Descriptive Statistics

Pain Study
“The kappa opioid nalbuphine produces gender-and dose-dependent analgesia and antianalgesia in patients with postoperative pain” was a study that was performed to observe gender-specific patient response to varied doses of nalbuphine, an opioid pain medication, following oral surgery (Gear, Miaskowski, Gordon, Paul, Heller, & Levine, 1999). In this study, the researchers asked participants to rate their pain on a 10 cm visual analog scale (VAS) just before drug administration to obtain a baseline measurement, and again at 20 minute intervals thereafter (Gear et al., 1999). The demographic characteristics and descriptive statistics of the 131 participants are provided in Table 1 of the study (Gear et al., 1999). To aid in interpretation of the data collected in the research experiment, the researchers provide the reader with information using both ratio and ordinal data measurements.
The weight of the participants is given as a mean, or average, and is considered ratio measurement. This is important data because weight is a variable that is considered when calculating dosage requirements. For each dose of pain medication given, as well as the placebo, the weight in kilograms for both men and women is averaged in the table. The data appropriate and meaningful since the average weight of participants in each dose category is similar save for the weight differences between men and women. Ratio measurement is considered the highest level of measurement (Polit & Beck, 2012). The participants’ weight in kilograms provides meaningful arithmetic information for interpretation.
Valium dosage, given in mg/kg, is also a ratio measurement since the dosage has an absolute zero and can provide information regarding the attribute’s ordering (Polit & Beck, 2012). As with weight, this data is appropriate because the dose of valium given to participants was weight-based. Reading the table, one can clearly see that the average amount of valium given corresponds to the average weight of the participants in kilograms. The data is represented with the highest level of measurement and is clearly demonstrated via Table 1 (Gear et al., 1999).
A third ratio measurement in the pain study is the time to drug administration. The time that the administration task was performed is not clearly defined in the table, nor is it clearly stated anywhere in the text of the research study. One can assume that the time is measured in minutes given the data and information provided in the reading, but it is not clearly delineated anywhere in the study. The average time to nalbuphine administration is similar among all groups, and can be measured arithmetically, resulting in data that is meaningful and appropriate (Gear et al., 1999).
The mean age (in years) of the study participants is also provided in Table 1 as a ratio measurement (Gear et al., 1999). Again, the average age of participants in each group is similar, producing meaningful results since different age groups would react differently to the same dose of pain medication. For example, the elderly population may not metabolize medication in the same way that younger participants would. This results in information that is appropriate for use in comparison among groups in the study since all participants are around the same age, but not generalizable to the general population. To enhance generalizability, the researchers may wish to replicate the study using a group of elderly participants.
The surgical severity of the participants is given as an average and is explained in the footnotes under Table 1 (Gear et al., 1999). The surgical severity is described by assigning numbers from 0.25-2 according to the complexity or severity of the surgery. Because the participants are ranked, or ordered, on this surgical severity scale, the level of measurement utilized would be categorized as ordinal measurement. Although mathematical operations are limited with this level of measurement, this statistical technique is appropriate in the study because a relationship between surgical complexity ranking and other factors or results can be analyzed (Polit & Beck, 2012).
The baseline visual analog scale (VAS) is another measurement that is described in Table 1 of the pain study (Gear et al., 1999). Due to the fact that it cannot be mathematically determined whether the difference between one and two is equivalent to the difference between five and six; or if a participant who rates their pain at a six out of ten is experiencing twice as much pain as the participant rating their pain at a three out of ten, this data is ordinal measurement (Polit & Beck, 2012). Although pain is subjective, and it is difficult to tell what a number on the pain scale really means, the visual analog scale uses an appropriate level of measurement for the study as it provides information regarding the relative ranking of pain among participants.
62 men and 69 women participated in the pain study, resulting in a total sample size of 131 participants (Gear et al., 1999). The lowest level of measurement, nominal measurement, was used to categorize participants according to gender. Although this level of measurement provides no quantitative meaning, is it appropriate for representation of gender (Polit & Beck, 2012).
When considering the operational definition of the study, the variables measured make appropriate use of the relative levels of measurement for analysis. The aim of the study was to establish relationships between gender differences and analgesic response to the opiate pain medication, nalbuphine. Variables other than gender, such as weight, age, and surgical severity that may influence a person’s response to pain medication were considered and measured using the highest level of measurement appropriate (Gear et al., 1999). The table is well laid out and descriptive, aiding in generalizability. It would have been beneficial, however, for the research team to specify the units of time measured (e.g. minutes), and to define SEM. If one was not familiar with inferential statistics and this sampling distribution, the information in this column would be meaningless.
Staffing Study
“Hospital Nurse Staffing and Patient Mortality, Nurse Burnout, and Job Dissatisfaction” was a landmark nursing study conducted to observe the ways in which patient outcomes are impacted by nurse to patient ratios and factors of nurse retention (Aiken, Clarke, Sloane, Sochalski, & Silber, 2002). This study utilized three data sources for data collection, including nurses and nurse outcomes, hospitals, and patients and patient outcomes.
