## Next section: to Inferential statistics (testing hypotheses)

### Type I error: The null hypothesis is rejected when it is true.

In statistics terminology, the students in the study are the **sample** and the larger group they represent (i.e., all statistics students on a graduate management degree) is called the **population**. Given that the sample of statistics students in the study are representative of a larger population of statistics students, you can use hypothesis testing to understand whether any differences or effects discovered in the study exist in the population. In layman's terms, hypothesis testing is used to establish whether a research hypothesis extends beyond those individuals examined in a single study.

### Type II error: The null hypothesis is not rejected when it is false.

When you conduct a piece of quantitative research, you are inevitably attempting to answer a research question or hypothesis that you have set. One method of evaluating this research question is via a process called **hypothesis testing**, which is sometimes also referred to as **significance testing**. Since there are many facets to hypothesis testing, we start with the example we refer to throughout this guide.

As such, by taking a hypothesis testing approach, Sarah and Mike want to **generalize** their results to a population rather than just the students in their sample. However, in order to use hypothesis testing, you need to re-state your research hypothesis as a null and alternative hypothesis. Before you can do this, it is best to consider the process/structure involved in hypothesis testing and what you are measuring. This structure is presented .

## Hypothesis Testing - Six Sigma Material

Before moving onto the second step of the hypothesis testing process, we need to take you on a brief detour to explain why you need to run hypothesis testing at all. This is explained next.

## Types of Errors in Hypothesis Testing | UniversalClass

In reviewing hypothesis tests, we start first with the general idea. Then, we keep returning to the basic procedures of hypothesis testing, each time adding a little more detail.

## Hypothesis Testing | Type I And Type Ii Errors | Hypothesis

The first step in hypothesis testing is to set a research hypothesis. In Sarah and Mike's study, the aim is to examine the effect that two different teaching methods – providing both lectures and seminar classes (Sarah), and providing lectures by themselves (Mike) – had on the performance of Sarah's 50 students and Mike's 50 students. More specifically, they want to determine whether performance is different between the two different teaching methods. Whilst Mike is skeptical about the effectiveness of seminars, Sarah clearly believes that giving seminars in addition to lectures helps her students do better than those in Mike's class. This leads to the following research hypothesis:

## Type I and Type II Errors in Hypothesis Testing

The inferential statistics do not directly address the testable statement (research hypothesis). They address the . Statistically, we test "not." Here are the null hypotheses:

## Test of hypothesis for proportions and standard error

One place where you can consistently see the general idea of hypothesis testing in action is in criminal trials held in the United States. Our criminal justice system assumes "the defendant is innocent until proven guilty." That is, our initial assumption is that the defendant is innocent.

## 3.0 - Hypothesis Testing | Statistics

When testing hypotheses about a mean or mean difference, a *t*-distribution is used to find the p-value. This is a close cousin to the normal curve. T-Distributions are indexed by a quantity called degrees of freedom, calculated as df = n – 1 for the situation involving a test of one mean or test of mean difference.