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Hypothesis Testing

### Definition of Hypothesis Testing

Hypothesis testing is an inferential procedure that uses sample data to evaluate the credibility of a hypothesis about a population.

### Logic of Hypothesis Testing Logic

Put simply, the logic underlying the statistical hypothesis testing procedure is:
1. State the Hypothesis: We state a hypothesis (guess) about a population. Usually the hypothesis concerns the value of a population parameter.
2. Define the Decision Method: We define a method to make a decision about the hypothesis. The method involves sample data.
3. Gather Data: We obtain a random sample from the population.
4. Make a Decision: We compare the sample data with the hypothesis about the population. Usually we compare the value of a statistic computed from the sample data with the hypothesized value of the population parameter.
• If the data are consistent with the hypothesis we conclude that the hypothesis is reasonable.
• If there is a big discrepency between the data and the hypothesis we conclude that the hypothesis was wrong

### Errors in Hypothesis Testing

The purpose of hypothesis testing is to make a decision in the face of uncertainty. We do not have a fool-proof method for doing this: Errors can be made. Specifically, two kinds of errors can be made:
1. Type I Error: We decide to reject the null hypothesis when it is true.
2. Type II Error: We decide not to reject the null hypothesis when it is false.

### Techniques for Hypothesis Testing

The technical aspects of hypothesis testing include:
1. Classical Non-directional (two-tailed) techniques. These are appropriate when the experimenter predicts an effect, but doesn't predict the direction of the effect.
2. Classical Directional (One-Tailed) techniques. These are appropriate when the experimenter does predict a direction of the effect.