Subjects: Business mathematics

This lesson goes a step farther in what can be done with categorical data. Researchers often look at questions that have more than two categorical outcomes, or they may study more than two groups at a time. This type of analysis was introduced in Lesson 7, which focused on two-way tables. You learned then that categorical data often falls into multiple classes or outcomes. Researchers want to know how those classes or outcomes compare to each other as a whole. In addition, they want to know if the results of their comparison are statistically significant.

This lesson returns to the topic of regression introduced in Lessons 5 and 6. While researchers benefit from knowing the correlation between two variables, they also want to be able to apply the same inferences to a correlation as they do for other quantitative measures, such as the mean. It’s often possible to see the correlation between two quantitative variables in a scatterplot, but, in addition, researchers want to make estimates for the population as a whole just as they do when they estimate population means and proportions.

This lesson expands on the last lesson on regression to consider cases in which there is more than one predictor variable. Statisticians often do regressions where more than one factor is known to affect a response variable. While one can often see the effects of multiple variables, in this lesson, you will learn how researchers quantify the exact effects of those variables on a single outcome. Statisticians also want to know whether or not all the variables under study actually have an impact on the response variable.

This lesson further examines multiple regression by closely examining the predictor variables involved in the regression model. Researchers often want to simplify a multiple regression to focus on just a few variables, or even on a single variable. There are several reasons why they might do this. One is that they may not have the resources to continuously measure all of the explanatory variables. Or they may want to focus on one or two explanatory variables that are the best predictors of the response variable. In this lesson, you will learn how researchers determine which predictor(s) to keep and which ones to discard as they build a more refined model.

In this lesson we learn about a second and important t procedure, the two-sample t test. This test is one of the most widely used statistical tests. It is used to compare the means of two groups of data. It is a quantitative assessment that deals with real values such as pulse rates or cholesterol levels between two groups of patients receiving different treatments.

This lesson returns to the topic of proportions, applying what you have learned about confidence intervals, margins of error, and tests of significance to this type of data. As you may recall, instead of examining a quantitative value like the population mean µ, researchers often want to examine a categorical value, such as the proportion of a sample group that meets a certain criterion. For instance, they might want to study what proportion of voters intend to cast their ballots for a certain candidate of interest, or what proportion of students in an incoming college class are of a certain ethnic background. The answers generated by these questions are often expressed in terms of percentages, since a percentage is a proportion.

This lesson extends what you learned in Lesson 19 about single-sample proportions to the concept of two-sample proportions. Researchers use two-sample proportions to compare one group to another, which often involves comparing one treatment to another. In Lesson 18, you learned how to use the two-sample method with means from quantitative data. Now you will learn how to use the same method with data expressed in terms of a proportion of defined successes, including how to find confidence intervals and do tests of significance.

This lesson is a review of what you have learned so far in the course. You have learned about proper study design, the types of variables under study, and the data studies generate. You have learned about inference and tests of significance, and that there are specific formulas to be used with certain types of data. You have also learned the basic assumptions behind these formulas. But when faced with several study designs, and different ways of collecting and reporting data, how do you know which test to use?

In previous lessons, you learned about the proper techniques researchers use when sampling a population, and how they infer meaning out of sample data. In this lesson, you will learn more about what investigators do with the numerical data they collect. You’ll see how statisticians use the average of values observed in samples to accurately determine the average in the population from which the sample was drawn. You will also learn about a theory that is central to all of statistics and which allows researchers to make approximations of population values based on a small sample of data.

Confidence intervals are something we see in the news almost daily, most frequently as polling results. They are the most commonly reported statistical results. Whether it involves who will win the next race for governor or what percentage of the population favors off shore drilling, the polls invariably report a percentage plus or minus some number. That range is the confidence interval, the subject of this lesson. It tells viewers the range of accuracy for that poll; in other words, by how much the results may be off. If the numbers in a poll are close and fall within this range, you know that the race or debate is not over.