Hypothesis Testing. Is It Significant?. Questions (1). What is a statistical hypothesis? Why is the null hypothesis so important? What is a rejection region? What does it mean to say that a finding is statistically significant ?
Is It Significant?
Based on the data we have, we will make a decision, e.g., whether means are different. In the population, the means are really different or really the same. We will decide if they are the same or different. We will be either correct or mistaken.
In the Population
Trained pilots same as control pilots
Nicorette has no effect on smoking
Personality test uncorrelated with job performance
Trained pilots perform emergency procedure better than controls
Nicorette helps people abstain from smoking
Personality test is correlated with job performanceSubstantive Decisions
Directional; 1 tail (need to adjust null for these to be LE or GE).
In practice, most tests are two-tailed. When you see a 1-tailed test, it’s usually because it wouldn’t be significant otherwise.
If the bound (141.3) was at the mean of the second distribution (142), it would cut off 50 percent and Beta and Power would be .50. In this case, the bound is a bit below the mean. It is z=(141.3-142)/2 = -.35 standard errors down. The area corresponding to z is .36. This means that Beta is .36 and power is .64.
The larger the difference in means, the greater the power.
This illustrates the choice of H1.
1 vs. 2 tails – rejection region
Sample size and population variability both affect the size of the standard error of the mean. Sample size is controlled directly. The standard deviation is influenced by experimental control and reliability of measurement.