Isen test 2

One-sample Z-test

used to compare a sample mean to a population mean

Important steps for a one-sample z-test

1. State the null and research hypotheses. 2. Set the level of risk associated with the null hypothesis. 3. Select the appropriate test statistic. 4. Compute the test statistic value (called the obtained value). 5. Determine the value needed for rejection of the null hypothesis using the appropriate table of critical values for the particular statistic. 6. Compare the obtained value and the critical value. 7. Make your decision.

Platykurtic

A distribution that is relatively flat compared with a normal, or bell shaped, distribution

Leptokurtic

A distribution that is relatively peaked compared with a normal, or bell shaped, distribution

If the obtained value is greater than the critical value, what should you do?

reject the null hypothesis

Standard scores

scores that are comparable because they are standardized in units of standard deviations

What does the z in Z-test represent? What similarity does it have to a simple z or standard score?

The big Z is similar to the small z because it is a standard score. The z score has the sample standard deviation as the denominator, whereas the Z-test value has the standard error of the mean as the denominator. They both use a standard measure that allows us to use the normal curve table to understand how far the values are from what we would expect by chance alone.

statistical significance

The degree of risk you are willing to take that you will reject a null hypothesis when it is actually true

type 2 error

The probability of accepting a null hypothesis when it is false

obtained value

The result or product of a specific statistical test

critical value

The value that you would expect the test statistic to yield if the null hypothesis is indeed true

significance level

The risk associated with not being 100% confident that what you observe in an experiment is due to the treatment or what was being tested

Write out a research hypothesis for this situation: Bob wants to know whether the weight loss for his group on the chocolate-only diet is representative of weight loss in a large population of middle-aged men

The weight loss of Bob's group on the chocolate-only diet is not representative of weight loss in a large population of middle-aged men who are on a chocolate-only diet

Type 1 error

Also known as the level of significance

Understanding effect size

A small effect size ranges from 0.0 to .20. A medium effect size ranges from .20 to .50. A large effect size is any value above .50.

Homogeneity of Variance

The assumption that the amount of variability in each of the two groups is equal Although this assumption is rarely violated, it still exists.

If you are examining relationships between two variables, what test should you use?

A t test

normal curve

A visual representation of a distribution of scores that has three characteristics

degrees of freedom

Approximates the sample size

Kurtosis

Has to do with how flat or peaked a distribution appears, and the terms used to describe this are relativeness

If you are examining relationships between more than two variables, what test should you use?

Regression, factor analysis, or canonical analysis

What are the three characteristics that a normal curve must have

The hump is right in the middle (the mean, median, mode must be equal) It is perfectly symmetrical about the mean. The tails of the normal curve are asymptotic

statistical significance is not very meaningful, unless...

The study that is conducted has a sound conceptual base that lends some meaning to the significance of the outcome

asymptotic

They come closer and closer to the horizontal axis but never touch

When is it appropriate to use a one sample z test

When you want to compare a sample mean with a population parameter

A t test for dependent samples...

indicates that a single group of the same subjects is being studied under two conditions.

Skewness

A measure of the lack of symmetry, or the lopsidedness of a distribution

degrees of freedom

The degrees of freedom approximate the sample size. Degrees of freedom can vary based on the test statistic selected. For t-test for dependent means: df = n − 1 (where n equals the number of pairs of observations)

One-sample z-test

We examine the differences between a sample and a population. There is only one group being tested. The appropriate test statistic is a one-sample z-test.

Computing the Test Statistic

1. State the null and research hypotheses. 2. Set the level of risk associated with the null hypothesis. 3. Select the appropriate test statistic. 4. Compute the test statistic value. 5. Determine the critical value(s). 6. Compare the obtained and critical values. 7. Make a decision.

effect size

A measure of how different two groups are from one another-it's a measure of the magnitude of the treatment

statistical significance cannot be...

Interpreted independently of the context within which the outcomes occur

We set out to _______ the hypothesis, not _________ it

Test, prove

confidence interval

The best estimate of the range of a population value that we can come with given the sample value (or sample statistic representing the population parameter