Management of Missing Data

Except in very small studies, researchers almost always use computers for data analyses. The first step of the process is entering the data into the computer using a systematic plan designed to reduce errors. Missing data points are identified during data entry. If enough data are missing for certain variables, researchers may have to determine whether the data are sufficient to perform analyses using those variables. In some cases, subjects must be excluded from an analysis because data considered essential to that analysis are missing. In examining the results of a published study, you might note that the number of subjects included in the final analyses is less than the original sample; this could be a result of attrition and/or subjects with missing data being excluded from the analyses. It is important for researchers to discuss missing data and its management in the study.

Description of the Sample

Researchers obtain as complete a picture of the sample as possible for their research report. Variables relevant to the sample are called demographic variables and might include age, gender, ethnicity, educational level, and number of chronic illnesses (see Chapter 5). Demographic variables measured at the nominal and ordinal levels, such as gender, ethnicity, and educational level, are analyzed with frequencies and percentages. Estimates of central tendency (e.g., the mean) and dispersion (e.g., the standard deviation) are calculated for variables such as age and number of chronic illnesses that are measured at the ratio level. Analysis of these demographic variables produces the sample characteristics for the study participants or subjects. When a study includes more than one group (e.g., treatment group and control or comparison group), researchers often compare the groups in relation to the demographic variables. For example, it might be important to know whether the groups’ distributions of age and chronic illnesses were similar. When demographic variables are similar for the treatment (intervention) and comparison groups, the study is stronger because the outcomes are more likely to be caused by the intervention rather than by group differences at the start of the study.

Research Example

Description of the Sample

Research Study

Kim, Chung, Park, and Kang (2012) conducted a quasi-experimental study to examine the effectiveness of an aquarobic exercise program on the self-efficacy, pain, body weight, blood lipid levels, and depression of patients with osteoarthritis. The study included 70 subjects, with 35 patients randomly assigned to the experimental group and 35 to the control group. We recommend that you obtain this article, and review this study. The results from this study are presented as examples several times in this chapter to facilitate your understanding of statistical techniques.

The demographic variables used to describe the sample in the Kim and colleagues’ (2012) study included age, educational level, marital status, religion, occupation, income, and health status. Descriptive statistics of frequency and percentage (%) were used to analyze the demographic data, and the experimental and control groups were compared for similarities. The results from these analyses are presented in Table 11-1

Table 11-1

Homogeneity Test of General Characteristics Between Experimental and Control Groups

Characteristics	Experimental Group n=35n%	Control Group n=35n%	p
Age (yr)
55-59	0 (0.0)	2 (5.7)	0.545*
60-64	11 (31.4)	9 (25.7)
65-69	15 (42.9)	17 (48.6)
≥70	9 (25.7)	7 (20.0)
Educational Level
None	4 (11.4)	1 (2.9)	0.373*
Elementary	5 (14.3)	11 (31.4)
Middle school	15 (42.9)	14 (40.0)
High school	5 (14.3)	5 (14.3)
College or more	6 (17.1)	4 (11.4)
Marital Status
Married	22 (62.9)	22 (62.9)	1.000*
Bereavement	11 (31.4)	12 (34.3)
Other	2 (5.7)	1 (2.9)
Religion
Christian	8 (22.9)	7 (20.0)	0.907*
Catholic	12 (34.3)	15 (42.9)
Buddhist	9 (25.7)	9 (25.7)
None	5 (14.3)	4 (11.4)
Occupation
Yes	4 (11.4)	3 (8.6)	1.000*
None	31 (88.6)	32 (91.4)
Income (per/mo)
<100	18 (51.4)	18 (51.4)	0.496*
100-200	5 (14.3)	9 (25.7)
201-300	7 (20.0)	6 (17.1)
>300	5 (14.3)	2 (5.7)
Health Status
Good	5 (14.7)	5 (14.3)	0.649
Fair	16 (47.1)	16 (45.7)
Bad	13 (38.2)	14 (40.0)

^*Fisher’s exact test.

