Statistics for the Social Sciences Quiz 4

MS296 Thomas College

What is the difference between research hypotheses and statistical hypotheses?

The research hypothesis is a general statement predicting the relationship between variables in a study, while statistical hypotheses are specific, formal statements about the parameters of a population that can be tested using statistical methods.

Is a research hypothesis or a statistical hypothesis stated in words? And which one is more precise?

A research hypothesis is stated in words. A statistical hypothesis is more precise, as it is formulated as a mathematical statement regarding population parameters.

What is the difference between a null and an alternative hypothesis?

A null hypothesis states there is no effect or no difference, while an alternative hypothesis suggests there is an effect or difference that can be tested.

Should a null hypothesis or an alternative hypothesis be stated in the positive?

An alternative hypothesis should be stated in the positive, indicating the expected effect or difference, while a null hypothesis is typically stated in the negative.

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

They must be mutually exclusive and exhaustive, ensuring that all possible outcomes are accounted for in hypothesis testing.

Which hypothesis, null or alternative, is actually tested?

The null hypothesis is tested through statistical analysis to determine if there is enough evidence to reject it in favor of the alternative hypothesis.

What is the basic logic of hypothesis testing?

It involves formulating a null and alternative hypothesis, collecting data, and using statistical analysis to determine if there is sufficient evidence to reject the null hypothesis.

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

The traditional criterion for rejecting the null hypothesis is a p-value less than 0.05, indicating that the observed data is statistically significant.

Experimental significance level

refers to the threshold for determining whether the results of an experiment are statistically significant, commonly set at 0.05.

Significance Level (Alpha)

The probability of making a Type I error, which is rejecting a true null hypothesis. In social sciences, it is typically set at 0.05.

Type I Error

Claiming there was an effect when there actually was not

Type II Error

Claiming there was no effect when there actually was

Which type of error is of greatest concern to social scientists?

Type I Errors

Nondirectional Hypothesis

Predict IV will affect the DV without specifying the direction (how)

Directional Hypothesis

Predict IV will affect the DV in a particular direction (a one tailed test)

What is a critical region?

A range of values in a statistical test that leads to rejection of the null hypothesis if the test statistic falls within it. It is determined by the significance level.

How are the critical regions for nondirectional and directional hypothesis testing different?

The critical region for a nondirectional hypothesis test is split between both tails of the distribution, whereas for a directional hypothesis test, the critical region is located entirely in one tail.

How does statistical decision making relate to critical regions?

Statistical decision making involves using critical regions to determine whether to reject the null hypothesis based on the test statistic's placement within these regions. If the statistic falls in the critical region, the null hypothesis is rejected, suggesting significant results.

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

When you reject the null hypothesis

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

When you keep (and DON’T) reject the null hypothesis

How does statistical decision making relate to critical regions?

Non-directional: risk (5%) must be split between both ends of the sampling distribution (two-tailed test)

Directional: risk is represented only by the predicted tail of the sampling distribution (one-tailed test)