 Confidence Intervals  Around a proportion  Significance Tests  Not Every Difference Counts  Difference in Proportions  Difference in Means

 The 95% confidence interval around a sample proportion is: And the 99.7% confidence interval would be:

 The margin of error is calculated by:

 In a poll of 505 likely voters, the Field Poll found 55% support for a constitutional convention.

 The margin of error for this poll was plus or minus 4.4 percentage points.  This means that if we took many samples using the Field Poll’s methods, 95% of the samples would yield a statistic within plus or minus 4.4 percentage points of the true population parameter.

 Perhaps the differences in our dependent variable that we observe from group to group in our sample could be due to random chance alone.  A “significance test” asks: How likely is it that we would observe a difference that large in our sample, if there were no difference in the population?

 Significance tests begin with the “null hypothesis,” the claim that there is no difference in the dependent variable from one group to another (measured as a mean or a proportion).  This is akin to saying that the independent variable that we use to group cases has no effect on the dependent variable.

 Mathematically, the null hypothesis says:  And the sample difference in means is normally distributed with a mean equal to the population difference in means with a standard error equal to:

 For interval and ratio dependent variables, you can conduct a difference in means test: Where

 For nominal and ordinal dependent variables, you can conduct a difference in proportions test: Where If the confidence interval does NOT include zero, we can reject the null hypothesis with 95% confidence.

 60.4% of the 1024 white residents in my survey voted, as did 24.5% of the 625 Latinos. This test tells us we can reject the null hypothesis.