From Kim, I., Chung, S., Park, Y., & Kang, H. (2012). The effectiveness of an aquarobic exercise program for patients with osteoarthritis. Applied Nursing Research, 25(3), p. 186 (Table 2 from the article).

Critical Appraisal

Kim and associates (2012) developed a table that clearly presented the results of their analysis of demographic variables, and they discussed this table in the results section of their research report. The demographic variables of age, educational level, marital status, occupation, and income are commonly used in many studies to describe the samples. The descriptive analysis techniques of frequency and percentage were appropriate for the demographic variables measured at the nominal or ordinal level. Age, educational level, income, and health status were measured at the ordinal level, and marital status, religion, and occupation were measured at the nominal level.

The study included two groups (experimental and control), and differences between these two groups were examined for each of the demographic variables using the chi-square or Fisher’s exact tests. These analytical procedures are appropriate for examining group differences for nominal-level variables and are discussed in more depth later in this chapter. The p values (probabilities in this study) were all greater than 0.05, indicating no significant differences between the experimental and control groups for the demographic variables. Therefore the groups could be considered demographically similar in this study, so any significant differences noted are more likely to be caused by the study intervention than by differences in the groups at the start of the study.

Implications for Practice

Kim and co-workers (2012) implemented a structured aquarobic exercise program that included two educational sessions, followed by selected aerobic exercises. The aquarobic exercises are detailed in a table in the article and involved an instructor leading the patients with osteoarthritis through various aerobic exercises in the water for 1 hour, three times a week, for a total of 36 sessions over 12 weeks. The researchers found that the “Aquarobic Exercise Program was effective in enhancing self-efficacy, decreasing pain, and improving depression levels, body weight, and blood lipid levels in patients with osteoarthritis” (Kim et al., 2012, p. 181). They recommended the use of this program in managing patients with osteoarthritis but also recognized the need for additional research to determine the long-term benefits of this program for these patients. The Quality and Safety Education for Nursing Institute (QSEN, 2013) provides competencies for prelicensure nurses. The QSEN implication of this research report is the evidence-based intervention of an aquarobic exercise program, which improved the health outcomes for these patients with osteoarthritis. Nurses and students are encouraged to use research findings in promoting an evidence-based practice (EBP) for nursing.

Probability Theory

Probability theory is used to explain the extent of a relationship, the probability that an event will occur in a given situation, or the probability that an event can be accurately predicted. The researcher might want to know the probability that a particular outcome will result from a nursing intervention. For example, the researcher may want to know how likely it is that urinary catheterization during hospitalization will lead to a urinary tract infection (UTI) after discharge from the hospital. The researcher also may want to know the probability that subjects in the experimental group are members of the same larger population from which the comparison or control group subjects were taken. Probability is expressed as a lower case letter p, with values expressed as percentages or as a decimal value, ranging from 0 to 1. For example, if the probability is 0.23, then it is expressed as p = 0.23. This means that there is a 23% probability that a particular outcome (e.g., a UTI) will occur. Probability values also can be stated as less than a specific value, such as 0.05, expressed as p < 0.05. (The symbol < means less than.) A study may indicate the probability that the experimental group subjects were members of the same larger population as the comparison group subjects was less than or equal to 5% (p ≤ 0.05). In other words, it is not very likely that the comparison group and the experimental group are from the same population. Put another way, you might say that there is a 5% chance that the two groups are from the same population, and a 95% chance that they are not from the same population. The inference is that the experimental group is different from the comparison group because of the effect of the intervention in the study. Probability values often are stated with the results of inferential statistical analyses. In critically appraising studies, it is useful to recognize these symbols and understand what they mean.

