7.4.1 - Hypothesis Testing

Five Step Hypothesis Testing Procedure Section

In the remaining lessons, we will use the following five step hypothesis testing procedure. This is slightly different from the five step procedure that we used when conducting randomization tests. 

  1. Check assumptions and write hypotheses. The assumptions will vary depending on the test. In this lesson we'll be confirming that the sampling distribution is approximately normal by visually examining the randomization distribution. In later lessons you'll learn more objective assumptions. The null and alternative hypotheses will always be written in terms of population parameters; the null hypothesis will always contain the equality (i.e., \(=\)).
  2. Calculate the test statistic. Here, we'll be using the formula below for the general form of the test statistic.
  3. Determine the p-value. The p-value is the area under the standard normal distribution that is more extreme than the test statistic in the direction of the alternative hypothesis.
  4. Make a decision. If \(p \leq \alpha\) reject the null hypothesis. If \(p>\alpha\) fail to reject the null hypothesis.
  5. State a "real world" conclusion. Based on your decision in step 4, write a conclusion in terms of the original research question.

General Form of a Test Statistic Section

When using a standard normal distribution (i.e., z distribution), the test statistic is the standardized value that is the boundary of the p-value. Recall the formula for a z score: \(z=\frac{x-\overline x}{s}\). The formula for a test statistic will be similar. When conducting a hypothesis test the sampling distribution will be centered on the null parameter and the standard deviation is known as the standard error.

General Form of a Test Statistic

This formula puts our observed sample statistic on a standard scale (e.g., z distribution). A z score tells us where a score lies on a normal distribution in standard deviation units. The test statistic tells us where our sample statistic falls on the sampling distribution in standard error units.