Overview of Inferential Statistics

In the United States, the goal of a criminal trial is to resolve accusations made against a person who is accused of committing a crime. In common law systems, most criminal defendants undergo a trial that is held before a jury and that is prosecuted by the prosecuting attorney/lawyer.

In criminal trials, there are four possible outcomes that comprise two correct outcomes and two incorrect outcomes. The two correct decisions are:

• The defendant did not commit a crime, and the jury determines the correct verdict of not guilty.
• The defendant did commit a crime, and the jury determines the correct verdict of guilty.

The two incorrect decisions are:

• The defendant is not guilty of a crime, but the jury determines an incorrect verdict of guilty. Statisticians refer to this error as a Type I error. Sometimes it is referred to as a false positive.
• The defendant is guilty of a crime, but the jury determines an incorrect verdict of not guilty. Statisticians refer to this error as a Type II error. Sometimes it is referred to as a false negative.

Consider the following table:

Table I: In a courtroom case, if a defendant is found not guilty, it does not necessarily mean innocence; rather, it means that there is not enough evidence to support the verdict that the defendant is guilty.

Table II: With the courtroom case above, the jury is trying to determine if the evidence presented corresponds to the guilt or innocence of the defendant. With inferential statistics, a researcher is trying to determine from the evidence whether or not a meaningful correlation exists between a dependent variable and an independent variable. To put it plainly, does a change in the independent variable correspond to a change in the dependent variable. If a relationship/difference is rejected, it does not mean that there is no relationship/difference; rather, it means that there is not enough evidence to support the decision that there is a relationship/difference.

Inferential statistics involves testing one or more hypotheses that stem from the research question(s) that attempt to establish whether a relationship/difference exists among the variable in the data. These hypotheses can test either for relationships or differences.

For this Discussion you will analyze types of data analyses that can be conducted using the General Linear Model.

To Prepare:

• Review and complete the General Linear Model Worksheet , identifying the most appropriate analysis for each worksheet item (i.e., correlation analysis, independent samples t test, or descriptive statistics).
• Select two scenarios from the worksheet that can best be analyzed using correlation analysis.
• Select two scenarios from the worksheet that can best be analyzed using independent samples t test.
• Identify a phenomenon in your field of study or discipline and consider how it could be studied using two types of analyses.

By Day 4,

Post two examples of research scenarios that are best studied using correlation analysis and two examples of research scenarios that are best studied using independent samples t test. Explain how these two types of analyses could be applied to study a phenomenon in your field or discipline.