Introduction to Hypothesis Testing

What is the most commonly used alpha level

.05

How do you complete the third step of hypothesis testing (obtain a sample from the population) (2)

1. Compare the sample means (data) with the null hypothesis 2. Compute the test statistic

How do you complete the fourth step of hypothesis testing and compare the data with hypothesized prediction? (2)

1. If the test statistic results are in the critical region, we can conclude that the difference is significant, or that the treatment has a significant effect 2. If the mean difference is not in the critical region we conclude that the evidence from the sample is not sufficient

Four steps of Hypothesis Test?

1. State hypothesis about the population 2. Use hypothesis to predict the characteristics the sample should have 3. Obtain a sample from the population 4. Compare data with the hypothesis prediction

The alternative Hypothesis (2)

1. States that there IS a change in the general population following an intervention 2. In the context of an experiment, the alternative hypothesis predicts that the independent variable DID HAVE AN EFFECT on the dependent variable

Null Hypothesis (2)

1. States that there is NO change in the general population before and after an intervention 2. In the context of an experiment the null hypothesis predicts that the Independent Variable had NO EFFECT on the dependent variable

What is the critical region? (2)

1. The critical region consists of outcomes that are very unlikely to occur if the null hypothesis is true 2. That is the critical region is defined by sample means that are almost impossible to obtain if the treatment has no effect

The purpose of the hypothesis test is to decide between two explanations, what are the two explanations?

1. The difference between the sample and the population can be explained by sampling error (there DOES NOT appear to be a treatment effect) 2. The difference between the sample and the population is too large to be explained by sampling error (there DOES appear to be a treatment effect)

A directional test includes (2)

1. The directional prediction in the statement of the hypotheses 2. Directional Prediction in the location of the critical region

What commonly causes Type II Errors (2)

1. Type II errors are commonly the result of a very small treatment effect 2. Although the treatment does have an effect, it is not large enough to show up in the research study

What are three different alpha levels used?

1. α= .01 2. α= .05 3. α= .001

How many types of errors are possible

2

What is it called when the researcher incorporates the directional prediction into the hypothesis test?

A directional test or a one tailed test

What is a hypothesis test

A statistical method that uses sample data to evaluate a hypothesis about a population

Why is the sample mean's difference from the original population not necessarily indicative that the treatment has caused a changed

Because there usually is some discrepancy between a sample mean and the population mean simply as a result of sampling error

How do you perform hypothesis step 2 and predict the characteristics that the sample should have?

By establishing an alpha level and a critical region

How do you complete step one of hypothesis test and state the hypothesis about the unknown population?

By establishing the Null hypothesis and the Alternative hypothesis

How are the hypothesis tests structured so that Type I errors are very unlikely

By having the Probability of a type I error equal the alpha level

How is a Type I error caused

By unusual, unrepresentative samples, falling in the critical region even though the treatment has no effect

What does the alpha level establish?

Establishes a criterion, or "cut off", for making a decision about the null hypothesis

If the mean difference is not in the critical region, and we conclude that the evidence from the sample is not sufficient what do we do?

Fail to reject the null hypothesis

How do you get evidence that a treatment has an effect?

If the individuals in the sample are noticeably different from the individuals in the original population

Just because the sample mean following treatment is different from the original population mean does not necessarily...

Indicate that the treatment has caused a change

What is also a possible explanation for the difference between the individuals obtained in the sample and the individuals in the original population?

It is also possible that the difference between the sample and the population is simply sampling error

When a research study predicts a specific direction for the treatment effect (increase or decrease) what can be done?

It is possible to incorporate the directional prediction into the hypothesis test

If the test statistic results are in the critical region and the difference is significance and the treatment had a significant effect what do we do?

Reject the null hypothesis

What is chance called in hypothesis testing?

Sampling error

The first step of hypothesis test is to

State the hypothesis about the unknown population

How does the researcher contribute to a Type II Error

The researcher will fail to reject the null hypothesis and falsely conclude that the treatment does not have an effect

What does computing the test statistic z-score do during the third step in hypothesis testing?

The test statistic (z-score) forms a ratio comparing the obtained difference between the sample mean and the hypothesized population mean versus the amount of difference we would expect without any treatment effect (the standard error)

Because the hypothesis test relies on sample data and because sample data are not completely reliable

There is always the risk that misleading data will cause the hypothesis test to reach a wrong conclusion

What is the general goal of a hypothesis test?

To rule out chance as a plausible explanation for the results from a research study

The alpha level determines the risk of what?

Type I error

The hypothesis test is structured so that

Type I errors are unlikely

How does the researcher impact a Type I error

When the researcher rejects the null hypothesis and falsely concludes that the treatment has an effect

When does a Type I Error Occur

When the sample data appear to show a treatment effect when, in fact, there is none

When does a Type II error occur

When the sample does not appear to have been affected by the treatment, when in fact the treatment does have an effect

What is the test statistic used during the third step in hypothesis testing?

Z-score

How is an alpha level denoted

α