Monday, August 19, 2013

The Language of Statistics

You may be asked to express the results of your work on a case in the language of statistics. What was your hypothesis? How did you test your hypothesis? You are offering an opinion. On what is your opinion grounded? If you believe that the man in the picture is the defendant, how do you express this belief? Would you enter into the discussion with some variation of Null = not the defendant / Alternative = the defendant? If you go down this road, be prepared to talk in the language of statistics.

Can We Accept the Null Hypothesis?

Some researchers say that a hypothesis test can have one of two outcomes: you accept the null hypothesis or you reject the null hypothesis. Many statisticians, however, take issue with the notion of "accepting the null hypothesis." Instead, they say: you reject the null hypothesis or you fail to reject the null hypothesis.

Why the distinction between "acceptance" and "failure to reject?" Acceptance implies that the null hypothesis is true. Failure to reject implies that the data are not sufficiently persuasive for us to prefer the alternative hypothesis over the null hypothesis.

How did you conduct your hypothesis tests?

Statisticians follow a formal process to determine whether to reject a null hypothesis, based on sample data. This process, called hypothesis testing, consists of four steps.

State the hypotheses. This involves stating the null and alternative hypotheses. The hypotheses are stated in such a way that they are mutually exclusive. That is, if one is true, the other must be false.

Formulate an analysis plan. The analysis plan describes how to use sample data to evaluate the null hypothesis. The evaluation often focuses around a single test statistic.

Analyze sample data. Find the value of the test statistic (mean score, proportion, t-score, z-score, etc.) described in the analysis plan.

Interpret results. Apply the decision rule described in the analysis plan. If the value of the test statistic is unlikely, based on the null hypothesis, reject the null hypothesis.

If you're not prepared to go down this road - DON'T. Simply explain your workflow and present your findings: this is what I did and this is what I found. If you are clarifying / enhancing images and video - don't talk in the language of stats about your results. You didn't conduct an experiment, you simply made the image / video more clear and usable for the trier of fact. In doing this, you didn't analyze the file, you just cleaned it up.

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