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

Sampling error

The difference between a sample statistic and a population parameter.

Sampling distribution of sample means

The result you would get if you took repeated samples from a given population, calculated the mean for each sample, and plotted the 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.

Standard Error

The standard deviation of the sampling distribution of sample means.

Formula:

σ/√n

When would you use a Z-test?

When σ (sigma) and µ (mu) 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.

Null Hypothesis

The hypothesis that states nothing is happening.

Example (IQ) Ho: µ = 100

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

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

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.

Rejection Region

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

Critical Value

This marks 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 (sigma) 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)

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.

Type II error (beta error)

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

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.

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)

Power

The ability to reject a false null hypothesis

Effect

The change in the dependent variable that is caused by the independent variable.

Hypothesis Testing

Method used to decide whether sample data provides enough evidence to support a belief about a population

Critical Region

contains all the values that allow you to reject the null

level of significance

probability of making a type I error

• Typically denoted as $\text{alpha}$ ((\alpha)), commonly set at 0.05 or 0.01.

probability

the chance of something happening