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