Statistics for the Social Sciences Quiz 4

Research hypothesis

what you expect to find in your study; it expresses your theory or prediction

Statistical hypothesis

mathematical or symbolic statement about a population parameter, derived from the research hypothesis

Is research or statistical hypothesis stated in words?

research hypothesis

Is research or statistical hypothesis more precise?

statistical hypothesis

null hypothesis

assumes no effect or no difference

alternative hypothesis

reflects your research question

Does null or alternative hypothesis have to be stated in the positive?

null hypothesis

What are the two fundamental criteria that the null and alternative hypotheses must meet?

they must be mutually exclusive (both cannot be true at the same time), they must be exhaustive (one must be true)

Which hypothesis, null or alternative, is actually tested?

null hypothesis

What is the basic logic of hypothesis testing?

we test whether the date provide sufficient evidence to reject H₀ in favor of H₁

In the social sciences, what is the traditional criterion for rejecting the null hypothesis?

α = 0.05 (5% significant level)

Type I error? (α)

rejecting H₀ when it is actually true

Type II error? (β)

failing to reject H₀ when H₁ is actually true

Under what conditions do we run the risk of committing a Type I error?

risk occurs whenever you set a significance level and test H₀)

Under what conditions do we run the risk of committing a Type II error?

risk occurs when the effect exists but your study does not detect it

Which error is of greatest concern to social scientists?

type I error is usually of greater concern because claiming a false effect can mislead research and policy

How can you reduce the likelihood of committing a Type I error?

lower α (example: from 0.05 to 0.01), increase sample size carefully

How can you reduce the likelihood of committing a Type II error?

increase sample size, reduce variability, increase effect size, and choose more sensitive measures

Nondirectional hypothesis

predicts a difference or effect but does not specify direction (example: group a will differ from group b)

Directional hypothesis

predicts a specific direction of the effect (example: group a will score higher than group b)

What is a critical region?

the area in the sampling distribution where, if the test statistic falls, we reject H₀

Critical regions for nondirectional hypothesis testing?

critical region is split across both tails of the distribution

Critical region for directional hypothesis testing?

critical region is in one tail only (depending on predicted direction)

How does statistical decision making relate to critical regions?

if the test statistic falls within the critical region, we reject H₀; otherwise, we fail to reject H₀