SOCI 2010 Final

Difference of means

Difference of means

Use two-sample test

Mean of difference

Use one-sample test

What is the confidence interval used for?

To determine how close x bar to unknown population mean likely to be (success rate if method)

Ex: 90% CI means there’s a 90% chance the population mean is within A and B

Test of significance

To test how likely is that a claim about a population parameter is true given the sample data

Statistical significance

An outcome that is very unlikely to occur by chance of claim about data is true

Test statistic

Measures how many standard deviations away from the hypothesized mean our statistic is

What is z-test used to test?

To test hypotheses about population means based on a single sample mean (population stdev is known)

What is proportion test used to test?

To test population proportion based on single sample proportion

What is the margin of error?

Variability of estimate (higher CI means higher MoE)

Why do significance and sample size have no correlation?

Because a small sample size that is significant doesn’t mean the effect is big

What are the conditions to use the procedure for the proportion confidence interval?

Successes and failures have to be at least 15.

What are the conditions to use the procedure for the proportion test significance?

Successes and failures have to be at least 10.

What happens when the degree of freedom increases? Why?

When dof increases, the graph gets closer to normal distribution because sample size is increasing.

List the steps for test of significance.

1. State the hypotheses

2. Find test statistic

3. Find critical value

   1. For z-tests, it’s the abs val.

   2. For t-tests, use dof and go down (IGNORE Z*)

4. Find corresponding p-values.

What are matched pairs? What kind of test is used?

Matched pairs are used when subjects who are ALIKE are matched in pairs and BOTH randomly assigned treatment and placebo.

A one-sample test is used because the purpose is to compare the mean of differences.

Sample size and skewness

<15 is close to normal.

15-39 is close to normal, mildly skewed

40+ is close to normal, mildly skewed, and clearly skewed

What are two sample tests? What is being compared?

Two sample tests are test of significance between two independent samples. The goal is to compare the responses of two treatments and compare the mean responses.

Robustness

Considered robust if it continues to work well under certain conditions. A larger sample size could be clearly skewed.