Statistics in Behavioral Science Exam 2

What are the 3 requirements for a random sample?

1. Everyone in the sample has an equal chance of being in any of the groups (Random Assignment)

2. Selection of one person does not affect the selection of another person

3. All combinations are possible

What is sampling error?

The difference between a sample statistic and a population parameter.

What is a sampling distribution of sample means?

A distribution made from multiple means made from random samples of the same size.

Example:

The researchers collect 8 random samples of size N=20 and then put each sample mean into a frequency distribution.

What is Standard Error?

The standard deviation of the sampling distribution of sample means.

Formula:

σ/√n

When would you use a Z-test?

When σ and µ are known. However, this is never the case in real life; it's just stats class :)

What do you need to generalize to the population?

A random sample and a large sample size.

Define Null Hypothesis

The hypothesis that states nothing is happening.

Example (IQ) Ho: µ = 100

Define Alternative Hypothesis

The hypothesis that states that something is happening, or that there is a change from the null

Example (IQ) Ha: µ ≠ 100

What are the only two possibilities in statistical testing?

Reject the null hypothesis; accept the alternative,

or fail to reject the null.

NEVER accept the null

When do you reject the null hypothesis?

If your calculated statistic is in the rejection region of the normal distribution.

If the calculated t is greater than the table t.

For SPSS, the significance needs to be less than .05

When do you fail to reject the null?

If the calculated statistic is NOT in the rejection region of the normal distribution.

If the calculated t is less than the table t.

For SPSS, the significance needs to be greater than .05

Explain the .05 level of significance for one-tailed and two-tailed tests.

For a one-tailed test, it's the top 5% or the bottom 5% of the normal distribution.

For a two-tailed test, it's the top and bottom 2.5% of the normal distribution.

Define the Rejection Region.

The area under the normal distribution where the null hypothesis gets rejected.

What is a critical value?

The start of the rejection region.

State the null and alternative hypotheses for this question:

Are AU students' IQs average?

Ho: µ = 100

Ha: µ ≠ 100

State the null and alternative hypotheses for this question:

Are AU students' IQs above average?

Ho: µ = 100

Ha: µ > 100

State the null and alternative hypotheses for this question:

Are AU students' IQs below average?

Ho: µ = 100

Ha: µ < 100

When would we use a t-test, and what is different about it from a Z-test?

When σ is unknown. This makes it applicable in the real world.

You use the sample standard deviation instead of the population standard deviation.

What does df stand for?

Degrees of freedom (typically N-1, but can also be N1+N2-2)

Explain a type I error (alpha error).

When we reject the null, but it is actually true.

The probability of making this error is 5%, or the alpha level.

Explain a type II error (beta error).

When we fail to reject the null, but it is actually false.

What is a matched samples (or paired samples) t-test?

This is a t-test that compares the means of the same people measured twice.

Example: measuring depression scores before and after counseling.

What is an independent samples t-test?

This is a t-test that compares the means of two totally separate groups.

Example: measuring the IQ of Chicago Cubs and Chicago White Sox fans (We all know who's smarter)

Define power.

Ability to reject a false null hypothesis.

Define effect.

Change in the dependent variable that is caused by the independent variable.

Hypothesis

A prediction based on a theory

Probability

The likelihood that something occurs.