Table 1 on page 1990 of the staffing study provides information on all three of these variables using nominal measurement (Aiken et al., 2002). The first characteristic considered when analyzing these data sources is staffing, or the number of patients per nurse. The results are provided both numerically, as well as in the form of a percentage. The same is true for the hospital size, level of technology, and teaching status. Technology is described as being either high or not high, while teaching status is measured as either none, minor, or major (Aiken et al., 2002). The limitation with using this level of measurement is that the numbers cannot be used mathematically (Polit & Beck, 2012). In other words, statistical tests of this data are limited.
Table 2 also makes use of nominal data when measuring characteristics of the nurses employed in the study hospitals (Aiken et al., 2002). The first variable, women, is a nominal data point as it is a measurement of gender. Similarly, the next variable, BSN degree or higher, is mutually exclusively, making it nominal. Clinical specialty of the nurses is categorized with no quantitative meaning, again resulting in nominal measurement. The Likert scale was used to measure data related to emotional exhaustion among nurses which is an example of nominal measurement as well. The same is true for the data corresponding to nurses dissatisfied with their current job.
Although nominal measurement was used in the data of all of these variables, and it is the lowest level of measurement, it remains statistically appropriate as it identifies the problem that the study is attempting to show. Providing the data numerically, as well as in the form of percentages, allows the reader to glean important information from the statistics. For example, the number of nurses, patients, and hospitals in the study is great. By providing the percentages of the outcomes in relationship to these factors, the point of the study is better presented. One can see, for instance, that nearly 50% of a very large sample of nurses are dissatisfied with their current job and are experiencing high emotional exhaustion (Aiken et al., 2002).
Table 3 is found on page 1991 of the study and analyzes the characteristics of surgical patients included in the mortality and failure-to-rescue analyses (Aiken et al., 2002). This table compares all patients versus patients with complications, and introduces a different central tendency within the table. As with tables one and two, the data is described in the form of a number as well as a percentage, resulting, again, in nominal data. The difference, however, is the analysis of age, which is given as a mean and standard deviation. Depending on how this table is read (from top to bottom or from left to right), this data has the potential to be confusing, or to simply be missed altogether.
A similar discrepancy occurs in table two of the study where the number of years worked as a nurse is given as a mean and standard deviation, as opposed to the rest of the data which is given as a number and percentage. The statistics related to the age of the patients and the number of years worked as a nurse is provided as ratio measurement. This data is meaningful as ratio measurement given the variables considered.
As in the previous tables in the study, not only is the nominal level of measurement appropriate for the data provided, it is also explained clearly in the text of the study, further reinforcing the data and making it more meaningful to the reader. For example, Aiken et al (2002) state, “Forty-three percent of the nurses had high burnout scores and a similar proportion were dissatisfied with their current jobs” (p. 1990). This is meaningful as it allows for comparison among important variables.
Death within 30 days of hospital admission and failure to rescue were other data considered in the staffing study. This data is presented as nominal measurement on page 1990 of the text and on page 1991 in Table 4 (Aiken et al., 2002). “Of the 232,342 patients studied, 53,813 (23.2%) experienced a major complication not present on admission and 4,535 (2.0%) died within 30 days of admission” (Aiken et al., 2002, p. 1990).
Since the researchers were consistent when categorizing and measuring these variables, the level of measurement utilized is adequate and appropriate. The tables in the study are descriptive, exhaustive, and generalizable. An improvement to the tables may be to more clearly show where there is a change in central tendency within the tables. When considering the operational definition of the study, the variables measured make appropriate use of the relative levels of measurement for analysis and aid the enhancement of generalizability.

References
Aiken, L. H., Clarke, S. P., Sloane, D. M., Sochalski, J., & Silber, J. H. (2002, October 23). Hospital nurse staffing and patient mortality, nurse burnout, and job dissatisfaction [Article]. The Journal of the American Medical Association, 288(16), 1987-1993. Retrieved from http://www.nursing.upenn.edu/media/Californialegislation/Documents/Linda%20Aiken%20in%20the%20News%20PDFs/jama.pdf
Gear, R. W., Miaskowski, C., Gordon, N. C., Paul, S. M., Heller, P. H., & Levine, J. D. (1999, November). The kappa opioid nalbuphine produces gender- and dose-dependent analgesia and antianalgesia in patients with postoperative pain [Magazine]. Pain, 83(2), 339-345. Retrieved from https://eds.b.ebscohost.com/eds/detail/detail?vid=3&sid=802137e7-b910-44a4-847f-97b101a58e9a%40sessionmgr112&hid=104&bdata=JnNpdGU9ZWRzLWxpdmUmc2NvcGU9c2l0ZQ%3d%3d#db=cmedm&AN=10534607
Polit, D. F., & Beck, C. T. (2012). Theoretical frameworks. In H. Surrena (Ed.), Nursing research: Generating and assessing evidence for nursing practice (9th ed., pp. 379-402). Philadelphia, PA: Wolters Kluwer Health, Lippincott Williams & Wilkins.