Duke@coursera 数据分析与统计推断unit5 inference for categorical variables

一、sampling variability & CLT for proportions

if the success-failure condition is notmet:

‣ the center of the sampling distributionwill still be around the true population proportion

‣ the spread of the sampling distributioncan still be approximated using the same formula for the standard error

‣ the shape of the distribution willdepend on whether the true population proportion is closer to 0 or closer to 1

二、confidence interval for a proportion

三、hypothesis test for a proportion

四、estimating the difference between two proportions

五、hypothesis tests for comparing two proportions

六、small sample proportion

七、chi-square GOF test

evaluating the hypotheses

‣ quantify how different the observedcounts are from the expected counts

‣ large deviations from what would beexpected based on sampling variation (chance) alone provide strong evidence forthe alternative hypothesis

‣ called a goodness of fit test sincewe’re evaluating how well the observed data fit the expected distribution

p-value

‣ p-value for a chi-square test is definedas the tail area above the calculated test statistic

‣ because the test statistic is alwayspositive, and a higher test statistic means a higher deviation from the nullhypothesis

八、chi-square independence test

evaluating the hypotheses

‣ quantify how different the observedcounts are from the expected counts

‣ large deviations from what would beexpected based on sampling variation (chance) alone provide strong evidence forthe alternative hypothesis

‣ called an independence test since we’reevaluating the relationship between two categorical variables

chi-square tests

‣ goodness of fit: comparing thedistribution of one categorical variable (with more than 2 levels) to ahypothesized distribution

‣ independence: evaluating therelationship between two categorical variables (at least one with more than 2levels)