Every analysis should begin by describing the data. Figure 5.7 Summary Statistics for State Health Care Expenditures through Figure 5.9 Summary Statistics for State Demographic Factors show summary statistics for the data grouped by health care expenditures, cessation expenditures, and demographic factors. These tables were produced from the Tabulate platform.

Summary tables such as these are frequently found in technical reports and journal articles. They acquaint the reader with the data that was collected. Grouping variables into separate tables by category makes it easier for the reader to assimilate the information.

Heat maps are effective for presenting geographic information and are easily created with Graph Builder. To create a heat map for Cessation Expenditures ($), drag State into the Map Shape drop zone and drag Cessation Expenditures ($) into the Color drop zone. JMP contains a library of map files located in the directory where JMP was installed. To use one of the built-in maps, the column describing the geographic region must match one of the formats given in the map shape file. For example, the US map shape file contains several columns with different designations for US states such as the full name (e.g., California), the United States Postal Service Code (e.g., CA) or the State FIPS code (e.g., 06). Figure 5.10 Heat Map of Cessation Expenditures by State shows a heat map for the total cessation expenditures by state.

In this heat map we see that New York State spends considerably more on cessation programs than any other state. Other states with large populations such as Florida and California also spend larger amounts on smoking cessation than less populated states, but this is not universally true. Oklahoma and Colorado as examples of less populated states that spend relatively large amounts on smoking cessation. This suggests that factors other than population size play a role in determining cessation expenditures. This pattern is different than what we observed using the heat map of total health care expenses created in the case “Health Care Costs Associated with Smoking: A National Perceptive.”

A heat map for cessation expenses per capita was created in a similar manner and is shown in Figure 5.11 Heat Map of Cessation Expense per Capita by State.

The heat map of the per capita cessation expense shows a different pattern compared to the state total cessation expense. New York no longer leads the nation in cessation expenditures when viewed on a per capita basis. Colorado is now the leading state. Texas’ spending on smoking cessation was relatively low on both a per capita and total basis. This suggests that factors other than population size are considered in a state’s determination of how much of its resources to allocate to smoking cessation programs. The heat maps shown here are useful to the analyst for exploring the data, postulating more detailed research questions, and choosing further analyses to perform.

Correlation analysis quantifies the linear association between two continuous variables. The correlation coefficient measures this linear association of a scale from -1 to 1 and expresses two aspects of the relationship. The sign of the correlation coefficient tells us whether there is a direct or inverse relationship between the two variables. The correlation coefficient for a direct relationship will have a positive sign while the correlation coefficient for an inverse relationship will have a negative sign. A correlation coefficient of 0 indicates that there is no relationship between the two variables. The correlation coefficient also describes the strength of the relationship. A larger correlation coefficient, in absolute value, indicates are stronger relationship, while a relatively smaller correlation coefficient indicates a weaker relationship. Examining the correlation coefficient helps the analyst describe the direction and strength of the relationships between two continuous variables. Correlation between two variables does not imply a causal relationship. For example, population size does not cause smoking-related health care costs. Smoking is caused by factors such as youthful experimentation, stress, or family history. The magnitude of state health care costs is associated with state population.

Correlation coefficients can be calculated using the JMP Multivariate Methods platform. To view a matrix of correlation coefficients, select Analyze > Multivariate Methods > Multivariate and enter the desired continuous variables in the Y, Columns field. Figure 5.12 Correlation Matrix and Scatterplot Matrix shows the JMP output for the pairwise correlations between total health care expense, cessation expense, and population.

Both total health care expense and cessation expense are directly associated with population size. Total health care expense and population size have a correlation coefficient of 0.9761 and cessation expense and population size have a correlation coefficient of 0.4088. Total health care is more strongly correlated to population size. This makes sense as a larger population will have more smokers and hence more smoking-related health care expenditures. Cessation expenditures are likely influenced by factors besides population size such as state public health priorities and policies.

The scatterplot matrix shows the relationships visually and allows outliers to be identified. The data points on the scatterplot for total health care expense and population size are tightly coupled as compared to the scatterplot for cessation expense and population size. Cessation expense and total health care expense have a modest correlation of 0.5274. In the associated scatterplot matrix, California, Texas, and New York, three large population states, appear to be outliers.

Other correlations can be similarly calculated from the remaining continuous variable given in the data set such as land area, state gross domestic product, and state cigarette taxes. For example, there is a direct and modest correlation of 0.491 between state cigarette tax and adjusted total health care expense. The correlation between state cigarette tax and total health care expense is quite close to zero at 0.088.