Subjects: Business mathematics

In this lesson, you’ll learn what statisticians do when they need to analyze data that does not meet the strict requirements for the tests covered so far in this course. In our previous lessons, the tests have required Normal distributions and proper sample sizes. But sometimes these conditions simply cannot be met. For instance, some investigations involve collecting data on human subjects with serious illnesses where it would be simply impossible or unethical to keep sampling in order to meet all the criteria for traditional statistical analysis. Other times, the sample sizes are limited due to expense or the availability of subjects to study. Rather than simply discard the data or abandon the study, statisticians have gotten around the problem by using the power of computers to simulate the necessary conditions in a way enables them to make reliable estimates and draw valid conclusions. While these methods make for a far more complex analysis, they allow researchers to investigate important data sets they could not have otherwise analyzed.

So far, all of the tests introduced in this course have required that the data have a Normal distribution. However, what about those studies in which the distribution is not Normal? Most of the tests studied thus far are robust with regard to Normality, and can be used as long as the sample size is large enough. However, there are times when a study has a small sample size that does not take a Normal distribution. What happens then?

Throughout this course, you’ve seen many real world examples of how statistics is applied when researchers want to gain new information. In this lesson, you’ll see how the statistical procedures you’ve learned are applied to business and manufacturing processes. While you will not be learning any new tests of significance in this lesson, it does apply what you have learned about descriptive statistics to events in the workplace.

This lesson describes another type of ANOVA. This ANOVA is used as a statistical test when two categorical explanatory variables are present. In the previous lessons, we used the one-way ANOVA F test to evaluate the differences in means between multiple groups that were cases of just one explanatory variable. But in many situations, there are at least two explanatory variables that affect the value of a response variable. In these situations, researchers often want to determine which variable is causing a change in the response variable, or whether the two explanatory variables may be working together to produce an effect on the response variable. The analysis is done through the use a different form of the ANOVA F test using computer software to make the calculations. While it makes for a more complex analysis, this powerful technique can allow researchers to investigate the simultaneous impact of two conditions on a response variable.

This lesson deals with a special type of regression in which the response variable is categorical and the explanatory variable is a quantitative variable. It is often the situation where researchers want to predict the outcome of a categorical variable, such as the survival of a patient given a variation of some measurable variable or the pass/fail of a device under changing conditions. Neither linear nor multiple regression will yield an answer in these cases. In this lesson, you will learn how statisticians do evaluate the success or failure of a categorical variable given a single predictive explanatory variable. In doing so, you will learn about yet another regression technique.

This lesson introduces another type of statistical test that evaluates the means of numerical data. In previous lessons, we used the two-sample t test to evaluate differences between the means of two groups. But many problems that researchers examine involve more than two groups. For instance, a study on smoking might require researchers to look at smokers, quitters, and lifelong nonsmokers; or a study about psychological health based on marriage status might involve looking at married, single, and divorced individuals. In this lesson, you’ll learn how statisticians examine the differences among the means of three or more groups using a test statistic you have seen before: the F test. This test was used to evaluate the variation seen in multiple regression. Now, you will learn another important application of this test: evaluating the means of multiple groups.

This lesson continues the analysis of multiple means begun in the previous lesson on ANOVA. It introduces yet another type of statistical test to the means of numerical data. The one-way ANOVA F test gives us valuable information about the groups under study by telling us whether or not the means of the groups are equal. As powerful as ANOVA is, however, it does not tell us which group is different, by how much, and whether the difference is significant. To discover that information, we need to compare the means of the groups.