STSCI 2150 Prelim 2 Quick Review

What goes into qchisq() and what comes out?

qchisq(1-alpha, df) = critical value

What goes into 1 - pchisq() and what comes out?

1 - pchisq(test statistic, degrees of freedom) = p-value

What R command do you use to find the critical value in a chi-squared test?

qchisq(1 - alpha, df)

What R command do you use to find the p-value in a chi-squared test?

1 - pchisq(test statistic, df)

What are the three assumptions of a binomial distribution?

(1) All trials are independent, (2) the probability of success is fixed, (3) the number of trials is fixed.

How do you find the p-value in a test of a single proportion?

Find binomial probabilities of getting values as extreme or more extreme than the test statistic in whichever direction the question specifies and add them up.

How can you graph expected vs observed values on a graph?

bars = observed, line = expected

When the variance is greater than the mean, the data have a (clumped/dispersed) distribution.

clumped

When the variance is less than the mean, the data have a (clumped/dispersed) distribution.

dispersed

When putting a test statistic chi squared value on a chi-squared null distribution, which side do you shade?

right

What is the TEA for determining if an observed percentage matches an expected percentage?

T: test of a single proportion, test statistic = # successes

E: p-value = add up binomial probabilities in whichever direction is specified in the alternative hypothesis

A: assess

What is the TEA for determining if an observed distribution matches an expected distribution?

T: goodness-of-fit test, test statistic = chi sq

E: (1) compare test stat to chi-squared from null distribution (if test stat is greater than chi sq, reject the null) (can also be calculated using qchisq(1-alpha, df)), (2) find range for p-value by looking for your test stat on the chi sq table, compare to alpha level

A: assess

What is the TEA for determining if two categorical variables are significantly different (difference of two proportions)?

T: test of association, test stat = chi sq

E: (1) compare test stat to chi-squared from null distribution (if test stat is greater than chi sq, reject the null) (can also be calculated from qchisq(1-alpha, df)), (2) find p-value range from table

A: assess

What is the test statistic in a test of a single proportion?

# of successes

What is the test statistic in a goodness-of-fit test?

chi sq

What is the test statistic in a test of association?

chi sq

What are the three assumptions for a binomial distribution? *Note: different from sample size assumptions!

(1) Number of trials is fixed, (2) individual trials are independent, (3) probability of success is the same for each trial.