square is not a measure of relationship, although there are a number of chi-square-based measures of association such as phi, phi-square, contingency coefficient, and Cramer’s V. Of these, phi-square is of the greatest utility in that it is a PRE measure. A PRE measure is most useful in that it has in common with other such statistics a direct operational interpretation—variance explained. In addition to having descriptive or inferential functions, statistics can also be either parametric or nonparametric in nature. Parametric statistics assume interval level measurement, normal distributions, and linearity. Nonparametric statistics are “distribution free”; that is, they make few assumptions regarding the distribution of the population. Pearson’s r, Z, and F tests (ANOVA) are examples of parametric statistics, whereas gamma, Spearman’s rho, and chi-square are examples of nonparametric statistics. In inferential statistics, researchers do not directly test the research hypothesis or relationship they are attempting to demonstrate, but instead statistically assess the null hypothesis, a statement of non-relationship. Tests of significance measure whether results are due to chance or are so highly improbable of resulting from chance that they are significant at given levels of probability. The t test is a test of significance that compares sample means where the N of either sample is less than 30. For larger samples the Z test is more appropriate. ANOVA (analysis of variance) is appropriate for testing, by means of the F ratio, three or more samples. It assumes that the variance between groups should be large, and the variance within groups small. At appropriate degrees of freedom, the F ratio is compared with a table of expected values to test statistical significance. All of the statistical procedures that have been discussed in this chapter are applicable to only certain types of data, and the researcher is advised to check these assumptions carefully prior to choice of the statistical measure. Central to much scientific investigation is the notion of relationship indicates that, as one variable increases, the other increases; a negative relationship (inverse) indicates that, as one variable increases, the other decreases in value. Finally, if one variable has absolutely no impact on another, this is indicative of no relationship. Pearson’s correlation coefficient (r) is one of the most widely used measures of relationship. It is appropriate for interval level data that exhibit linearity and varies from -1.00 (perfect inverse relationship) to +1.00 (perfect positive relationship). The square of r (r2) is a PRE measure and indicates variance explained. A regression equation enables one to predict values of one variable (Y), given knowledge of a predictor variable (X). Some measures of relationship that are alternatives to Pearson’s r for working with ordinal (ranked) data are Spearman’s rho and gamma. Both calculations can have PRE interpretation. Multivariate analysis includes partial correlation, in which controls for a third or more variables exist, as well as multiple correlation and regression. Multiple correlation (R) looks at the impact of multiple predictors (independent variables) on the dependent variable. Multiple regression provides a formula that enables the calculation of predicted values of the dependent variable, given values of independent variables. Finally, the reader is urged to follow the maxim caveat emptor (let the buyer beware) in reading statistical findings. Be wary of assumptions regarding the meaning of statistical significance, the misuse of statistical techniques, overgeneralizations beyond the data in discussions, and overlooked assumptions that are required in appropriately utilizing statistical measures. Ecological fallacy is the error that occurs when the researcher’s target is individuals, but the analysis is of groups. If the units of an analysis are individuals, then data aggregated into groups are not likely to reflect the real relationship.

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