Please enable JavaScript.
Coggle requires JavaScript to display documents.
Chapter 8 Hypothesis Testing - Coggle Diagram
Chapter 8 Hypothesis Testing
Hypothesis testing
is a statistical method that uses sample data from a population to test a hypothesis about a population.
Hypothesis Process:
State the hypothesis about the population, use the hypothesis to predict what the sample results should look like if the hypothesis is true, obtain a random sample from the population, compare the sample data with the prediction, and finally decide whether the sample data are consistent with the hypothesis.
The purpose of a hypothesis is to determine whether a treatment has an effect on individuals in a population. It is an inferential process because it uses limited sample information to reach a generalized conclusion.
A researcher wants to determine what would happen if the treatment is given to everyone within the population.
Two hypothesis
The null hypothesis
states that the treatment has no effect, no change, no difference. It is the primary hypothesis being evaluated.
The alternative/scientefic hypothesis
is the opposite of the null hypothesis. It states that the treatment has an effect on the dependent variable. The sample data are used to determine whether the data are consistent with the null hypothesis or provide evidence against it.
The null hypothesis
is used to predict what sample means should look like. Two categories: first, sample means that are likely if the null hypothesis is true, meaning the values are close to the value predicted by the null hypothesis. Second, sample means that are unlikely if the null hypothesis is true; these values are far from the value predicted. The hypothesis test determines where the boundary lies between these two categories.
Alpha Level
: The alpha, or significance level, is the probability used to identify sample results that are considered unlikely if the null hypothesis is true. Common alpha levels include: a=.05, a=.01, a=.001
An alpha level determines how much probability is placed in the critical region.
For example, a=.05 in a two-tailed test: 5% of the distribution is in the critical region, which is 2.5% in each tail. The remaining 95% represents the central area.
The Critical region
consists of extremely unlikely sample values. If a sample statistic falls in the critical region would mean the result would be unlikely if the Null Hypothesis was true, the null hypothesis is rejected, there is evidence of a treatment effect.
If the sample statistic
does not fall in the critical region, this means the results are consistent with the null hypothesis; the research fails to reject the null hypothesis, and there is not enough evidence for a treatment effect.
If the sample falls in the critical region, the null hypothesis is rejected, meaning the treatment had an effect. If the sample does not fall in the critical region means fail to reject the null hypothesis, which means the data did not provide strong enough evidence to state that the treatment had an effect.
A test statistic is a specific statistic calculated from sample data and used to test a hypothesis.
A z-score hypothesis test process
: State the hypothesized value of the population mean, insert the hypothesized value, and examine the resulting z-score.
A z-score near zero indicates that the sample is close to what the null predicts. An extreme z-score indicates a large discrepancy between the sample data and the null hypothesis.
The obtained difference
is the difference between the sample mean and the population mean specified by the null hypothesis. The expected difference is the standard error, which represents the expected amount of difference between a sample mean and the population mean when there is no treatment effect.
A large absolute z-score
indicates a large discrepancy between the observed sample and what would be expected. under the null hypothesis.
Type 1 error
occurs when a researcher rejects a null hypothesis that is actually true. The researcher concludes that there is evidence that the treatment has an effect when, in reality, it does not.
A type two error
occurs when the sample does not fall in the critical region even though a treatment effect actually exists. The effect is not detected by the hypotehsis test and the resreacher fails to reject the null hypothesis. Type two erros can occur when the treatment effect is relatively small.
A smaller alpha level reduces the risk of type 1 errors. For example, an a=.05 allows for more risk of type 1 errors, while a=.001 is more conservative. Meaning more evidence would be needed to prove that treatment has an effect.
A statistically significant r
esult occurs when the test statistic is sufficiently extreme to fall in the critical region.
High variability
in statistical data makes it harder to detect clear patterns in research statistics and significant results.
Statistical significance does not necessarily mean that there is a treatment effect.
Random Sampling
assumes in hypothesis testing that participants are selected randomly to ensure that the sample is representative of the population.
Two observations
are independent when there is no consistent, predictable relationship between them. The occurrence of one event does not affect the probability of another event. Independent observations are a basic requirement for nearly all hypothesis testing.
One-tailed test
specifies the direction of a predicted effect. The hypothesis predicts either an increase or a decrease.
A two-tailed test
does not specify a particular direction. It looks for an extreme difference in either direction.