Decision Theory, Hypothesis Testing, and Level of Significance

Decision theory assumes that all of the groups in a study (e.g., experimental and comparison groups) used to test a particular hypothesis are components of the same population relative to the variables under study. This expectation (or assumption) traditionally is expressed as a null hypothesis, which states that there is no difference between (or among) the groups in a study, in terms of the variables included in the hypothesis (see Chapter 5 for more details of types of hypotheses). It is up to the researcher to provide evidence for a genuine difference between the groups. For example, the researcher may hypothesize that the frequency of UTIs that occurred after discharge from the hospital in patients who were catheterized during hospitalization is no different from the frequency of such infections in those who were not catheterized. To test the assumption of no difference, a cutoff point is selected before data collection. The cutoff point, referred to as alpha (α), or the level of statistical significance, is the probability level at which the results of statistical analysis are judged to indicate a statistically significant difference between the groups. The level of significance selected for most nursing studies is 0.05. If the p value found in the statistical analysis is less than or equal to 0.05, the experimental and comparison groups are considered to be significantly different (members of different populations).

Decision theory requires that the cutoff point selected for a study be absolute. Absolute means that even if the value obtained is only a fraction above the cutoff point, the samples are considered to be from the same population, and no meaning can be attributed to the differences. It is inappropriate when using decision theory to state that the findings approached significance at p = 0.051 if the alpha level was set at 0.05. Using decision theory rules, this finding indicates that the groups tested are not significantly different, and the null hypothesis is accepted. On the other hand, once the level of significance has been set at 0.05 by the researcher, if the analysis reveals a significant difference of 0.001, this result is not considered more significant than the 0.05 originally proposed (Slakter, Wu, & Suzaki-Slakter, 1991). The level of significance is dichotomous, which means that the difference is significant or not significant; there are no “degrees” of significance. However, some people, not realizing that their reasoning has shifted from decision theory to probability theory, indicate in their research report that the 0.001 result makes the findings more significant than if they had obtained only a 0.05 level of significance.

From the perspective of probability theory, there is considerable difference in the risk of occurrence of a type I error (saying something is significant when it is not) when the probability is between 0.05 and 0.001. If p = 0.001, the probability that the two groups are components of the same population is 1 in 1000; if p = 0.05, the probability that the groups belong to the same population is 5 in 100. In other words, if p = 0.05, then in 5 times out of 100, groups with statistical values such as those found in these statistical analyses actually are members of the same population, and the conclusion that the groups are different is erroneous.

In computer analysis, the probability value obtained from each data analysis (e.g., p = 0.03 or p = 0.07) frequently is provided on the printout and is often reported by the researcher in the published study, along with the level of significance set before data analysis was conducted. In summary, the probability (p) value reveals the risk of a type I error in a particular study. The alpha (α) value, set prior to the study, usually at α = 0.05, reveals whether the probability value for a particular analysis in a study met the cutoff point for a significant difference between groups or a significant relationship between variables.

Inference and Generalization

An inference is a conclusion or judgment based on evidence. Statistical inferences are made cautiously and with great care. The decision theory rules used to interpret the results of statistical procedures increase the probability that inferences are accurate. A generalization is the application of information that has been acquired from a specific instance to a general situation. Generalizing requires making an inference; both require the use of inductive reasoning. An inference is made from a specific case and extended to a general truth, from a part to the whole, from the concrete to the abstract, and from the known to the unknown. In research, an inference is made from the study findings obtained from a specific sample and applied to a more general target population, using the results from statistical analyses. For example, a researcher may conclude in a research report that a significant difference was found in the number of UTIs between two samples, one in which the subjects had been catheterized during hospitalization and another in which the subjects had not. The researcher also may conclude that this difference can be expected in all patients who have received care in hospitals. The findings are generalized from the sample in the study to all previously hospitalized patients. Statisticians and researchers can never prove something using inference; they can never be certain that their inferences and generalizations are correct. The researcher’s generalization of the incidence of UTIs may not have been carefully thought out—the findings may have been generalized to a population that was overly broad. It is possible that in the more general population, there is no difference in the incidence of UTIs based on whether the patient was catheterized or not. Generalizing study findings are part of the discussion section of a research report (see later).

