Two populations are exposed to different stimuli. The two populations produce different results. Get a brief explanation of the types of issues these techniques can inform.
- Confidence intervals and hypothesis testing. You've now been introduced to both of these important statistical foundations. Confidence intervals allow us to take a single sample and create an interval, which we're fairly confident contains the population proportion. Hypothesis testing allows us to see if this one sample was likely the result of chance, or if an external force may have impacted the sample data. We're now moving on to comparing two populations.
In this section we'll look to answer questions like: Does taking aspirin reduce the chance of a heart attack? Are young male drivers more likely to get into car accidents than young female drivers? Are people in Los Angeles more likely to be victims of violent crime than people in New York City? Are male high school teachers more likely to have higher salaries than female high school teachers? Notice, we keep using the wording "more likely".
Even with our comparisons, we can't be sure, but we can create confidence intervals. But, what makes all of these questions similar is that each situation can be analyzed by comparing two independent random samples. One from each population: an experimental population and a control population. Those that take aspirin versus those that take a placebo. The placebo is the control group.
A sample of young male drivers versus a sample of young female drivers. In this case, either gender can be used as the control. A sample of citizens of Los Angeles versus a sample of New Yorkers. In this case, either city could be used as a control. And of course, a sample of male high school teacher salaries versus a sample of female high school teacher salaries. Again, either gender can be used as the control. In this first section, we will look at the comparison of two proportions of two independent populations.
We'll use our knowledge of basic proportions. We'll work to create a confidence interval for the difference between these two population proportions, and finally, we will use hypothesis testing to compare the difference between the proportions for each independent sample. Yeah, I know, that sounds like a whole lot of work, but rather than just talk about it, let's walk through a problem.
- Working with small sample sizes
- Using t-statistic vs. z-statistic
- Calculating confidence intervals with t-scores
- Comparing two populations (proportions)
- Comparing two population means
- Chi-square testing
- ANOVA testing
- Regression testing