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Chapter 8 Introduction to Hypothesis Testing - Coggle Diagram
Chapter 8 Introduction to Hypothesis Testing
The Elements of a Hypothesis Test
The known population is the individuals as they exist before treatment
Basic assumption: If the treatment has any effect, it is simply to add/subtract a constant amount to/from each individual's score
The purpose of the research is to determine what happens to the population after the treatment is administered (unknown population)
Effect Size
If the sample size is large enough, any treatment effect, no matter how small, can be enough for us to reject the null hypothesis.
A measure of effect size is used to show the actual size or strength of a treatment's effect without being influenced by the number of samples.
Cohen's d = mean difference / standard deviation
d = 0.2 --> small effect
d = 0.5 --> medium effect
d = 0.8 --> large effect
Uncertainty & Errors in Hypothesis Testing
Type I Error
: the researcher rejects a null hypothesis that is actually true
The alpha level is the probability that the test will lead to a Type I error.
The smaller the alpha level, the less probability of a Type I error.
As the alpha level gets smaller, the distance between the sample mean and the population mean gets larger.
Type II Error
: the failure to reject a false null hypothesis (designated as Beta)
A treatment effect really exists but the hypothesis test fails to detect it.
The sample mean is not in the critical region showing that while the treatment influences the sample, the magnitude of the effect is not large enough.
The Four Steps of a Hypothesis Test
2) Set the criteria for a decision and locate the critical region.
If there is a big discrepancy between the data and the hypothesis, we will conclude that the hypothesis is wrong.
The alpha level of significance defines the concept of "very unlikely" in a hypothesis test.
If sample data falls in the critical region, the null hypothesis is rejected.
1) State the hypothesis and select and alpha level.
The null hypothesis states that there is no change, no effect, no difference.
The alternative hypothesis predicts that the IV does not have an effect on the DV.
3) Collect data and compute the sample statistic.
The main point of the hypothesis test is to compare the data with the hypothesis using a test statistic.
Z score = (sample mean - hypothesized population mean) / standard error between sample and population means
4) Make a decision about the null hypothesis.
Reject the null hypothesis
The sample data are located in the critical region so the sample is inconsistent with the null hypothesis.
Fail to reject the null hypothesis
Sample data is not in the critical region, therefore reasonably close to the population mean and not providing evidence for a treatment effect.
We do not state there is/is not an effect, but instead there is/is not
evidence for
an effect.
More About Hypothesis Tests
A result is said to be statistically significant if it is very unlikely to occur when the null hypothesis is true.
Factors that influence a hypothesis test
Increasing the variability of the scores or decreasing the number of scores in the sample produces a larger standard error and a smaller value for the z-score
Assumptions for hypothesis tests with z-scores:
--random sampling
--independent observations
--the value of standard deviation is unchanged by the treatment
--normal sampling distribution
One-Tailed Tests
The directional prediction (increase or decrease in the population mean) is incorporated into the statement of the hypothesis.
A one-tailed test allows you to reject the null hypothesis when the difference between the sample and the population is relatively small as long as it is in the specified direction.
If a two-tailed test fails to reach significance, you should never follow up with a one-tailed test as a second attempt on the same data.
In an directional (one-tailed) test, t
Statistical Power
The power of a statistical test is the probability that the test will identify a real effect when one exists.
p(Type II error) = B
p(rejecting a false null hypothesis) = 1-B
Step 1: Sketch the distributions for the null and alternative hypotheses
Step 2: Locate the critical regions and compute M critical
Step 3: Compute the z-score for the alternative distribution & find power
Holding other factors constant (such as effect size & alpha level), a larger sample produces greater power for a hypothesis test.
As the effect size increases, the probability of rejecting the null hypothesis increases, and the power of the test increases.
As the sample size increases, power also increases.
Reducing the alpha level also reduces the power.
Changing from a two-tailed test to one-tailed increases the power.