Normal Curve

A normal curve is a theoretical frequency distribution of all possible values in a population; however, no real distribution exactly fits the normal curve (Figure 11-1). The idea of the normal curve was developed by an 18-year-old mathematician, Johann Gauss, in 1795. He found that data from variables (e.g., the mean of each sample) measured repeatedly in many samples from the same population can be combined into one large sample. From this large sample, a more accurate representation can be developed of the pattern of the curve in that population than is possible with only one sample. Surprisingly, in most cases, the curve is similar, regardless of the specific variables examined or the population studied.

Levels of significance and probability are based on the logic of the normal curve. The normal curve presented in Figure 11-1 shows the distribution of values for a single population. Note that 95.5% of the values are within 2 standard deviations (SDs) of the mean, ranging from − 2 to + 2 SDs. (Standard deviation is described later in this chapter; see “Using Statistics to Describe.”) Thus there is approximately a 95% probability that a given measured value (e.g., the mean of a group) would fall within approximately 2 SDs of the mean of the population, and there is a 5% probability that the value would fall in the tails of the normal curve (the extreme ends of the normal curve, below − 2 (− 1.96 exactly) SDs [2.5%] or above + 2 (+ 1.96 exactly) SDs [2.5%]). If the groups being compared are from the same population (not significantly different), you would expect the values (e.g., the means) of each group to fall within the 95% range of values on the normal curve. If the groups are from (significantly) different populations, you would expect one of the group values to be outside the 95% range of values. An inferential statistical analysis performed to determine differences between groups, using a level of significance (α) set at 0.05, would test that expectation. If the statistical test demonstrates a significant difference (the value of one group does not fall within the 95% range of values), the groups are considered to belong to different populations. However, in 5% of statistical tests, the value of one of the groups can be expected to fall outside the 95% range of values but still belong to the same population (a type I error).

Frequency Distributions

Frequency distribution describes the occurrence of scores or categories in a study. For example, the frequency distribution for gender in a study might be 42 males and 58 females. A frequency distribution usually is the first method used to organize the data for examination. There are two types of frequency distributions, ungrouped and grouped.

Grouped Frequency Distributions

Grouped frequency distributions are used when continuous variables are being examined. Many measures taken during data collection, including body temperature, vital lung capacity, weight, age, scale scores, and time, are measured using a continuous scale. Any method of grouping results in loss of information. For example, if age is grouped, a breakdown into two groups, younger than 65 years and older than 65 years, provides less information about the data than groupings of 10-year age spans. As with levels of measurement, rules have been established to guide classification systems. There should be at least five but not more than 20 groups. The classes established must be exhaustive; each datum must fit into one of the identified classes. The classes must be exclusive; each datum must fit into only one (Grove et al., 2013). A common mistake occurs when the ranges contain overlaps that would allow a datum to fit into more than one class. For example, a researcher may classify age ranges as 20 to 30, 30 to 40, 40 to 50, and so on. By this definition, subjects aged 30, 40, and so on can be classified into more than one category. The range of each category must be equivalent. For example, if 10 years is the age range, each age category must include 10 years of ages. This rule is violated in some cases to allow the first and last categories to be open-ended and worded to include all scores above or below a specified point. Table 11-4 is an example of a grouped frequency distribution for income for registered nurses (RNs), in which the categories are exhaustive and mutually exclusive.

Table 11-4

Income of Full-Time Registered Nurses (n = 100)

Income	Frequency (%)
Below $60,000	5 (5%)
$60,000-69,999	20 (20%)
$70,000-79,999	35 (35%)
$80,000-90,000	25 (25%)
Above $90,000	15 (15%)

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Related posts:

1. Outcomes Research
2. Research Problems, Purposes, and Hypotheses
3. Clarifying Quantitative Research Designs
4. Examining Populations and Samples in Research

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