Books and Articles by Alan Anderson

Statistics make it possible to analyze real-world business problems with actual data so that you can determine if a marketing strategy is really working, how much a company should charge for its products, or any of a million other practical questions. The science of statistics uses regression analysis, hypothesis testing, sampling distributions, and more to ensure accurate data analysis.

You can use the Central Limit Theorem to convert a sampling distribution to a standard normal random variable. Based on the Central Limit Theorem, if you draw samples from a population that is greater than or equal to 30, then the sample mean is a normally distributed random variable. To determine probabilities for the sample meanthe standard normal tables requires you to convertto a standard normal random variable.

After you estimate the population regression line, you can check whether the regression equation makes sense by using the coefficient of determination, also known as R2 (R squared). This is used as a measure of how well the regression equation actually describes the relationship between the dependent variable (Y) and the independent variable (X).

Summary statistical measures represent the key properties of a sample or population as a single numerical value. This has the advantage of providing important information in a very compact form. It also simplifies comparing multiple samples or populations. Summary statistical measures can be divided into three types: measures of central tendency, measures of central dispersion, and measures of association.

A frequency distribution shows the number of elements in a data set that belong to each class. In a relative frequency distribution, the value assigned to each class is the proportion of the total data set that belongs in the class. For example, suppose that a frequency distribution is based on a sample of 200 supermarkets.

Compared with other types of hypothesis tests, constructing the test statistic for ANOVA is quite complex. The first step in finding the test statistic is to calculate the error sum of squares (SSE). Calculating the SSE enables you to calculate the treatment sum of squares (SSTR) and total sum of squares (SST).

Two of the most widely used measures of association are covariance and correlation. These measures are closely related to each other; in fact, you can think of correlation as a modified version of covariance. Correlation is easier to interpret because its value is always between –1 and 1. For example, a correlation of 0.

The uniform distribution is used to describe a situation where all possible outcomes of a random experiment are equally likely to occur. You can use the variance and standard deviation to measure the "spread" among the possible values of the probability distribution of a random variable. For example, suppose that an art gallery sells two types of art work: inexpensive prints and original paintings.

When you're testing hypotheses about two population means, where the variances of the two populations aren't equal, and the size of both samples are large (30 or greater), the appropriate test statistic is This test statistic is based on the standard normal distribution. As an example, say that a restaurant chain is interested in finding out whether the average sale per customer is the same in its domestic and foreign restaurants.