# Term Paper: Meticulous Construction of the Data

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[. . .]
Social Support: For Question 18 the mean for on-pump was 2.20 and for off pump it was 1.97. For Question 19 the mean for on-pump was 1.84 and for off pump it was 2.02. These two questions were Likert scale questions asking about family members and pets in the home. Since these three questions moved from less to more, the higher the mean the stronger the score.

Thus as can be seen from Figure 15 above, with a level of significance set at =0.05 the two groups are virtually identical in all categories. Descriptive statistics on quality of life questions showed slight differences in some cases. However, none of these results were clinically significant. Virtually no differences were observed regarding quality of life for the two surgical procedures.

Demographics

Descriptive statistics indicate that no significant differences exist between the two CABG surgery patients. These results must be compared to various demographic groups in order to validate sampling procedures and determine if the minor differences that were reported may be due to demographic features, rather than surgical procedures.

The following summarizes the demographic findings. Less than 1% of patients reported that they smoke; 17.2% reported that they do not exercise at all; 57.6% reported that they were overweight; 61.4% reported that their income was below fifty thousand dollars annually, with 31.2% reporting an income below twenty-five thousand; education levels ranged from 8.8% completing graduate school to 4.2% completing grade school or below, the highest level reported were high school graduates at 31.2%; 7% reported that they followed their cardiac diet every day of every month and 47.4% reported that they followed it most days of every month, but 17.7% reported that they never followed their prescribed diet.

The most noteworthy demographic statistics came from the ethnicity question. Patients reported that their ethnicity was 3.7% African-American, 1.4% Asian, 70.7% Caucasian, 19.1% Native American, 0% Hispanic, 3.7% Middle Eastern or Arab-American, and 0.5% other. The participating physicians estimated that Hispanic surnames accounted for about 25% of the entire patient group and yet, not a single person claimed to be Hispanic or Mexican-American. A surname does not necessarily indicate a persons ethnicity, but in light of the fact that the bulk of the patients (70%) came from Louisiana and Texas and these states have large Hispanic population, perhaps this was an error in the research design and questionnaires should have been sent in English and Spanish, and perhaps, the return rate would have been higher from the Latin community, thus giving the study a better basis for comparisons. Cultural differences may contribute a person's ability to cope with stress and recover from an illness.

The following pages show the actual percentages of all demographics, which are important when looking at the multivariate data analysis for all dependent variables, co-variables, and fixed variables.

Figure 16: Chart of Gender Distribution

Figure 17: Chart of Age Distribution

Figure 18: Chart of Cardiac Diet Frequencies

Figure 19: Chart of Weight Frequencies

Figure 20: Chart of Exercise Frequencies

Figure 21: Chart of Income Frequencies

Figure 22: Chart of Education Frequencies

Figure 23: General Linear Model of All Demographics

Multivariate Data Analysis

Demographics can effect the outcome of the research question. If demographics are found to effect the outcome of the research question significantly, this could indicate sampling error and serve to cause sampling bias in the test results. Severe sample bias can make the results of the research inapplicable for the general population. To determine if demographics have affected the results multivariate data analysis is used. This technique examines the pattern of relationships between several variables simultaneously. Multivariate statistics helps the researcher to summarize data and reduce the number of variables necessary to describe it. Most commonly multivariate statistics are employed:

For developing taxonomies or systems of classification;

To investigate useful ways to conceptualize or group items;

To generate hypotheses; and finally,

To test hypotheses.

There are certain assumptions about multivariate analyses. The first assumption is that all of the models require that input data be in the form of interrelationships -- this means correlations for factor analysis. Multidimensional scaling and cluster analysis can use a variety of different input data -- distances, or measures of similarity or proximity. This means that multidimensional scaling and cluster analysis can be somewhat more flexible than factor analysis. The second assumption of these methods is that the data itself is valid. Because these methods do not use the same logic of statistical inference that dependence methods do, there are no robust measures that can overcome problems in the data. These methods, therefore, are only as good as the input one has.

In each case of multivariate data analysis, the output will look somewhat different, but in all of the techniques, the researcher is required to look at the results and make some determination of how many factors, dimensions or clusters to use in further analysis in order to represent the data. What the researcher should not forget is that each case or variable used in the analysis is simultaneously classified on all the dimensions. While this is most apparent in multidimensional scaling, it applies equally well to the other techniques.

The first task was to determine if the researcher-designed mental health questions were affected by any of the demographics, followed by the condition-specific questions and finally the social support questions. The six tables below are multivariate analysis and analysis between subjects. The tests between-subject effects is an analysis of variance table. The column labeled Source lists the effects in the model. The second column displays the sum of squares for each effect. The degrees of freedom for each sum of squares is displayed in the column labeled df. The mean square of each effect is calculated by dividing the sum of squares by its degrees of freedom. The F. statistic and its significance value are displayed in the next columns. The F. statistic is calculated by dividing the mean square by the mean square error. Effects with a small significance value (smaller than 0.05) are significant. The multivariate tests table displays four multivariate tests of significance of each effect in the model. Pillai's trace is the first multivariate test listed. Wilks' lambda is sometimes called the U. statistic. Lambda ranges between 0 and 1, with values close to 0 indicating the group means are different and values close to 1 indicating the group means are not different (equal to 1 indicates all means are the same). Hotelling's trace is based on the sum of eigenvalues. Roy's largest root is the largest eigenvalue. Of the four test statistics, Wilks' lambda is convenient and related to the likelihood-ratio criterion. For some practical situations, however, Pillai's trace may be the most robust and powerful criterion among the others. Choice of these multivariate statistics depends on the situation. The value of the test statistic is displayed followed by the F. statistic, which is a transformed value of the corresponding test statistic and has an approximate F. distribution. The hypothesis and error degrees of freedom of the F. distribution are shown. When the significance level is relatively small (less than 0.05) for the effect being tested, then it can be concluded that the effect is significant.

On the between-subjects tests, with the level of significance set at =0.05 Question 12b has a significant effect of 0.016 with gender and Question 12c has a significant effect of 0.037 with education. Question 12b asked, "Have you had two (2) years or more in your life when you felt depressed or sad most days, even if you felt okay sometimes?" Question 12c asked, "Have you felt depressed or sad much of the time in the past year?" The multivariate tests for the mental health questions had no significant effects.

On the multivariate test, with the level of significance set at =0.05 the researcher-developed condition-specific questions had several significant effects. All four tests -- Pillai's trace, Wilks' lambda, Hotelling's trace, and Roy's Largest Root -- had effects between education (0.025), ethnicity (0.006), exercise (0.050), the surgeon (0.003) and the type of surgery (0.019). On the between-subjects tests, ethnicity had significant effects between: Question 13 (0.024), which asked, "My cognitive (thinking) ability since I had my heart operation is?"; Question 14 (0.026) which asked, "My memory since I had my heart operation is?"; Question 15 (0.005) which asked, "The discomfort (pain) that I had during the first four weeks following my heart operation was?"; and finally, Question 17 (0.041), which asked, "Since my cardiac surgery, I have had cardiac arrhythmia?" There was also a significant effect between exercise and Questions 14 (0.026). The effect between education and Question 15(0.041), and Question 16 (0.004), which asked, "The discomfort (pain) I have now is?" There was also a significant effect between Question 16 (0.004) and weight and Question 15 (0.018) and gender. Questions 13 (0.001), 14 (0.025), 16 (0.002), and 17 (0.008) had significant effects between the surgeons, while Questions 13 (0.001), 14 (0.014), and 17 (0.008) had significant effects…
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