## Significance Tests / Hypothesis Testing

### Writing a Hypothesis for Your Science Fair Project

Statistical computing packages provide exact p-values as part of their standard output for hypothesis tests. In fact, when using a statistical computing package, the steps outlined about can be abbreviated. The hypotheses (step 1) should always be set up in advance of any analysis and the significance criterion should also be determined (e.g., α =0.05). Statistical computing packages will produce the test statistic (usually reporting the test statistic as t) and a p-value. The investigator can then determine statistical significance using the following: If p __ α then reject H___{0}.

### Proper hypothesis format - Positive Pilates

In one sample tests for a discrete outcome, we set up our hypotheses against an appropriate comparator. We select a sample and compute descriptive statistics on the sample data. Specifically, we compute the sample size (n) and the proportions of participants in each response

category ( , , ... ) where k represents the number of response categories. We then determine the appropriate test statistic for the hypothesis test. The formula for the test statistic is given below.

## How to write a null and alternative hypothesis

If (that is, ), we say the data are consistent with a population mean difference of 0 (because has the sort of value we expect to see when the population value is 0) or "we **fail to reject the hypothesis that the population mean difference is 0**". For example, if t were 0.76, we would fail reject the hypothesis that the population mean difference is 0 because we've observed a value of t that is unremarkable if the hypothesis were true.

## How to Test Hypotheses - Statistics and Probability

The exact form of the research hypothesis depends on the investigator's belief about the parameter of interest and whether it has possibly increased, decreased or is different from the null value. The research hypothesis is set up by the investigator before any data are collected.

## 7.3 - Decision Making in Hypothesis Testing | STAT 500

The decision rule is a statement that tells under what circumstances to reject the null hypothesis. The decision rule is based on specific values of the test statistic (e.g., reject H_{0} if Z __>__ 1.645). The decision rule for a specific test depends on 3 factors: the research or alternative hypothesis, the test statistic and the level of significance. Each is discussed below.

## Social Research Methods - Knowledge Base - Hypotheses

There are two approaches for making a statistical decision regarding a null hypothesis. One is the **rejection region approach **and the second is the ** p-value (or probability value) approach**. Of the two methods, the latter is more commonly used and provided in published literature. However, understanding the rejection region approach can go a long way in one's understanding of the

*p*-value method. Regardless of method applied, the conclusions from the two approaches are exactly the same. In explaining these processes in this section of the lesson, we will build upon the prior steps already discussed (i.e. setting up hypotheses, stating the level of significance α, and calculating the appropriate test statistic).

## Hypothesis Examples - Science Notes and Projects

Let's start out here by having Dr. Wiesner walk through a comparison of the *p*-value approach with the rejection region approach to hypothesis testing.