Trend Projection with Time Series Analysis

We present two forecasting methods in this section that are appropriate for time series exhibiting a trend pattern. First, we show how simple linear regression can be used to forecast a time series with a linear trend. Next we show how the curve-fitting capability of regression analysis can also be used to forecast time

Seasonality and Trend in Time Series Analysis

In this section we show how to develop forecasts for a time series that has a seasonal pattern. To the extent that seasonality exists, we need to incorporate it into our forecasting models to ensure accurate forecasts. We begin by considering a seasonal time series with no trend and then discuss how to model

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Time Series Decomposition

In this section we turn our attention to what is called time series decomposition. Time series decomposition can be used to separate or decompose a time series into seasonal, trend, and irregular components. While this method can be used for forecasting, its primary applicability is to get a better understanding of the time series.

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Sign Test

The sign test is a versatile nonparametric method for hypothesis testing that uses the binomial distribution with p = .50 as the sampling distribution. It does not require an assumption about the distribution of the population. In this section we present two applications of the sign test: one involving a hypothesis test about a

Wilcoxon Signed-Rank

In Chapter 10, we introduced a matched-sample experimental design where each of n experimental units provided a pair of observations, one from population 1 and one from population 2. The parametric test for this experiment requires quantitative data and the assumption that the differences between the paired observations are normally distributed. The t distribution

Mann-Whitney-Wilcoxon

In Chapter 10, we introduced a procedure for conducting a hypothesis test about the difference between the means of two populations using two independent samples, one from population 1 and one from population 2. This parametric test required quantitative data and the assumption that both populations had a normal distribution. In the case where

Kruskal-Wallis Test

In this section we extend the nonparametric procedures to hypothesis tests involving three or more populations. We considered a parametric test for this situation in Chapter 13 when we used quantitative data and assumed that the populations had nor­mal distributions with the same standard deviations. Based on an independent random sample from each population,

Rank Correlation

The Pearson product moment correlation coefficient introduced in Chapter 3 is a measure of the linear association between two variables using quantitative data. In this section, we provide a correlation measure of association between two variables when ordinal or rank-ordered data are available. The Spearman rank-correlation coefficient has been developed for this purpose. Let

Problem Formulation

The first step in the decision analysis process is problem formulation. We begin with a verbal statement of the problem. We then identify the decision alternatives, the uncertain future events, referred to as chance events, and the consequences associated with each decision alternative and each chance event outcome. Let us begin by considering a

Decision Making with Probabilities

Once we define the decision alternatives and the states of nature for the chance events, we can focus on determining probabilities for the states of nature. The classical method, the relative frequency method, or the subjective method of assigning probabilities may be used to identify these probabilities. After determining the appropriate probabilities, we show

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Decision Analysis with Sample Information

In applying the expected value approach, we showed how probability information about the states of nature affects the expected value calculations and thus the decision recommenda­tion. Frequently, decision makers have preliminary or prior probability assessments for the states of nature that are the best probability values available at that time. However, to make the

Computing Branch Probabilities Using Bayes’ Theorem

In Section 19.3 the branch probabilities for the PDC decision tree chance nodes were specified in the problem description. No computations were required to determine these probabilities. In this section we show how Bayes’ theorem can be used to compute branch probabilities for decision trees. The PDC decision tree is shown again in Figure

Price Relatives

The simplest form of a price index shows how the current price per unit for a given item compares to a base period price per unit for the same item. For example, Table 20.1 reports the cost of one gallon of gasoline for the years 2000 through 2017. To facilitate comparisons with other years,

Aggregate Price Indexes

Although price relatives can be used to identify price changes over time for individual items, we are often more interested in the general price change for a group of items taken as a whole. For example, if we want an index that measures the change in the overall cost of living over time, we

Computing an Aggregate Price Index from Price Relatives

In Section 20.1 we defined the concept of a price relative and showed how a price relative can be computed with knowledge of the current-period unit price and the base-period unit price. We now want to show how aggregate price indexes like the ones developed in Section 20.2 can be computed directly from information

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Some Important Price Indexes

We identified the procedures used to compute price indexes for single items or groups of items. Now let us consider some price indexes that are important measures of business and economic conditions. Specifically, we consider the Consumer Price Index, the Producer Price Index, and the Dow Jones averages. 1. Consumer Price Index The Consumer

Deflating a Series by Price Indexes

Many business and economic series reported over time, such as company sales, indus­try sales, and inventories, are measured in dollar amounts. These time series often show an increasing growth pattern over time, which is generally interpreted as indicating an increase in the physical volume associated with the activities. For example, a total dollar amount

Price Indexes: Other Considerations

In the preceding sections we described several methods used to compute price indexes, discussed the use of some important indexes, and presented a procedure for using price indexes to deflate a time series. Several other issues must be considered to enhance our understanding of how price indexes are constructed and how they are used.

Quantity Indexes

In addition to the price indexes described in the preceding sections, other types of indexes are useful. In particular, one other application of index numbers is to measure changes in quantity levels over time. This type of index is called a quantity index. Recall that in the development of the weighted aggregate price index

Philosophies and Frameworks of Statistical Methods for Quality Control

In the early twentieth century, quality control practices were limited to inspecting finished products and removing defective items. But this all changed as the result of the pioneering efforts of a young engineer named Walter A. Shewhart. After completing his doctorate in physics from the University of California in 1917, Dr. Shewhart joined the